Why herd immunity to COVID-19 is reached much earlier than thought

By Nic Lewis

Introduction

A study published in March by the COVID-19 Response Team from Imperial College (Ferguson20[1]) appears to have been largely responsible for driving government actions in the UK and, to a fair extent, in the US and some other countries. Until that report came out, the strategy of the UK government, at least, seems to have been to rely on the build up of ‘herd immunity’ to slow the growth of the epidemic and eventually cause it to peter out.

The ‘herd immunity threshold’ (HIT) can be estimated from the basic reproduction rate of the epidemic, R0 – a measure of how many people, on average, each infected individual infects. Standard simple compartmental models of epidemic growth imply that the HIT equals {1 – 1/R0}. Once the HIT is passed, the rate of new infections starts to decline, which should ensure that health systems will not thereafter be overwhelmed and makes it more practicable to take steps to eliminate the disease.

However, the Ferguson20 report estimated that relying on herd immunity would result in 81% of the UK and US populations becoming infected during the epidemic, mainly over a two-month period, based on an R0 estimate of 2.4. These figures imply that the HIT is between 50% and 60%.[2] Their report implied that health systems would be overwhelmed, resulting in far more deaths. It claimed that only draconian government interventions could prevent this occurring. Such interventions were rapidly implemented in the UK, in most states of the US, and in various other countries, via highly disruptive and restrictive enforced ‘lockdowns’.

A notable exception was Sweden, which has continued to pursue a herd immunity-based strategy, relying on relatively modest social distancing policies. The Imperial College team estimated that, after those policies were introduced in mid-March, R0 in Sweden was 2.5, with only a 2.5% probability that it was under 1.5.[3] The rapid spread of COVID-19 in the country in the second half of March suggests that R0 is unlikely to have been significantly under 2.0.[4]

Very sensibly, the Swedish public health authority has surveyed the prevalence of infections by the SARS-COV-2 virus in Stockholm County, the earliest in Sweden hit by COVID-19. They thereby estimated that 17% of the population would have been infected by 11 April, rising to 25% by 1 May 2020.[5] Yet recorded new cases had stopped increasing by 11 April (Figure 1), as had net hospital admissions,[6] and both measures have fallen significantly since. That pattern indicates that the HIT had been reached by 11April, at which point only 17% of the population appear to have been infected.

How can it be true that the HIT has been reached in Stockholm County with only about 17% of the population having been infected, while an R0 of 2.0 is normally taken to imply a HIT of 50%?

The importance of population inhomogeneity

A recent paper (Gomes et al.[7]) provides the answer. It shows that variation between individuals in their susceptibility to infection and their propensity to infect others can cause the HIT to be much lower than it is in a homogeneous population. Standard simple compartmental epidemic models take no account of such variability. And the model used in the Ferguson20 study, while much more complex, appears only to take into account inhomogeneity arising from a very limited set of factors – notably geographic separation from other individuals and household size – with only a modest resulting impact on the growth of the epidemic.[8] Using a compartmental model modified to take such variability into account, with co-variability between susceptibility and infectivity arguably handled in a more realistic way than by Gomes et al., I confirm their finding that the HIT is indeed reached at a much lower level than when the population is homogeneous. That would explain why the HIT appears to have been passed in Stockholm by mid April. The same seems likely to be the case in other major cities and regions that have been badly affected by COVID-19.

Figure 1. New COVID-19 cases reported in Stockholm County, Sweden, over the 7 days up to the date shown. Note that in Sweden testing for COVID-19 infection was narrowed on 12 March, to focus on people needing hospital care, so from then on only a tiny proportion of infections were recorded as cases. This would account for the lack of growth in cases during the first week plotted. Since hospitalisation usually occurs several days after symptom onset, this change also increases the lag between infection and recording as a case. Accordingly,  from mid- March on the 7-day trailing average new cases figure will reflect new infections that on average occurred approximately two weeks earlier.

The epidemiological model used

Like Gomes et al., I use a simple ‘SEIR’ epidemiological model,[9] in which the population is divided into four compartments: Susceptible (uninfected), Exposed (latent: infected but not yet infectious), Infectious (typically when diseased), and Recovered (and thus immune and harmless). This is shown in Figure 2. In reality, the Recovered compartment includes people who instead die, which has the same effect on the model dynamics. The entire population starts in the Susceptible compartment, save for a tiny proportion that are transferred to the Infectious compartment to seed the epidemic. The seed infectious individuals infect Susceptible individuals, who move to the Exposed compartment. Exposed individuals gradually transfer to the Infectious compartment, on average remaining as Exposed for the chosen latent period. Infectious individuals in turn gradually transfer to the Recovered compartment, on average remaining as Infectious for the selected infectious period.


Figure 2
. SEIR compartment epidemiological model diagram.

In the case of COVID-19, the diseased (symptomatic) stage is typically reached about 5 days after infection, but an infected individual starts to become infectious about 2 days earlier. I therefore set the average latent period as 3 days.[10]

The infectious period depends mainly on the delay between infectiousness and symptoms appearing and on how quickly an individual reduces contacts with others once they become symptomatic, as well as on how infectious asymptomatic cases are. In an SEIR model, the infective period can be derived by subtracting the latent period from the generation time – the mean interval between the original infection of a person and the infections that they then cause.

The Ferguson20 model assumed a generation time of 6.5 days, slightly lower than a subsequent estimate of 7.5 days.[11] I use 7 days, which is consistent with growth rates near the start of COVID-19 outbreaks.[12] The infectious period is therefore 4 (=7 − 3) days.

I set R0=2.4, the same value Ferguson20 use. On average, while an individual is in the Infectious compartment, the number of Susceptible individuals they infect is R0 × {the proportion of the population that remains in the Susceptible compartment}.

With these settings, the progression of a COVID-19 epidemic projected by a standard SEIR model, in which all individuals have identical characteristics, is as shown in Figure 3. The HIT is reached once 58% of the population has been infected, and ultimately 88% of the population become infected.

Figure 3. Epidemic progression in an SEIR model with R0=2.4 and a homogeneous population. The time to reach the herd immunity threshold, which depends on the strength of the seeding at time zero, is arbitrary.

Modifying the basic SEIR model for variability in individual susceptibility and infectivity

The great bulk of COVID-19 transmission is thought to occur directly from symptomatic and pre-symptomatic infected individuals, with little transmission from asymptomatic cases or from the environment.[13] There is strong evidence that a small proportion of individuals account for most infections – the ‘superspreaders’.

A good measure of the dispersion of transmission – the extent to which infection happens through many spreaders or just a few – is the coefficient of variation (CV).[14] Two different estimates of this figure have been published for COVID-19. A Shenzhen-based study[15] estimated that 8.9% of cases were responsible for 80% of total infections, while a multi-country study[16] estimated that 10% were so responsible. In both cases a gamma probability distribution was assumed, as is standard for this purpose. The corresponding CV best estimates and 95% uncertainty ranges are 3.3 (3.0–5.6) and 3.1 (2.2–5.0). These figures are slightly higher than the 2.5 estimated for the 2003 epidemic of SARS.[17]

CV estimates indicate the probability of transmission of an infection. They reflect population inhomogeneity regarding individuals’ differing tendency to infect others, but it is unclear to what extent they also reflect susceptibility differences between individuals. However, since COVID-19 transmission is very largely person-to-person, much of the inhomogeneity in transmission rates will reflect how socially connected individuals are, and how close and prolonged their interactions with other individuals are. As these factors affect the probability of transmission both from and to an individual, as well as causing variation in an individual’s infectivity they should cause the same variation in their susceptibility to infection.

A common social connectivity related factor implies that an individual’s susceptibility and infectivity are positively correlated, and it is not unreasonable to assume a quite strong correlation. However, it seems unrealistic to assume, as Gomes et al. do in one case, that an individual’s infectivity is directly proportional to their personal susceptibility. (In the other case that they model, they assume that an individual’s infectivity is unrelated to their susceptibility.)

Some of the variability in the likelihood of someone infecting a susceptible individual during an interaction will undoubtedly be unrelated to social connectivity, for example the size of their viral load. Likewise, susceptibility will vary with the strength of an individual’s immune system as well as with their social connectivity. I use unit-median lognormal distributions to reflect such social-connectivity unrelated variability in infectivity and susceptibility. Their standard deviations determine the strength of the factor they represent. I model an individual’s overall infectivity as the product of their common social-connectivity related factor and their unrelated infectivity-specific factor, and calculate their overall susceptibility in a corresponding manner.[18]

I consider the cases of CV=1 and CV=2 for the common social connectivity factor that causes inhomogeneity in both susceptibility and infectivity. For unrelated lognormally-distributed inhomogeneity in susceptibility I take standard deviations of either 0.4 or 0.8, corresponding to a CV of 0.417 or 0.947 respectively. Where their gamma-distributed common factor inhomogeneity is set at 1, the resulting total inhomogeneity in susceptibility is respectively 1.17 or 1.65 when the lower or higher unrelated inhomogeneity standard deviations respectively are used; where set at 2 the resulting total inhomogeneity in susceptibility is respectively 2.17 or 2.98. The magnitude of variability in individuals’ social-connectivity unrelated infectivity-specific inhomogeneity factor does not affect the progression of an epidemic or the HIT, so for simplicity I ignore it here.[19]

Results

Figure 4 shows the progression of a COVID-19 epidemic in the case of CV=1 for the common social connectivity factor inhomogeneity, with unrelated inhomogeneity in susceptibility having a standard deviation of 0.4. The HIT is 60% lower than for a homogeneous population, at 23.6% rather than 58.3% of the population. And 43% rather than 88% of the population ultimately becomes infected. If the standard deviation of unrelated inhomogeneity in susceptibility is increased to 0.8, the HIT becomes 18.9%, and 35% of the population are ultimately infected.

Figure 4. Epidemic progression in an SEIR model with R0=2.4 and a population with CV=1 common factor inhomogeneity in susceptibility and infectivity and also unrelated multiplicative inhomogeneity in susceptibility with a standard deviation of 0.4.

Figure 5 shows the progression of a COVID-19 epidemic in the case of CV=2 for the common social connectivity factor inhomogeneity, with unrelated inhomogeneity in susceptibility having a standard deviation of 0.8. The HIT is only 6.9% of the population, and only 14% of the population ultimately becoming infected. If the standard deviation of unrelated inhomogeneity in susceptibility is reduced to 0.4, those figures become respectively 8.6% and 17%.

Figure 5. Epidemic progression in an SEIR model with R0=2.4 and a population with CV=2 common factor inhomogeneity in susceptibility and infectivity and also unrelated multiplicative inhomogeneity in susceptibility with a standard deviation of 0.8.

Conclusions

Incorporating, in a reasonable manner, inhomogeneity in susceptibility and infectivity in a standard SEIR epidemiological model, rather than assuming a homogeneous population, causes a very major reduction in the herd immunity threshold, and also in the ultimate infection level if the epidemic thereafter follows an unconstrained path. Therefore, the number of fatalities involved in achieving herd immunity is much lower than it would otherwise be.

In my view, the true herd immunity threshold probably lies somewhere between the 7% and 24% implied by the cases illustrated in Figures 4 and 5. If it were around 17%, which evidence from Stockholm County suggests the resulting fatalities from infections prior to the HIT being reached should be a very low proportion of the population. The Stockholm infection fatality rate appears to be approximately 0.4%,[20] considerably lower than per the Verity et al.[21] estimates used in Ferguson20, with a fatality rate of under 0.1% from infections until the HIT was reached. The fatality rate to reach the HIT in less densely populated areas should be lower, because R0 is positively related to population density.[22] Accordingly, total fatalities should be well under 0.1% of the population by the time herd immunity is achieved. Although there would be subsequent further fatalities, as the epidemic shrinks it should be increasingly practicable to hasten its end by using testing and contact tracing to prevent infections spreading, and thus substantially reduce the number of further fatalities below those projected by the SEIR model in a totally unmitigated scenario.

Nicholas Lewis                                               10 May 2020


[1] Neil M Ferguson et al., Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand. Imperial College COVID-19 Response Team Report 9, 16 March 2020, https://spiral.imperial.ac.uk:8443/handle/10044/1/77482

[2] A final infection rate of 81% implies, in the context of a simple compartmental model with a fixed, homogeneous population, that the ‘effective R0‘ is between 2.0 and 2.1, and that the HIT is slightly over 50%. Ferguson20 use a more complex model, so it is not surprising that the implied effective R0 differs slightly from the basic 2.4 value that Ferguson20 state they assume.

[3] Flaxman, S. et al., Estimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in 11 European countries. Imperial College COVID-19 Response Team Report 13, 30 March 2020, https://www.imperial.ac.uk/mrc-global-infectious-disease-analysis/covid-19/report-13-europe-npi-impact/

[4] Based on the Ferguson20 estimate of a mean generation time of 6.5 days, which appears to be in line with existing evidence, an R0 of 2.0 would result in a daily growth rate of 2.0^(1/6.5)= 11%. That is slightly lower than the peak growth rate in cases in late March in Stockholm County, and in early April in the two regions with the next highest number of cases, in both of which the epidemic took off slightly later than in Stockholm, and in line with the growth rate in Swedish COVID-19 deaths in early April

[5] https://www.folkhalsomyndigheten.se/contentassets/2da059f90b90458d8454a04955d1697f/skattning-peakdag-antal-infekterade-covid-19-utbrottet-stockholms-lan-februari-april-2020.pdf

[6] John Burn-Murdoch, Financial Times Research, 2 May 2020. http://web.archive.org/web/20200507075628/https:/twitter.com/jburnmurdoch/status/1256712090028576768

[7] Gomes, M. G. M., et al. Individual variation in susceptibility or exposure to SARS-CoV-2 lowers the herd immunity threshold. medRxiv 2 May 2020. https://www.medrxiv.org/content/10.1101/2020.04.27.20081893v1

[8] The 81% proportion of the population that Ferguson20 estimated would eventually become infected is only slightly lower than the 88% level implied by their R0 estimate of 2.4 in the case of a homogeneous population.

[9] https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology#The_SEIR_model

[10] Gomes et al. instead set the latent period slightly longer, to 4 days and treated it as a partly infectious period, unlike in the standard SEIR model.

[11] Li Q, Guan X, Wu P, et al.: Early Transmission Dynamics in Wuhan, China, of Novel Coronavirus-Infected Pneumonia. N Engl J Med. 2020; 382(13):1199–1207.https://www.nejm.org/doi/10.1056/NEJMoa2001316

[12] Once a SEIR model has passed its start up phase, and while a negligible proportion susceptible individuals have been infected, the epidemic daily growth factor is R0^(1/generation time), or 1.10–1.13 for R0=2.0–2.4 if the generation time is 7 days.

[13] L. Ferretti et al., Science 10.1126/science.abb6936 (2020).

[14] The coefficient of variation is the ratio of the standard deviation to the mean of its probability distribution. It is usual to assume a gamma distribution for infectivity, the shape parameter of which equals 1/CV2.

[15] Bi, Qifang, et al. “Epidemiology and transmission of COVID-19 in 391 cases and 1286 of their close contacts in Shenzhen, China: a retrospective cohort study.” The Lancet Infectious Diseases 27 April 2020. https://doi.org/10.1016/S1473-3099(20)30287-5

[16] Endo, Akira, et al. “Estimating the overdispersion in COVID-19 transmission using outbreak sizes outside China.” Wellcome Open Research 5.67 (2020): 67. https://wellcomeopenresearch.org/articles/5-67

[17] Lloyd-Smith, J O et al. “Superspreading and the effect of individual variation on disease emergence.” Nature 438.7066 (2005): 355-359. https://www.nature.com/articles/nature04153

[18] For computational efficiency, I divide the population into 10,000 equal sized segments with their common social connectivity factor increasing according to its assumed probability distribution, and allocate each population segment values for unrelated variability in susceptibility and infectivity randomly, according to their respective probability distributions.

[19] A highly susceptible but averagely infectious person is more likely to be removed from the susceptible pool early in an epidemic, reducing the average susceptibility of the pool. However, no such selective removal occurs for a highly infectious person of averagely susceptibility. Therefore, as Gomes et al. point out, variability in susceptibility lowers the HIT, but variability in infectivity does not do so except to the extent that it is correlated with variability in susceptibility.

[20] On 8 May 2020 reported total COVID-19 deaths in Stockholm County were 1,660, which is 0.40% of the estimated 413,000 of its population who had been infected by 11 April 2020. COVID-19 deaths reported for Stockholm County after 8 May that relate to infections by 11 April 2020 are likely to be approximately balanced by deaths reported by 8 May 2020 that related to post 11 April 2020 infections.

[21] Verity R, Okell LC, Dorigatti I, et al. Estimates of the severity of COVID-19 disease. medRxiv 13 March 2020; https://www.medrxiv.org/content/10.1101/2020.03.09.20033357v1.

[22] Similarly, the HIT may be significantly higher in areas that are very densely populated, have much less inhomogenous populations and/or are repeatedly reseeded from other areas. That would account for the high prevalence of COVID-19 infection that has been found in, for instance, some prisons and residential institutions or in city districts.

Originally posted here, where a pdf copy is also available

535 responses to “Why herd immunity to COVID-19 is reached much earlier than thought

  1. Nick: My question is: now what? Neither the UK nor the USA nor Canada have followed the Swedish policy. Assuming your approximation of between 7% and 24% is right, what policy implication follows for these and similar total lockdown countries? And what testing should be done to confirm the inhomogeneity as this new policy is being followed?

    • Inhomogeneity can be assumed. As no two immune systems are the same

    • Nick might add to the short list of Bayesian priors germane to this case the mere fact of our non-extinction in the face of an uncertain but large number of previous viral pandemics.

      The present human herd , and those of man other primates as well , are all products of eons of harshly Darwinian selection favoring herds prone to the rapid development of herd immunity.

  2. Your narrative about Sweden isn’t exactly matching the facts. Click on link for current numbers:

    https://tinyurl.com/yaz3fj5q

    Sweden’s the third worst performing country in the world in new infections per day per capita, after the completely incompetent pandemic responses by the US and the UK. Nor is there evidence that it is “over the peak.”

    “On a plateau” is a better descriptor.

    When you fold in the lower population density of Sweden this comparison looks even worse. Comparing it to its closet neighborhood, it has hardly been a success story, except in right-wing fiction I mean.

    Other notes:

    Plotting an exponentially varying function on a linear scale can be very deceptive—the dominant noise sources are typically multiplicative. On a linear scale, short period deviations will look more important than they actually are.

    Also you need to look at seven-day smoothed data because of lags in reporting. The wiggles in the unaveraged data aren’t representative of the true day-to-day variation in actual cases, just variations in how long it takes for the new cases to appear on the books.

    • Great website at that link.

      Could you post again adding Denmark and Austria? I could add them at the site (pretty dramatic) but couldn’t see how to get a URL on my phone to post with those added.

      It’s easy to make Sweden look good if you don’t compare it to other countries that did do shelter in place measures.

    • Also, don’t forget to consider –

      > More than half of Swedish households are single-person, the highest proportion in the EU, according to Eurostat. Official figures given to the BBC by the Swedish government’s number-crunching agency Statistics Sweden suggest that includes around one in five 18- to 25-year-olds, although its researchers estimate that the real number could be higher, since many remain registered at their parents’ address while they stay in sublet rentals.

      • russellseitz

        Thanks for a real epiphany , Josh !
        Greta Garbo was not alone in uttering her famous one-liner.

    • Confirmed cases per million is not a meaningful statistic because “confirmed cases” are strongly dependent on the level of testing. I would have expected better from you Carrick.

      By this flawed measure, it looks like New York is about the worst state. That must mean no mitigation (Dakotas) is better than very strict lockdowns. :-). This reasoning of course is not scientific.

      • Thank you for the nod to confirmed case trap. So many people fall into that pit whole. Norway was heavily compared to Sweden and was doing a gajillion times (official number;) the amount of testing.

    • The actual prevalence also appears to be much lower at ~5-10%. The 26% prevalence that the Swedish authorities claim appears to arise from a faulty assumption about when people are infectious versus when they test positive.

    • The prevalence of 26% also seems to arise from a faulty assumption that positive test = infectious. Correcting for this gives a prevalence of 5-10%.

    • Michelle Louw

      Belgium, Italy, Spain, UK, Netherlands and France all have higher numbers of deaths per million citizens than Sweden. The argument that only comparisons to close neighbours are valid ie, Norway and Finland, also doesn’t hold, unless you accept that Belgium is proof that longer and more severe lock downs caused more deaths than Germany’s much less stringent lock down.

      • This is fair. But Swedes have been self-distancing in a manner similar to government imposed lockdown compliance in the U.S.

      • Michelle –

        > Belgium, Italy, Spain, UK, Netherlands and France all have higher numbers of deaths per million citizens than Sweden

        Comparing across countries is fraught. There are many comparison variables that are hard to control for. That said, if yi really think there is something to be gained from comparing, Sweden has about the 9th highest deaths per million among some 220 countries at Worldometers.

        It is 30% higher than Switzerland. 3x higher than Germany and Denmark. 6x higher than Finland. And it is rising in the ranks. Not long ago it was lower than the Netherlands. Only maybe two weeks ago it was lower than Switzerland.

        Also, Sweden ranks considerably lower in tests per million than it does in cases per million. Now that’s a bit tricky because different countries have different testing politicies. Some are more likely than others to limit tests to people who are symptomatic or essential workers. But in general it’s not a good sign that they rank lower in testing per million than in cases per million – by a significant amount.

      • mesocyclone

        The idea that Sweden didn’t order a lockdown is true only if you use a harsh definition of lockdown – a reason I don’t like the term. Sweden ordered a number of measures to be taken. Recently, they closed a number of bars that violated social distancing rules.

        Also, Swedes, like people elsewhere, voluntarily socially distance in a dangerous epidemic – which is one reason that their measures of mobility are similar to other countries. As an aside, that behavior means that if a country completely eliminated all rules, the life of its citizens, and its economy, would not “go back to normal.”

      • One needs to keep in mind that CoVid19 statistics are pretty political. Belgium has chosen to over-report: any suspect death in nursing homes (not even tested, or for which no evidence shows that CoVid19 is the cause of the death) was counted while other countries don’t even report deaths outside hospitals. Intention is to use stats as a crisis management tool and not as political competition. Real figures will be adapted later on the base of over fatality.

        In no case, Belgium’s intensive care sections have been saturated. I don’t mean that Belgium did well: they completely failed in the protection of aged people in rest homes but I doubt they were much worse than neighbor countries who are more selective in their statistics publications.

    • Gary Mullennix

      The real issue is understanding the role played by Niall Ferguson and his falsely designed model. Millions of people will suffer and die from economies that will not recover, perhaps ever.

    • You have confused the position in Sweden as a whole with that in Stockholm.
      For Stockholm County, cases and hospitalisations have fallen substantially from their peak, as I show.
      It isn’t surprising that they may not have done so for Sweden as a whole, for which the epidemic is some time behind Stockholm. One might expect herd immunity not to have been reached yet in other regions.
      Nothing in my exposition depends on the experience in Sweden as a whole.
      When comparing countries, the appropriate metric IMO is not how many cases or deaths they have per million population, but the number of their total deaths (or lost life years) divided by the proportion of the herd immunity threshold that they have reached (or, strictly, had reached when the people who died were infected).

      Where Sweden has done badly, along with the UK and various other countries, is in letting COVID-19 spread in hospitals and – often from them – to care (nursing) homes. Around 50% of total COVID-19 related deaths have been in care homes in many countries. In the UK, this was mainly caused by deliberate actions taken empty hospitals of old people early in order to “protect the NHS” from a threat of it being overwhelmed that was wrongly predicted by the Ferguson20 model to occur.

      • To reiterate, your basis hinges on the modeled extrapolation of the 2.5% infected cases over 5 days that is likely flawed as explained by Kucharski. If Kucharski’s calculation is right, you have to argue that HIT was achieved at a 5-10% prevalence. Such a prevalence calculation would also be consistent with an IFR in the 0.7-1% range seen from data in NYC, UK etc. The more plausible explanation is that the curve flattening in Stockholm is well explained by the documented fall in social mobility from voluntary self-distancing in Sweden comparable to that achieved by U.S/UK lockdowns.

      • As explained here, their extrapolation from PCR positive=infectious is a mistake

      • Actual testing (albeit 454 samples) as opposed to testing+extrapolation by Swedish authorities is consistent with ~7.5% prevalence

    • Also you need to look at seven-day smoothed data because of lags in reporting.

      “smoothing” will not remove a lag. Much of the 7 day variations are real, not just low logging at w/e or similar. ( UK may be low logging ).

      When you fold in the lower population density of Sweden this comparison looks even worse. Comparing it to its closet neighborhood, it has hardly been a success story, except in right-wing fiction I mean.

      Because you are failing to realise that Sweden chose to deal with infections instead of postpone them. Norway still has to pay the price. Your conclusions are premature and uninformed.

      Thanks for declaring your left/right bias on how you look at the world. That explains why you see what you want to see to bolster your prejudice instead of what is there.

    • “Sweden’s the third worst performing country in the world in new infections per day per capita, after the completely incompetent pandemic responses by the US and the UK.”

      It’s illuminating how many people will go to such bizarre depths to be completely inaccurate for their sad politics.
      Sweden isn’t the “third worst” of anything. If you think the handling of the pandemic has been “incompetent” in the US and UK, you must be ready to hang politicians in Belgium, the Netherlands, France, Spain, Italy…
      All of that arm-waving and diversion is meant to get us to miss what you can’t accept for political reasons- densely packed urban landscapes with high adoption of public transportation were hit hard by this epidemic. Policies regarding nursing homes- moving old people to them and, as in New York, forcing them to take Covid-positive cases, killed thousands.

      Here’s an interesting stat- New York is the fourth most populous state in the US. Almost five times (4.8) as many people died in New York as did in the top three most populous states combined.
      Combined.
      You won’t be able to paper that over by claiming Texas has no cities, Florida no old people, or that Trump isn’t the president of California. Just like you won’t be able to ignore the fact that the capital of the EU handled the virus with far less competency than Boris in the UK (by your own measurements).
      This pandemic was hard on anyone who lived in a city that doesn’t use automobiles (New York City v Los Angeles), did a better job of avoiding visits to grandma, and didn’t have the NHS or Andrew Cuomo’s bad policies toward nursing homes.
      And you want us to forget about China, which will depend a lot on how Russia fares. If they have a Swedish death rate, or get really lucky and have same rate as the “incompetent” US, the Russians may not be as angry at China. But if Russia ends up with France or Belgium’s level of “competency” and death rate the global anger at China could get ugly.

      • Population density in US as a whole is about 34/km2, in NYC 4027/km2. In UK 278/km2, Germany 234/km2, Italy 200/km2, France 123/km2, Spain 92/km2. Sweden 23/km2. For Sweden to be close to the other countries in Western Europe in fatality per capita [.04% vs. spain .05% vs. Germany .009%] suggests a less than effective approach

    • Turn of the log feature and switch to linear and it’s pretty incredible how little Sweden’s rate is comparatively speaking

    • 1. (Excess) Death is what matters. Number of persons catching flu looks ominous but irrelevant. Are death numbers O(10) more or are they O(1)?

      2. Lockdown goal posts keep shifting. First it was deaths. That did not hold up indeed the data. Then it was protecting healthcare workers. That did not hold up either. Now it seems to be just infections.

    • Patrice Poyet

      Whatever the final result be in Sweden, they will be way ahead of all other nations which have totally destroyed our most fundamental freedoms, ruined our businesses and lives for no better results, or only marginally.

  3. > A recent paper (Gomes et al.[7]) provides the answer. It shows that variation between individuals in their susceptibility to infection and their propensity to infect others can cause the HIT to be much lower than it is in a homogeneous population.

    > And the model used in the Ferguson20 study, while much more complex, appears only to take into account inhomogeneity arising from a very limited set of factors – notably geographic separation from other individuals and household size – with only a modest resulting impact on the growth of the epidemic

    > > The do not assume a uniform IFR. See page 5 in https://spiral.imperial.ac.uk:8443/bitstream/10044/1/77482/14/2020-03-16-COVID19-Report-9.pdf

    https://statmodeling.stat.columbia.edu/2020/05/08/so-the-real-scandal-is-why-did-anyone-ever-listen-to-this-guy/#comment-1332014

    –snip–

    Table 1: Current estimates of the severity of cases. The IFR estimates from Verity et al.12 have been adjusted
    to account for a non-uniform attack rate giving an overall IFR of 0.9% (95% credible interval 0.4%-1.4%).
    Hospitalisation estimates from Verity et al.12 were also adjusted in this way and scaled to match expected
    rates in the oldest age-group (80+ years) in a GB/US context. These estimates will be updated as more data
    accrue

    • Co-author of Gomes et al. …

      > As a coauthor in this study I’m going to start by saying what its conclusions are NOT: (i) it does NOT conclude that lockdowns/social distancing are unnecessary; (ii) it does NOT say “herd immunity” is ~20% regardless. In fact that number is conditional on social distancing 1/6

      > As @joel_c_miller put it recently, heterogeneity/variation is complicated, and often doesn’t change significantly the conclusions from “homogeneous” models. The point is that here it just might, but we are mostly ignorant of the actual parameter values 3/6

    • This is a misleading comment. I was writing about inhomgeneity in susceptibility to infection. Inhomgeneity by age in infection fatality rates has nothing to do with that.
      I wrote that the Ferguson20 model “appears only to take into account inhomogeneity arising from a very limited set of factors – notably geographic separation from other individuals and household size – with only a modest resulting impact on the growth of the epidemic”.
      I did not say that those were the only two factors used in their modelling.
      I agree that age related variation in attack rates is a component of inhomgeneity in assumed susceptibility, but I estimate that it only would only reduce the final infected proportion of the population by circa 1% point, which is a minor part of the 7% points that the Ferguson20 model achieves.

      • Ok, so when you said:

        >And the model used in the Ferguson20 study, while much more complex, appears only to take into account inhomogeneity arising from a very limited set of factors – notably geographic separation from other individuals and household size

        What you meant to convey was:

        > And the model used in the Ferguson20 study, while much more complex, appears only to take into account inhomogeneity [with respect to rates of infection] arising from a very limited set of factors – notably geographic separation from other individuals and household size

        Now what do you think about one of the co-authors saying?:

        > As @joel_c_miller put it recently, heterogeneity/variation is complicated, and often doesn’t change significantly the conclusions from “homogeneous” models. The point is that here it just might, but we are mostly ignorant of the actual parameter values

        and

        > it does NOT conclude that lockdowns/social distancing are unnecessary; (ii) it does NOT say “herd immunity” is ~20% regardless. In fact that number is conditional on social distancing

        Did I misunderstand you there as well, and you actually weren’t arguing against the idea that heterogeneity/variation…often doesn’t change significantly the conclusions from homogeneous models, and you actually weren’t arguing that lockdowns/social distancing are unnecessary?

  4. The SEIR model misses the fifth group in the population, those immune due to genetic and/or other factors that have not been researched.

    • Yes, I thought about mentioning that. But I concluded that the common inhomogeneity in susceptibility and infectivity arising from social connectivity related variability can adequately model this group, without needing an extra compartment for it. In effect, this group can be treated as having zero or near zero social connectivity.

    • If there exist people who are naturally immune, you just put them in the “recovered” category at the start of the SEIR run. Whether that immunity exists at all for this disease is unknown.

  5. > A notable exception was Sweden, which has continued to pursue a herd immunity-based strategy, relying on relatively modest social distancing policies

    Funny thing about that….

    –snip–

    Anders Tegnell, chief epidemiologist at Sweden’s Public Health Agency – the nation’s top infectious disease official and architect of Sweden’s coronavirus response –denied that “herd immunity” formed the central thrust of Sweden’s containment plan, in an interview with USA TODAY. Yet he also said the country may be starting to see the impact of “herd immunity.”

    • “The Swedish constitution does not allow for a state of emergency in peacetime”

      Funny how much divisiveness the Swedes arouse.

      The US has comparably bad COIVD numbers.
      Sweden has comparably bad GDP numbers.

      This thing sucks, but it seems to suck everywhere.

      • Yup.

      • Skeptical Realist

        Treating the entire USA as one entity in comparison to the nation states of the EEA and others is a poor representation of reality. Texas, 2nd most populous state with five large cities, three of the top ten most populous metro areas in the nation is doing well.

        Italy, Spain, France, the UK, Belgium are far worse than the US and the EEA in general. And the USA had done better than the EEA.

      • The vast majority of countries have done much better than the US (on the measure of deaths per capita).

        Even breaking it down in the US, particularly if you don’t break it down elsewhere, is problematic.

        Beware of comparisons across national, cultural, behavioral, ethnic, racial, social, etc., boundaries, .

        Be skeptical of selective comparisons

        Respect uncertainty. You are the easiest person for you to fool.

      • Realist –

        You say we shouldn’t treat the entire US as a singular entity – then you do so by comparing the US to other countries.

        And then, you consider those other countries as singular entities.

        Think about that a bit.

      • “The vast majority of countries have done much better than the US (on the measure of deaths per capita).”

        That’s true, but as you note, a lot of variation within the US.
        Exclude the Northeast around NYC and the US has done much better than other countries:

        Also, the US is the fattest country, so we’d expect the most deaths because from pre-existing conditions.

        https://ourworldindata.org/grapher/share-of-adults-defined-as-obese

    • Everyone interviewing Tegnell asks him about this. He’s been really consistent and clear that at the outset developing herd immunity was not a central part of their planning. It was sustainability, evidence-based measures, trusting people, not overwhelming the system, etc… Herd immunity was the UK narrative for a time, and that’s what everyone interviewing him knows – they try and slot him into that narrative. If you watch his interviews there isn’t really a contradiction here.

  6. I would suggest (as you infer) that there are actually 5 groups to be considered:
    > Innately Immune
    > Susceptible Uninfected
    > Exposed Latent
    > Infectious Deceased
    > Recovered Harmless

    From the few antibody/serological tests the number of people who were infected but asymptomatic (recovered harmless) were ~4% and infectious deceased (the normal count of cases/deaths) ~1%. The number of uninfected is in the 95% range. Yet we see in areas where there were crowded ideal infection conditions only ~5% at most infected. The London Underground is a good example with 5milion passenger journeys a day most tightly crowded into poorly ventilated carriages for tens of minutes. Yet the number infected in UK as a whole is ‘only’ ~220,000. So this is either not a very infectious virus – OR – there is a large proportion of innately immune. I would suggest that this number is ~90% in UK and USA. The people in the innately immune have one or more of a genetic immunity of some sort, or a sufficiency of Vitamin D, Zinc and Selenium giving immunity, a strong innate immune system.
    So now consider a population with 5% susceptible uninfected possibly not well mixed. For example populations in the North East in winter with a community with genetic disposition to infection will be different to a populations in the South in winter sun and no genetic disposition. The infection will not be consistent in some areas with a lot of susceptible individuals having a large case and death rate.
    I propose that the model for the infection should be looked at as a predator prey algorithm (which is what herd immunity implies). The large number of Innately Immune means that the ‘herd immunity’ is almost there anyway. But importantly as you describe herd immunity, the virus will stop. But with a large innately immune proportion the virus will just stop after most of the prey have either been infected and survived or died. There can then be no ‘second wave’ of this or closely similar virus with the same infection method.
    SARS and MERS both just stopped.
    It should be noted that ensuring a sufficiency of Vitamin D, Zinc and Selenium is likely to move most people from susceptible to innately immune. This is simple to do and cheap why this is not being recommended by governments is extremely puzzling.

    • Curious George

      Is there an estimate of the percentage of the “innately immune” population? Do models really ignore that fraction?

      • I am just basing my estimates on the opposite of the number of cases even adding the serology tests. It is natural for the press to emphasize the number of cases/deaths that gets clicks and advertisers – but I was more struck by the reports of antibody testing in Los Angeles County (population over 10 million) and the reports were:
        USC and the health department released preliminary study results that found that an estimated 4.1% of the county’s adult population has antibodies to the coronavirus, estimating that between 221,000 adults to 442,000 adults in the county have had the infection.
        So look at the obverse, antibody testing indicates that 95.9% of the population were not infected. If everyone can be infected by a short period inside 2 meters of an infected person – then the number of infections would be in the millions.
        But that number seems to hold in New York and in London ~95% of the population are innately immune. It does not suit people for various reasons to put the information that way. To be generous it may be that the population will let their guard down and the full 5% susceptible would be infected. But the response to throw away the lessons of all previous pandemics and keep everyone indoors at home the most likely place to be infected makes zero sense – as New York has found out 60%+ infections in NY are to people staying at home.
        So no information on how to raise innate immunity with vitamin D and zinc etc, and then putting people at risk by making them ‘stay indoors at home’ – both completely counter to what should have been done

      • There are a couple of prisons in Ohio where around 70% tested positive for COVID-19 infection, so it seems unlikely that, the innately immune proportion can be much above 30%, and it might be well under 30%.
        However, in addition there are likley some fraction of people who are quite resistant to infection in normal conditions, even if they wouldn’t be able to resist infection in prison conditions.

      • Curious George

        Nic, thanks, but .. there is some limited data from the Grand Princess and the Diamond Princess, showing a much lower infection rate – but then it is more difficult to test a cruise ship passenger than a prisoner. Also data from the Theodore Roosevelt point to only 1/6 of the crew being infected.

      • Keep in mind that probably about half of those inmates were black.

        The Vitamin D Status of Prison Inmates
        https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3944727/

        Results:
        Serum 25(OH)D levels peaked in summer and autumn, and decreased in winter and spring. Vitamin D deficiency occurred in 50.5% of blacks, 29.3% of whites, and 14.3% of Asian inmates (p = 0.007).

    • “This is simple to do and cheap why this is not being recommended by governments is extremely puzzling.”

      Yes, it follows the authority’s clearly greater interest in the success of Remdesivir under patent by Gilead Sciences at the low-low price of $9/ day when they ramp up. https://www.bloomberg.com/news/articles/2020-04-10/potential-coronavirus-drugs-may-cost-as-little-as-1-study-says

      They genuinely feel unethical about promoting home-grown actions beyond hand washing and face protection. Promoting vitamin and mineral supplements smacks of hawking store merchandise. By the way, I finally received by back ordered online zinc supplements yesterday. I was eating cashews (high in zinc other minerals) in the meanwhile as a stop-gap. So far they worked. :)

    • As I replied to Paul Kielpinski , I thought about mentioning the Innately Immune group, but I concluded that the common inhomogeneity in susceptibility and infectivity arising from social connectivity related variability would adequately model this group (by treating it as having near zero social connectivity), without needing an extra compartment for it.
      I agree that this group is probably sizeable, although I would be surprised if as much as 50% of the population was actually immune, as opposed to being difficult to infect and (if infected) not very infectious.

      • Thank you for the reply Nic
        As soon as the innately immune (or difficult to infect) are a sizeable majority then the algorithms should really change as using a generic average value for infectivity becomes misleading. This is why I suggested a more suitable algorithm would be predator/prey. This also leads to the logic of how can I move the prey into non-prey innately immune group (other than infecting them).
        The various governments have signally failed to do this. The politicians are not being assisted by the medical community who know how to increase immunity to SARS-CoV-2 yet do not tell anyone – rather they let people including others in the medical community die a painful death.

    • From the modeling standpoint, you don’t need a fifth category. Put the innately immune into the “recovered” category and you get the same result (other than the graph of # recovered will look a bit odd).

    • It doesn't add up...

      The KCL symptom tracker suggests that over 2 million were infected in the UK at its estimate of the peak on 1st April.

      https://covid.joinzoe.com/data#levels-over-time

  7. The results are even more striking if the variability is combined with spacial structure, that is, if variability is applied between populations, rather than within populations.
    Let’s take a simple example of three equal populations: one population has a median R0, another population has twice the R0, and a third has one-half. This is a natural approximation for a lognormal with a standard deviation of 0.7 and a sample size of three. This would be a variation of 0.5 (whether it is connection related doesn’t matter in this model), or substantially less than the 1.16 (sum of both connection related and unrelated) variation in your smallest model.
    In a situation where there are multiple entries of the disease into a population set, the population with the highest R0 will quickly dominate the spread, and R0 for the population will reflect it. Hence the highest population will have an R0 of 2.4, the middle an R0 of 1.2, and the lowest an R0 of 0.6. Combining the equations for herd immunity, we get 0% for the R0 0.6 population, 17% for the R0 1.2 population, and 58% for the R0 2.4 population, for an average of 25%. The whole population set has an immunity threshold of 25%.

  8. ‘Balanced’ or ‘maintained’ genetic polymorphism in species is supposed in part to be a protection against diseases. I guess this turns up mainly as ‘social-connectivity unrelated variability in susceptibility’, which should also manifest as more than just differences in the immune system. I lost track in the text of the relative importance of this compared to social connectivity factors, and indeed whether this is determinable. Is it so? (The spread of genetic variance over at least some nations must be known, as these have been been sampled pretty often by now I guess, which is maybe helpful in estimating this from a different angle).

    • I’m not aware that the relative importance of the social connectivity unrelated variability in susceptibility has been determined for COVID-19. Possibly it may have been for another infectious disease.
      I have mainly focused on cases where social connectivity related variability is the more important factor. In the case I mention where that variability has a CV of 1 and the standard deviation of the unrelated lognormally-distributed variability is 0.8, the two factors contribute similar proportions of the total variability in susceptibility.

      • Thanks, got it. As the populations are large and the variety is also large (apart from minor pockets of interbreeding, we are very far from clones), I presumed the protections from variability would be similar across at least similar classes of disease. But indeed I don’t know if this is so or whether it has been distilled down to an actual figure.

      • P.S. the relatively immune you and Paul K mention above, would be part of the distribution created by genetic variability.

      • Without a vaccine, reducing R just prolongs the outbreak but does save some lives, although economic collapse will cost more lives.

      • Clive –

        > Without a vaccine, reducing R just prolongs the outbreak but does save some lives, although economic collapse will cost more lives.

        What are you attributing as the cause for economic collapse?

      • Right now the government is paying 80% wages of several million people to stay at home. That cannot be sustained for 9 months.

      • And to what degree would saving some lives (and having fewer people hospitalized, and fewer people sick, and less strain on health professionals) help reduce the level of economic collapse?

      • “Right now the government is paying 80% wages of several million people to stay at home. That cannot be sustained for 9 months.”

        Yes it can, and quite easily. Any government issuing a fiat currency can always pay its bills. It never has to turn to the printing press and say, OK bud, how much do I owe ya?

        So long as too few goods aren’t chased by too much money, inflation isn’t a problem.

        Not saying I agree this should happen, but I am saying that it’s entirely possible for the US government to keep us on life support indefinitely.

        Here’s is a good essay that describes Modern Monetary Theory in relation to where we are today.
        https://seekingalpha.com/article/4345783-simulation-game

        The money quote: “On April 23, Lloyd Blankfein tacitly contended that the US needs to “borrow dollars.” His purpose … was simply to drive home the same point that countless other “luminaries” have attempted to make recently. Thanks to the spending associated with virus relief efforts, the deficit is set to balloon to around $4 trillion in 2020, which “should” entail higher bond yields, and all manner of other scary things that you’ve been indoctrinated to believe invariably accompany fiscal largesse.

        “What these folks are inadvertently doing, though, is laying bare the absurdity in this type of thinking for the issuer of a reserve currency. I implore you: Step back from this situation and ask yourself whether it makes any sense to say that the US needs another nation to “lend” America “dollars.”

        “Simply put, that is self-referential nonsense. The US can always buy whatever there is to buy that’s denominated in US dollars. It has no need to borrow dollars from anyone else because it is the issuer of those dollars. The US can spend too much, which risks stoking inflation, but the US does not, will not, and has never, needed to borrow dollars. Suggesting otherwise is to traffic in patent nonsense, as Blankfein is doing in the tweet above.”

        Heisenberg is, I’ve found, astute in many matters having to do with markets and finance. He’s right here, too. https://www.amazon.com/Deficit-Myth-Monetary-Peoples-Economy/dp/1541736184

      • Don Monfort

        Ah, AOC’s Modern Monetary Policy. I could stop there. But:

        reserve currency:”A reserve currency (or anchor currency) is a foreign currency that is held in significant quantities by central banks or other monetary authorities as part of their foreign exchange reserves.”

        Modern Monetary Policy says: “What these folks are inadvertently doing, though, is laying bare the absurdity in this type of thinking for the issuer of a reserve currency. I implore you: Step back from this situation and ask yourself whether it makes any sense to say that the US needs another nation to “lend” America “dollars.”

        “Simply put, that is self-referential nonsense. The US can always buy whatever there is to buy that’s denominated in US dollars.”

        Ask yourself why for example, Zimbabwe’s and Venezuela’s currencies are not reserve currencies.

        I will help you: Why would central banks hold as foreign currency reserves the currencies of nations that print the crap willy nilly? Why would anybody not forced to by their own foolish government accept payment in those currencies for anything?

        The big flaw in socialist/Marxist theory is that they think they can come along and appropriate the wealth created by a capitalist economic system, transfer it to the have nots and no disruption to the creation of goods, services and wealth will occur.

      • Don

        You do realize that puts you shoulder to shoulder with AOC. In some ways I envy you. In other ways, not so much.

      • “ Why would central banks hold as foreign currency reserves the currencies of nations that print the crap willy nilly? ”

        Um, the US is doing a pretty good job of running their printing presses these days.

      • Seems like my (longish) comment was lost in moderation.

        Short answer: I’m not left, I lean right, and any country issuing its own currency can indeed pay all its bills denominated in that currency. When you have hyperinflation for whatever reason, and you have to convert your currency to dollars (or some other reserve currency) in order to buy something you don’t produce, then yes, that’s a problem. The US doesn’t have that problem. Whether you think MMT is leftest or not is immaterial to whether or not it describes how the monetary system actually works, and whether some want to use it to rob the rich to pay the poor is also immaterial. And no, I do not believe in Universal Income, although yes, I may become a heroin addict if the government decides I have nothing else more useful to do and pays me to become one. And yes, I’m joking.

        Heisenberg is correct, whether we like it or not. And no, I did not come across MMT just now by reading Heisenberg.

        That’s as short as I can manage, except that no, I won’t bother debating this further as it’s really off-topic and doesn’t matter.

      • dougbadgero

        Regarding MMT and other issues with the economics of what we are doing:

        The belief that we can continue to pay millions to do nothing forgets the purpose of a capitalist system. The purpose isn’t to make money, it is to produce goods and services. Those millions of people are no longer producing goods and services, but they are receiving the medium of exchange (money) to allow them to buy goods and services. This will eventually reduce the standard of living for everyone since millions are now consumers but not producers.

      • Don Monfort

        Sr. 132:”I’m not left, I lean right, and any country issuing its own currency can indeed pay all its bills denominated in that currency.”

        Tell the formerly well off countries that have insufficient hard currency to import food, medicine and other necessities, to insist on having the bills for their imports denominated in there crap currencies. That is not the only problem that countries with debased currencies create for themselves. Google “debased currency”. Take a contemplative week off, then come back and talk.

        Mr. Big:”Um, the US is doing a pretty good job of running their printing presses these days.”

        We are not printing money willy nilly. What we are doing is spending money that we will borrow. We can borrow a lot of money, because we have a yuuge economy that produces a lot of stuff we can sell, our currency is the reserve currency of the World, and we have a good credit rating. We also have in our reserves over 8,000 metric tonnes of gold.

        We are not yet debasing our currency. That’s an inglorious feat the socialist/Marxists will accomplish, if they can convince enough economic illiterates to vote them into power. They are obviously plowing fertile ground.

      • Don M: you’re confusing the issue of a debased or hyper-inflated currency with the basic question of: can a government that issues its own fiat currency always pay any bills that are denominated in that currency? Yes, it can. Would you have real “debt” if you owned the only printing press in town?

        Once again: I’m not a socialist and never will be. Not arguing for government support, simply stating the basic truth that MMT has laid bare. That doesn’t mean I support any socialist agenda based on MMT; I do not, any more than I support taxing the rich at 95% just because this is possible.

      • “Why would central banks hold as foreign currency reserves the currencies of nations that print the crap willy nilly?”

        What recently happened to the price of oil overall because the demand dropped? It went negative.

        If you remove a nation from your list of places you are prepared to export to you end up with a load of surplus production in flow that then has nowhere to go. In any commodity market that collapses the price for *all* the production in flow at that time.

        You don’t want that to happen for what should be obvious reasons.

        “Export led growth” is a trick to hide the issuing of your own currency by the central bank by making it look like it is discounting foreign currency or assets. In reality the foreign financial asset stuff is throw in some drawer somewhere and never sees the light of day again. Which helps keep the exchange rate down so your exports continue to flow. China does it explicitly, places like Norway use a “Sovereign Wealth Fund” where they store foreign assets out of the way so they can’t cause a Dutch disease problem.

        The “stuff in a drawer somehwhere” is an asset, which requires a balancing liability in the denomination. That’s what a government deficit is – the balancing item. To get rid of it requires you to confiscate the excess savings held by people who export to you, and who save domestically in your denomination.

        In summary exporters gotta export. And they will take whatever “crap” you have because they have no choice if they want to maintain the “export led growth” fiction.

      • Don Monfort

        You are lost in a lot of silly mumbo jumbo, Neil. Tell the starving and toilet paper deprived people of Venezuela and other failing countries with crap currencies your convoluted story that is as bogus as it is elaborate. Try to order a MB from Germany and tell them you’ll pay for it in Bolivars, or Zimbabwe dollars. They will tell you they don’t have any use for that crap.

  9. Could you go into more detail on how you implemented your connectivity and infectiousness parameters?

    When I did something similar last night (with a quick-and-dirty SIR model) I simply assigned each member of the population a respective gamma-distributed R0 value. And the likelihood that in infectious person would infect a randomly selected uninfected person within a given time interval (six hours) I merely took as the square root of respectively probability figure equal to the ratio of the respective R0 value and that ratio of that time interval’s duration to the (uniform) infectiousness duration.

    Obviously your approach is more sophisticated, but I couldn’t quite that part.

  10. My question is, should the governments advisors have known this and could it be seen in the data prior to lockdown, in which case lockdown with all its consequences should not have taken place.

    • IMO governments should have realised (through being advised competently) that it was quite possible that the HIT was much lower that predicted by the Ferguson20 model or by simple models that ignored population heterogeneity.
      They should also have realised that that, in the absence of an effective vaccine or drug, for which the outlook is very murky, a lockdown that does not continue indefinitely saves few lives except to the extent that, through “flattening the curve”, it avoids health systems being overwhelmed.
      There has never been any evidence that the UK health system was about to be overwhelmed, just erroneous predictions from the Ferguson20 model.
      IMO it was very stupid to impose a pretty hard lockdown at the stage that the UK did, certainly on a UK wide basis.
      However, the position may have been different in some countries, particularly in regions where their health systems were becoming overwhelmed, in which case a temporary hard lockdown to flatten the curve might have been the least bad option.

  11. Interesting.

    A low HIT, provided exposure has been large,
    implies two testable hypotheses:

    1. No second wave, and
    2. No return in the autumn

    I’m guessing we’re nominating Sweden as the test case.

    We shall see.

    • Bad idea to try to infer too much from cross-country comparisons. Means comparing lots o’ uncontrolled variables.

      Almost as bad as extrapolating from non-representarive and non-random sames.

      Like a Rorschach test for political biases.

      • Hi Joshua, Isn’t it You that is prejudging the results, (as biased), before the analysis? All I see TE doing is postulating there is a potential test. I find it hard to support your skepticism with the mountains of data from thousands of localities, all with known demographics. Shouldn’t you reconsider? The only place we have seen second waves so far are in places where the strong mitigation stopped the virus very early, like in Singapore.

      • “lots o’ uncontrolled variables.”

        Yes, including the strain of the virus in question.

        Evidently, the Euro variant is much more communicable in Europe and America than the Asian variant:

        Why the Mutated Virus Spreads Faster in America and Europe Than East Asia

      • TE –

        Sure, could be for all I know. Then again:

        > There’s no clear evidence that the pandemic virus has evolved into significantly different forms—and there probably won’t be for months.

        https://www.theatlantic.com/health/archive/2020/05/coronavirus-strains-transmissible/611239/

      • Steven Mosher

        ButUncontrolledVariables.

        Climate skeptics use this too joshua

      • All better scientists recognize that there are unknowns, and uncontrollable aspects. That’s why we do many experiments and get a good signal to noise ratio when we can.

      • I’m not arguing arguing one way or the other.

        What I’m saying is thst I can see people selecting comparison points, inevitably, to prove associations that agree with their ideological preferences.

        I’ll give TE credit for at least bucking that trend. Nic, not so much. What it boils down to is the comprehensiveness of your treatment of the variables.

        People are comparing to the economic effect of Sweden’s no lockdown policy without even attempting to control for the effect of the lockdowns in other countries as distinguished from the impact of a raging epidemic. They are making assumptions about the benefits economically to Sweden from no lockdown without even evaluating the economic state of Sweden. Your friend was comparing virus trends in Sweden and Switzerland a few weeks ago – not doing that now, is he? Why do you think he stopped? Maybe because he was making that comparison before enough time had passed to make the comparison meaningful.

        “Skeptics” are often right when they raise questions about incontrolled variables. I have often said so.

        It’s like when Nic tried to extrapolate from non-representative data on the Princess Diamond, and then had a double down by doing it too soon (missing a high percentage of deaths).

        Above all, the question is really about consistency and evenly applied standards.

        There are other rules that apply to appeals to uncertainty.

        TE gets good marks on this issue in my opinion. He’s applying due skeptical diligence.

      • Extrapolating from unrepresentative data, trying to draw causal conclusions from cross-sectional (non longitudinal) data, and trying to infer causality from associations without presenting a plausible causal mechanism, get black marks in my book.

        Selective treatment of uncertainty gets the biggest black mark.

        Not even attempting to control for obvious variables, particularly ones that are quite likely explanatory, failing to do any kind of sensitivity analysis of similar variables, not addressing obvious potential confounds? Black mark, black mark, black mark, black mark, in my book.

        The point isn’t to be perfect. The point isn’t to be correct. The point is to be transparent so that people can at least see that you’re trying to integrate the reality that you are the easiest person for you to fool. With that transparency you can be vulnerable and ask for help. It provides you that space to observe and breathe. You can be less reflexive. You can become detached.

  12. Chelsea MA.

    Serological survey suggested over 30% infected (warning, the sampling methodology wasn’t really that random).

    Infections (and fatalities) still growing (40,000 population, 124 currently died from COVID – which at @ 30% infected works out to @ a 1.0% IFR).

    • The Chelsea survey results aren’t inconsistent with what I wrote. See note [22], where I said that the HIT might be significantly higher in areas that are, for instance, very densely populated or have much less inhomogenous populations.
      I note that the Boston Globe article reporting the Chelsea MA survey results says:
      “about 65 percent of its residents are Latino. Many live in three-decker houses, Ambrosino said, where it’s hard for people to isolate themselves. Many work in the hospitality industry and health-related fields, where exposure to the virus is greater.”
      All those factors would cause both R_0 and the HIT to be higher than their US wide population averages.
      I don’t think it’s true that infections are still growing in Chelsea. This article ( https://www.bostonherald.com/2020/05/06/coronavirus-in-massachusetts-chelsea-brockton-show-signs-of-hope-even-as-infection-rates-rise/ ) says:
      “We’re feeling some level of relief that the rise in cases has stopped and that we’re starting to see less cases a week,” Chelsea City Manager Thomas Ambrosino told the Herald. “That’s certainly good, positive news.”

      • Nic –

        > I don’t think it’s true that infections are still growing in Chelsea.

        Obviously, that quote suggest that the rate of increase has flattened, not that # of infections isn’t rising. What I said is that infections are still growing (along with deaths). Do you actually doubt that?

        And so anyway, what do you see as the value of some kind of generic supposition that in some generic context there might be a particular generic herd immunity rate, given that the herd immunity rate is very likely to be significantly lower or higher than your generic estimate *depending on a whole slew of much more influential variables?* What matters is how those variables play into particular contexts.

        Since you’re prescribing policy for the UK, than perhaps you should work on that the herd immunity rate for the UK might be – more than likely significantly higher than Stockholm, don’t you think? Then why do you keep using Sweden as some point of comparison?

        If you look at the quote from the co-author that I’ve posted, his point is exactly that so much depends on the particulars of the context.

        > All those factors would cause both R_0 and the HIT to be higher than their US wide population averages.

        Well, that’s the point, now is it? How useful are the conditions for Stockholm for understanding the herd immunity % in any particular other locations?

  13. It’s worth mentioning an article in the Telegraph today by Matt Ridley and David Davis (MP) which states:

    “Is the chilling truth that the decision to impose lockdown was based on crude mathematical guesswork?”

    Including this: “Details of the model his [Ferguson] team built to predict the epidemic are emerging and they are not pretty. In the respective words of four experienced modellers, the code is “deeply riddled” with bugs, “a fairly arbitrary Heath Robinson machine”, has “huge blocks of code – bad practice” and is “quite possibly the worst production code I have ever seen”.”

    https://www.telegraph.co.uk/news/2020/05/10/chilling-truth-decision-impose-lockdown-based-crude-mathematical/

    Paywalled but easy to hurdle.

    • While Lewis’ code was poor, his results were consistent with what is known about epidemiology. My own model got similar results, and the code was very simple – maybe 100 lines of python for a discreet time SEIR model.

      A lot of code used in science is poor. Scientists are not often good programmers, plus most of the code is written by grad students – one after another on the same code if it survives for long.

  14. Nic Lewis, thank you for the essay.

    Is there an operational definition of “herd immunity”, that is, a criterion by which we can decide from counts of newly diseased/newly dead that “herd immunity” has been achieved? Is it where the new case count reaches 0 and stays (nearly) there?

    • matthewrmarler, thanks for your comment. Herd immunity is perhaps best seen as a process rather than a defined specific state. But the “herd immunity threshold” is the state where, through individuals becoming infected and thereby immune, herd immunity has risen to the point that, on average, each individual who is infected in turn infects exactly one susceptible individual. Until that point, the number of infected individuals is continuously increasing. Beyond that point the number is shrinking.
      The new case count doesn’t reach zero until the ultimately infected proportion is reached, which is higher than the HIT. I state both proportions for the examples that I give (see text just above Figures 4 and 5).

      • Nic Lewis: Herd immunity is perhaps best seen as a process rather than a defined specific state.

        I get it. But you did say “reached”. Could you recognize a point at which you might say to a President or a Governor something like “We have reached it. Now you can end the social distancing measures”?

        I feel like I’m pushing you unfairly. I was thinking more like, when the time derivative of the smoothed daily new case count was 0 or consistently lower after peaking. What if it becomes endemic like measles or polio before the vaccines, with recurrent outbreaks?

    • It doesn't add up...

      You may find this pair of articles from Simon Anthony a useful backgrounder on SIR models in relation to herd immunity and second waves and the putative effect of lockdowns.

      https://hectordrummond.com/2020/05/05/simon-anthony-covid-19-myths-misunderstandings-and-omissions/

      https://hectordrummond.com/2020/05/07/simon-anthony-covid-19-and-lockdown-myths-misunderstandings-and-omissions/

      • It doesn’t add up … : You may find this pair of articles from Simon Anthony a useful backgrounder on SIR models in relation to herd immunity and second waves and the putative effect of lockdowns.

        Thank you for the links.

  15. Ireneusz Palmowski

    The drop in temperature in the east of the US is conducive to viruses.

  16. I find a similar result.

    http://clivebest.com/blog/?p=9498

    Ferguson’s model was originally developed for a 1918 type flu pandemic with a homogeneous population distribution

  17. There is much more to transmission than R0 = X. X has many factors being how transmissible the disease is with regard to humidity and temperature as well as interpersonal interface with others. In New York, London, Paris, Northern Italy, with it’s high densities and people using the same public transport it means with people living in the same proximity and pushing the same elevator buttons and door handles of cabs it means much higher transmissibility and infection rates. A simple R0=X isn’t very realistic in Idaho when people often have their personal cars going to a small company and have 10’s of people they have interpersonal interface with instead of tens of thousands every day of those in high density high interpersonal interface cities.

  18. Pingback: Variation in R – Markets Fail

  19. Nic –

    You say:

    > Accordingly, total fatalities should be *well under 0.1%* of the population by the time herd immunity is achieved.

    In NYC, they’re already slightly above 0.1% of the population dead. That number is obviously only going to increase. And that’s without even factoring the likely under-reporting of deaths (people dying at home and long term care facilities w/o tests, a lag in death reports being officially counted, etc.)

    Help me to understand what it is about NYC that is different from your projection? Is it that even after reaching herd immunity people continue to die, or even to still get infected and die?

    In Chelsea MA, with a population of 40k, and 124 deaths (already, with a probable undercount as mentioned above), they’ve already exceeded the population fatality rate or 0.1% by a considerable amount. To what do you attribute that difference from your projection?

    > The Population Fatality Rate (PFR) has reached 0.22% in the most affected region of Lombardia and 0.57% in the most affected province of Bergamo,which constitutes a lower bound to the Infection Fatality Rate (IFR)…Combining PFR with the Princess Diamond cruise ship IFR for ages above 70 we estimate the infection rates(IR) of regions in Italy, which peak in Lombardia at 23% (12%-41%, 95% c.l.), and for provinces in Bergamo at 67% (33%-100%, 95% c.l.).

    https://www.medrxiv.org/content/10.1101/2020.04.15.20067074v2

    Why did that infection rate and PFR get so high in Bergamo?

    • The authorities failed to protect the elderly from COVID-19 infection. So deaths spread in care homes, and account for ~50% of deaths in many countries, nearly doubling the averaage infection fatality rate. In the UK this appears to have been caused primarily by deliberate (but totally unnecessary) actions by the authorities t clear hospital beds, prompted by the Ferguson20 model predictions, to “protect the National Health Service”.

      Also, lockdowns, school closures and general encouragement of social distancing probably reduce the rate of infection among children and the highly connected younger sections of the adult community, relative to that of older people.

      Deaths to reach the HIT would be minimised if the ratio of young, healthy people being infected were as high as possible relative to the number of old and vulnerable people being infected, since the fatality rate increases very steeply with age. Lockdowns and enforced social distancing generally may well have acted to reduce rather than increase this ratio.

      • > So deaths spread in care homes, and account for ~50% of deaths in many countries, nearly doubling the averaage infection fatality rate.

        It isn’t simply a matter of them living in care homes. It’s also a factor of their age. Communities where people tend to live together or work in close quarters (prisons, meat packing companies) also have high infection rates – but other such communities don’t have the same high mortality rates because they don’t tend to be as old on average.

        And there are a lot of older people who don’t live in such communities and who are presumably relatively isolated now – in a way that won’t be the case if countries just “open up,” and in particular if they do so before they have a robust infrastructure for testing/tracing/isolating.

        > Deaths to reach the HIT would be minimised if the ratio of young, healthy people being infected were as high as possible relative to the number of old and vulnerable people being infected,

        This is based on a really speculative assumption – that you can actually isolate those older people and keep them isolated while the infections are spreading around the younger people until her immunity is reached. Experience tells us that is a very questionable assumption – and also that embedded in that assumption is a willingness accept a disproportionate number of deaths among essential workers and particular communities at relatively high risk – such as minority communities. Keep in mind that at least part of the reason they’d be at higher risk is because they are less able to stay isolated.

        > . Lockdowns and enforced social distancing generally may well have acted to reduce rather than increase this ratio.

        Again, that is highly speculative – and is directly based on an assumption that over time, with slower spread, more effective treatments wouldn’t take place and also that a more robust infrastructure for testing/tracing/isolating wouldn’t be built that would slow the morbidity and mortality rates down, leading to much, much less hardship if a vaccine is developed and distributed.

        You are gambling a huge amount on speculation. And there is no clear indication that government mandated shelter in place orders have a significant differential economic impact. You seem to be taking that merely on faith.

      • Joshua,

        On the contrary, it is you who are taking things too much on faith. If you are in favor of an extraordinary measure like a lockdown, it is up you to justify it. Lockdowns have severe public health consequences, both psychologically and physically. In addition to precipitating what appears to the first global depression in almost 100 years (with incalculable negative impacts), the lockdowns have created skyrocketing rates of alcoholism plus spousal and child abuse. Plus, as has been well documented, other causes of mortality are accelerating as people are unable or unwilling to visit hospitals. Even the cancer wards are running well behind normal levels.

        We are now getting better data that suggests many of the lockdown measures were honest mistakes. In particular, tracing studies in France and China indicate that children are not significant vectors of infection and re-opening schools for younger children is appropriate. Also clusters very rarely arise from outdoor events – so taking a walk on a beach is quite safe with moderate social distancing. Many countries are looking at this data and adjusting their measures appropriately (Australia, Netherlands, Switzerland among others). Hell, even the WHO came out and said that Sweden could be the model. Full credit to those who are able to amend their preconceptions based on new data. Not so much credit for others who seem stuck in in their views…

  20. Nic-

    The Swedish paper you linked to appears to be the one that was retracted soon after it was published. AFAIK, they have not explained what the error was that led to retraction, but they have also not re-issued any of these prediction. https://www.forbes.com/sites/davidnikel/2020/04/22/sweden-health-agency-withdraws-controversial-coronavirus-report/#708abaf04349

    I don’t speak Swedish, so it’s entirely possible this is a different paper or a version of the paper with errors corrected. But I can’t find any mention of such a correction in any English source, and I can’t find any mention of these high Swedish infection rates past the 4/22 retraction of the paper.

    • Re: “The Swedish paper you linked to appears to be the one that was retracted soon after it was published”

      Good catch. I highly doubt something like this would have made it into a peer-reviewed article written by a competent expert in this topic (ex: an epidemiologist or infectious disease expert). Make it rather ridiculous when people say that this pandemic will make the previous model of peer review obsolete.

      “The rate of epidemiological and immunological research that is getting conducted and published is breathtaking; after all this settles, the old publication model with peer review and paywall will arguably be dead.”
      https://judithcurry.com/2020/03/19/coronavirus-uncertainty/

      “Like the vast range of other non-peer-reviewed material produced by the denial community, book authors can make whatever claims they wish, no matter how scientifically unfounded.
      […]
      The general lack of peer review for the denial books is a common feature of the vast body of literature produced by the climate change denial community, ranging from blogs to newspaper op-eds to policy briefs from CTTs.”

      https://journals.sagepub.com/doi/pdf/10.1177/0002764213477096

      • Atomsk’s Sanakan: The general lack of peer review for the denial books is a common feature of the vast body of literature produced by the climate change denial community, ranging from blogs to newspaper op-eds to policy briefs from CTTs.”
        https://journals.sagepub.com/doi/pdf/10.1177/0002764213477096

        Boy, what a load of junk that is! a short quote (quote mining) will have to suffice for now: Whereas scientific knowledge slowly but surely accumulates through testing, and then rejecting, modifying, and/or verifying hypotheses and theories,12 the denial literature is cumulative in the literal sense. Regardless of how thoroughly discredited in the scientific literature, denialist claims (the recent warming trend reflects a natural cycle, is the result of solar activity, won’t produce harmful impacts, etc.) are retained and reused whenever convenient. Non-peer-reviewed books espousing climate change denial offer an ideal means of presenting these claims, accounting for the growing popularity of such books. Strikingly, many of
        these books not only provide fallacious critiques of climate science but also present an alternate reality in which global warming is a hoax created by a conspiracy of supposedly greedy scientists, liberal politicians, and environmentalists (McKewon, 2012).

        The idea that the present warming trend is natural has been “discredited”? All of the disputations rest on (so far) untestable assumptions. Nothing yet explains the apparent periodicity in the temperature proxies, or how the recent warming is about “on time” if there is a persistent periodic causal driver.

        What harmful effects have resulted from the warming so far? None. Net Primary Productivity of natural and cultivated plant stands is up (that has been published in peer-reviewed articles in Science Magazine and Nature). No vector-borne disease has increased in intensity or prevalence.

        “Supposedly greedy scientists”? Do you really not understand that grant-funded scientists depend on money to pay their food bills and mortgages just the same as industry-funded scientists, and that all scientists are susceptible to money?

        If that is what results from peer review, then peer review seriously needs help.

      • Matthew, it’s not my job to walk you through the published literature on global warming being attributed to greenhouse gas increases (ex: tropospheric warming + deep ocean warming + stratospheric cooling that increases with increasing height + mesospheric cooling + thermospheric cooling + decreasing diurnal temperature range + decreased annual cycle + …). The evidence-based scientific consensus on this is clear; it’s clear to the vast majority of experts in this field, and it’s clear to those of us who read the peer-reviewed literature in which the evidence is discussed. The fact that you don’t accept it is no more my problem than is anti-vaxxers refusing to accept that evidence-based scientific consensus that vaccines don’t cause autism, simply because they read some nonsense on a non-peer-reviewed blog. I’m sure those anti-vaxxers will make the same sorts of evidence-free pleas as you (ex: “[a]ll of the disputations rest on (so far) untestable assumptions”), while the rest of us roll our eyes.

      • Atomsk’s Sanakan: Matthew, it’s not my job to walk you through the published literature on global warming being attributed to greenhouse gas increases (ex: tropospheric warming + deep ocean warming + stratospheric cooling that increases with increasing height + mesospheric cooling + thermospheric cooling + decreasing diurnal temperature range + decreased annual cycle + …). The evidence-based scientific consensus on this is clear; it’s clear to the vast majority of experts in this field, and it’s clear to those of us who read the peer-reviewed literature in which the evidence is discussed.

        You don’t pay much attention to what I read and write, but I base my opinions about CO2 and climate on published research in peer-reviewed journals. My disagreements with the “consensus” are on the magnitude of the CO2 effect and whether all possible effects have been adequately quantified.

        The combination of increased CO2, increased temp, and increased rainfall since the late 1800s has been of net benefit to net primary vegetative productivity and agricultural productivity. Papers to that effect, from peer-reviewed journals, have been referenced and linked to here at ClimateEtc..

    • Re: “But I can’t find any mention of such a correction in any English source, and I can’t find any mention of these high Swedish infection rates past the 4/22 retraction of the paper.”

      They apparently updated it in late April. But given their screw-up, and how implausible their results are, I wouldn’t rely on it until it goes through peer review.

      “Coronavirus: Has Sweden got its science right?
      […]
      That was later revised down to 26% after the agency admitted a calculation error.”

      https://www.bbc.com/news/world-europe-52395866

      “”A variable had been set at the wrong value and it affected the entire analysis. Now, the estimated date for the peak of the infection curve has been set at April 8 and not April 15 as was previously said. Also, in Stockholm 26 percent of residents are likely to have been infected by May 1, which is somewhat lower than the previous estimate,” said Wallensten.”
      http://www.xinhuanet.com/english/2020-04/24/c_139003043.htm

    • Nonsense.

      The Swedish Public Health Authority report that I cited has not been withdrawn. The article you link to is dated 22 April and relates to an early version of the report.

      An Englsih version of the current report is here, BTW: https://www.folkhalsomyndigheten.se/contentassets/e1c3b83fa24f4d019e4842053ffd8300/estimates-peak-day-infected-during-covid-19-outbreak-stockholm-feb-apr-2020.pdf

  21. Thank you Nic Lewis. I understand the situation a bit more now.

  22. Excellent study and observations. In addition, my alma mater, MIT, has had their economists looking at optimum lockdown strategies, and it seems no country is paying attention……https://www.nber.org/papers/w27102?mod=article_inline

  23. It doesn't add up...

    It looks as though Figure 1 displays clear evidence of a shortage of test capacity. This short piece from the Santa Fé Insitute explains the underlying maths:

    Click to access t-022-savage.pdf

  24. It doesn't add up...

    On the scaling laws that apply to population density, Santa Fé Insititute has a short introduction here:

    Click to access t-025-kempes-west.pdf

    and a rather fuller paper that suggests a functional form for adjusting R according to city populations to reflect the greater social interconnectedness of larger cities here:

    Click to access 2003.10376.pdf

    I produced a chart of case density against population density of English Local Authorities as at April 30th (just before the testing regime changed, which could affect the results) using PHE and ONS data here:

    https://datawrapper.dwcdn.net/K3uOD/1/

    It supports the Santa Fé analysis, although I did the chart first and then went there to see if they had done anything – they didn;t publish until some days after I did.

    • IDAU –

      > This is a large effect. Based on data of mobile phone social networks (8), people living in a city of 500,000 have, on average, 11 people in their mobile phone social network, while people living in a city of 5,000,000 people have approximately 15. This is relevant to disease transmission as the average contact rate is proportional to degree β ∝ k(N) (see Materials and
      Methods). Therefore, we expect that initial growth rates of COVID-19 cases to be higher in larger cities (see Materials and Methods). This is what is found empirically (see Figure 1A).

      What is the empirical method that prioritizes urban vs. rural setting over cultural factors (like being a rural active church-goer vs being an urban-dweller who passes a lot of people on the street but has no such regular group activity) for determining contact rate in urban vs. rural settings? Does it really scale as described?

    • Thanks for the links, I’ll take a look.

    • I’ve now had a quick look at the papers that you link to. They make sense to me and your graph looks impressive, although I’m not totally sure what exactly the points on it represent. Could you post a link to the data plotted, and to the source of that data, please?

      If I understand your graph correctly, the fitted line implies that cases per head are proportional to population density raised to the power of about 2.3. It would be good to use bivariate regression to separate out the effect of city population (for one might also expect a positive relationship, but with a much smaller power) and pure population density.

  25. South Korea does fit the theory – too effective a lock down causes a second wave.

    South Korea warns of second wave of cases as it shuts night clubs and bars

    South Korea on Sunday warned of a second wave of cases as a new cluster formed around a number of night clubs, according to Reuters.

  26. Nic, thanks for following up on the paper. I have believed from the start of looking at the epidemic that there is a bucket of people who are exposed but uninfected, so in my SEIR schematic, I start with the population, then you would move it to exposed with a contact model that hopefully would have the correct age, sex, comorbidity, population density, type of residence, etc. factors, properly distributed for the population of interest. But in the exposed compartment, not everyone gets infected. Those who don’t get infected could be a dose issue (somewhere in the models, either in the contacts portion or elsewhere you have to deal with the dose issue), could be genetic variation, could be some other factor we don’t understand (more research shows smokers don’t seem to get infected as often or to have as serious and illness), not likely to be antibodies, the most recent research shows little cross-reactivity between other strains of coronavirus and this one. But from the cruise ship and other examples, there are people who are exposed but not infected. (One clear way to see this is look at the number of cases among people 18 and under in the US versus their percent of the population. And this group is estimated to have three times or more the number of contacts as other groups.) In any event, I move the exposed but uninfected group directly to Recovered, but I call that bucket Uninfected/Uninfectable, because for some reason they don’t get infected, or they have been infected and they have antibodies so can’t be infected (several papers in the last week found almost universal and strong antibody responses to infection).

    Then the exposed and infected proceed to asymptomatic, which appears to be a very large cohort, mild illness, and serious illness that requires hospitalization compartments, and from their to either death or recovery.

    But a bigger issue than figuring out who gets infected and what the rate of serious illness is, is that you can’t run the whole population in one model, even with the contact model adjustments noted above. This is a phenomenally bifurcated epidemic between the general population and nursing home residents and other senior living facility residents. In Minnesota, congregate care living settings, primarily for the elder, account for over 80% of deaths. Every other state has a huge percent of their deaths in similar settings, and a large number of elderly deaths are occurring at home, but to people doing hospice at home or with advance directives. Using Minnesota as an example, we have 5,600,000 residents, 80,000 of whom live in these senior congregate settings (note that skilled nursing facilities also have a younger population doing long-term rehab from serious illnesses). When I did this analysis a couple of days ago, we had 508 deaths, 407 in those settings (the pattern has remained the same the last two days)(the 407 also doesn’t include those elderly who died at home or the nursing home staff who have died). So 407 divided by 80,000 is a death rate of .51%. 101 divided by 5,520,000 is a death rate of .002%. That is a 255 times greater death rate among that congregate living group. The pattern has been the same for a long time and while there will be more deaths that creep the death rate up, the pattern will stay the same.

    For the general population, there are many, many causes of death that kill more people. The models need to be run separately for the general population and the senior congregate care groups. And as you can see from the analysis above, it is crazy to have a general lockdown instead of a focus on the vulnerable. Meanwhile the CDC issued a report on Friday indicating the vaccine dose ordering was done over 3 million doses and measles alone down over 400,000 doses. Scaring the crap out of the population is making people avoid needed health care, and is literally killing children, far more children than will be killed by coronavirus. (60 deaths in the whole US to people aged 24 and under). But maybe those lives don’t count. I have a lot more analysis on all of this at my blog site, http://www.healthy-skeptic.com

    • thanks Kevin; should we not start to use the phrase “end of life residential homes” to describe nursing homes? One does not go into such places to get better: we are in the waiting room for the next life; these tragic folks are dying when their life expectancy suggests they will die. It will come to us all.

    • Mr. Roche has got it right:

      “Using Minnesota as an example, we have 5,600,000 residents, 80,000 of whom live in these senior congregate settings (note that skilled nursing facilities also have a younger population doing long-term rehab from serious illnesses). When I did this analysis a couple of days ago, we had 508 deaths, 407 in those settings (the pattern has remained the same the last two days)(the 407 also doesn’t include those elderly who died at home or the nursing home staff who have died). So 407 divided by 80,000 is a death rate of .51%. 101 divided by 5,520,000 is a death rate of .002%. That is a 255 times greater death rate among that congregate living group. The pattern has been the same for a long time and while there will be more deaths that creep the death rate up, the pattern will stay the same.”

      My thinking is along the same lines. We know who are the vulnerable populations. We know this because they are dying grossly disproportionately. Have been all along. No need to test the whole herd. We can far more easily and cheaply just count those who need burying. Then we focus our resources and actions on protecting those populations. The rest of us go back to work, earn money, buy things, pay taxes.

      • On the surface that should have been the most effective way to reducing deaths. A closed system with total control over who breaks the seal. It hasn’t been all of the long term facilities that are responsible for the disproportionate rate. For those states who publicize the data, it’s a few bad actors with really high cases and deaths. In some situations,
        if the entire US had the same ratio of deaths to population as the worst long term health facilities, we would be losing 40 to 50 million people.

        Just last night, I read a quote by a governor about plans to implement stricter controls at their nursing homes. Sorry buddy, but that should have been done early March not Mid May. We don’t need a lethal virus to know well in advance who are the most vulnerable among us.

    • Kevin Roche | May 10, 2020 at 10:21 pm

      Good post.

  27. Kevin –

    > Scaring the crap out of the population…

    Why to you have such a low opinion of the population – as if they’re just a bunch of passive little sheep running around with no agency and who are just scared by the big, bad..what….media? government? liberals? CDC and Birx and Fauci and Redfield and Trump?

    What do you expect, for the media to just not report on the tens of thousands of deaths thus far, and hundreds of thousands of his hospitalizations and debilitating illnesses for weeks? Do you expect people who are ill to just be quiet and not tell their friends and families about being infected and ill? Should the 1.3 million people identified in this country as infected just hide that news away?

    Should Italy and the UK and Spain and France and Brazil and Ecuador get in on the plan to keep the news of this “plague,” as the president calls it, from the population?

    Do you expect government and public health officials to just all agree to keep what’s going on a secret somehow?

    People are going to be scared in the midst of a pandemic where even if the fatality rate is lower than it seems, and herd immunity is reached sooner than expected, and effective treatments are developed, and a vaccine is developed quickly and distributed, there will be maybe 130 thousand dead, and maybe 500,000 who are hospitalized, and many more taken ill for a couple weeks, over the next year?

    That’s how humans are. You msy have disdain for them in their weakness – but it’s kind of inevitable, isn’t it?

  28. Pingback: Covid19: A Taxa de Imunidade natural é 7% – 24% e não 70%, revela um Estudo Epidemiológico | O Economista Português

  29. @MannockDavid

    OK, Firstly I’m not an MD or a virologist. My roots are in biological sciences/biophysics & phys chem. This is my opinion & like most reasonable people I’m open to corrections if I’m in error.

    I put some info on Twitter yesterday to Willis that adds reality to what are fundamentally human geography-based statistical models without realistic infection transmission/virulence/human immune response variables. As mentioned above there are still unknowns which become estimates that don’t represent the true variables. One of those is infectiousness. It will vary not depending on geographic or social circumstances, but because of the underlying biology. On YT watch this video: https://www.youtube.com/watch?v=qwSjvIixzP8

    Covid-19 may be a different virus, but many viruses have the same/similar infection route – musosa & targeting mechanisms. In the video, there’s a regional difference between N & S England & with France. N England & France included the low countries that are primarily of Norse decent, hence ‘Normans’. So where that ‘cultural’ sub-type is dominant, the infection is low/mild. The basis of this differential is ABO blood type as seen for other viruses & some cancers. For types A & B CHO antigens are on the cell surface, whereas for type O they are in the circulation. There is an extra molecule that’s ABO related (all 3 glycolipids), called the Forssman antigen. The distribution of this molecule varies by animal, by mammal, by tissue origin & by blood type. If the population is predominantly type O, then infection is low/mild, but for type A (moi) it is more prevalent with worse symptoms & outcomes. I do not know if these differ in their ability to transmit the virus. There are more blood types, B & AB plus many A & B sub-types – not Rhesus related. I’ve not looked at these sub-types presently, but they may show small differences in symptoms & central locations of infection within the body dependent on the presence of the Forssman antigen per tissue type. I have downloaded & read papers on these issues & have added links in my tweets to various govts for their experts.

    Another variable is the virulence of the virus. From what I’ve said above the tissue distribution & expression of the virus varies with asst’d biological variables & consequently ethnic groups. One contributing factor seems to be vit D levels & the skin melanin content & the need for longer sun exposure to synthesize & convert Vit D3 to active form D2. Hence the recommendation to take a vit D + zinc supplement. The explanation of the mechanism of the virus disease prevention is in my twitter bookmarks, but is widely known as is the role of the Forssman antigen.

    An added problem with RNA viruses is their ability to mutate. There’s a story of a patient in Wuhan who initially had 1 strain, then 3! Mutations occur at the genetic level & it’s almost pot-luck. The result is a strain that may be more or less infectious/virulent. As you can see a simple statistical model which assumes the exponential spread of the pathogen on cultural/geographic grounds may not accurately model a mutating virus in a non-homogeneous population, thus at best all that’s possible is rough approximations. This is the case with many natural phenomena, like AGW!

    There’s another wrinkle in these models which is the willingness of people to follow lock down, distance. mask advisories. Basically anything that reduces transmission reduces the number of hospital cases. The idea of herd immunity is nice, but those of us who are immune suppressed (probably too many cousins marrying in my case), the more time exists to create an effective treatment. It’s not just having a healthcare system becoming overwhelmed IMHO.

    From all of the above, it is apparent that darker skinned people of type A blood type with widespread FA distribution are most at risk. The final severe immune response results in organ failure. This is common to many virulent pathogens. The straw that breaks the camels back seems to be the accumulation of fluid in the lungs which reduces oxygen intake. There was recently something about a specific drug used to treat covid-19 – clot buster tPA below (MDs used this Xmas eve 2002 to save me). Many diuretics are used to decrease fluid in the lungs, as well as vasodilators.

    https://www.phauk.org/treatment-for-pulmonary-hypertension/diuretics/
    https://www.mayoclinic.org/diseases-conditions/pulmonary-edema/diagnosis-treatment/drc-20377014
    https://news.yale.edu/2020/04/23/yale-launches-clinical-trial-drug-treat-severe-covid-19-patients
    https://www.nationalgeographic.com/science/2020/03/as-coronavirus-surges-how-hospitals-are-treating-covid-disease/
    https://www.medicalnewstoday.com/articles/covid-19-could-a-clot-busting-drug-help-save-the-lives-of-patients-on-ventilators#Established-uses

    So the bottom line from Dr Dave is that these models are inaccurate. They are worthwhile however as there has to be a starting point to compare with real world data & later incorporation of new variables as they become known & understood.

    • Thank you for your informative comment. I am aware that, as well as social connectivity, there are biological factors involved, including blood group and vitamin D level.

      The factors you refer to relate prima facie to susceptibility, not infectivity. They will likely also indirectly affect infectivity, although to a different extent. A more susceptible person presumably has a greater chance of ending up with a more severe illness and a higher viral load and be more likely to infect a contact with the virus (although the time interval between becoming infectious and self isolating may be shorter in that case).

      I seek, in my simple model, to take account of variability in biological and other factors that affect susceptibility and infectivity differently through incorporating separate random variability in each of susceptibility and infectivity in addition to a common social connectivity related factor that affects susceptibility and infectivity identically. I agree that this can only provide a crude approximation, but the point of the model is to provide insight into the effects of the different types of variability rather than to attempt to provide quantitatively accurate estimates of the development of the epidemic.

  30. so the coronaviruses are part of a larger group described as respiratory viruses; their signature trick is they become evident in the cold and dark of a temperate northern hemisphere winter; they fade as spring passes, and are gone by summer.

    Please read things such as this: https://virologyj.biomedcentral.com/articles/10.1186/1743-422X-5-29

    and complementary reading: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2870528/pdf/S0950268806007175a.pdf

    I really recommend understanding the work of Hope-Simpson from the two articles:

    So the Swedes are about a month away from the summer solstice; how many folks have visited Stockholm in mid-June? It will be close to 24hrs a day of sunlight; if the Swedes can just hang in there; and avoid the baying for their blood of angry folks like Carrick, the season will purge the air of the corona; it will disappear away; mid to late June, the Swedes will largely melt away to their little cottages by the lakes and estuaries; they can swim; take in the sun; eat fish; get omega-3 and Vit D and replete their innate immunity; and (unlike everyone else), they may have an economy to come back to.

    .. whilst we will still be trying to impress each other with our knowledge about R0.

  31. Alberto Zaragoza Comendador

    It seems the FT got the numbers for Stockholm hospitalizations from here:

    Click to access ppt-presentation-fran-presstraff.pdf

    See page 3. The first day in the FT’s chart with week-on-week decline in hospitalized patients is April 21st, and that’s the case also in the presentation I just linked to (1,053 patients vs 1,073 seven days earlier).

  32. Hi. This is very interesting. I made a similar analysis a few days ago, with roughly the same findings:

    https://jsmp.dk/posts/2020-05-07-herdimmunity/

    Would you share you code? (Or even more details of the model.) I would like to contrast and compare.

    Best,
    Jonatan

    • Hi Jonatan
      Thanks for your comment. I will certainly share my code. Once I’ve tidied it up a bit I’ll put a link to it at the end of the version of this article that is on my webpages, here: https://www.nicholaslewis.org/why-herd-immunity-to-covid-19-is-reached-much-earlier-than-thought/ . But in the meantime, if you leave a comment there I’ll email you a copy of the code as it stands now.

      • Thanks very much for posting the code. It turns out that the above verbal description described it very well.

        I nonetheless managed to misinterpret it as saying the infectiousness duration is uniform. If my interpretation of your state-velocity routine SEIRfun() is correct, it instead makes the infectious population’s impulse response an exponential decay: some people instead remain infectious many times as long as others. (I also take it that this behavior is standard in SEIR implementations.)

        Obviously this issue is too germane to the point you’re trying to make, but my guess (as a total layman) is that the assumption of an exponential infectiousness-duration distribution is questionable and can have a significant effect on the infection peak. I’m guessing that’s why, in contrast to you (and no doubt most others) the guy Annan got his state-velocity routine from put the latent and infectious populations in two “boxes” each: to give the impulse responses double poles and thereby slow the initial decay.

        Again, this isn’t too germane to your demonstration. I just mention it because I do wonder how much their ignorance of what the real distribution is (or the convenience of that differential equation) affects the projections we get from epidemiology folks.

  33. However, the Ferguson20 report estimated that relying on herd immunity would result in 81% of the UK and US populations becoming infected during the epidemic, mainly over a two-month period, based on an R0 estimate of 2.4.

    I wrote a simple SIR model using an effective R0=2.5, IFR= 1% in about 80 lines of Python. For a UK population of 65 million the model shows an epidemic is over in 2 months with ~500,000 deaths. So basically this is the same result as Ferguson.

    However it is now emerging that the real death rate is probably lower at 0.4% so that would mean 200,000 deaths.

    R is not really a dependent variable of SIR models. It is instead derived from the effective contact rate (people/day) and the infection period (days).

    Lockdown efforts try to reduce the contact rate to move R below one, but this always extends the length of an epidemic and alone can’t stop it. You only need a handful of remaining cases after relaxation for the epidemic to spike again and another lockdown. This whole process can take up to one year !

    and you can still end up with 92,000 direct deaths, let alone the long term damage to the economy and health of the population. However, perhaps there is a natural way out of this. I think Nic is essentially saying the same thing.

    At the start of an infectious disease outbreak the probability of someone getting infected if they are a member of a large social network is very high. These are the super spreaders which force the initial reproduction rate R0 to very high values. It is no real surprise that Boris Johnson, Mat Hancock, Chris Whitty, Dominic Cummins and Neil Fergusson all got infected together as they formed part of the government’s own very large COVID/SAGE network!

    However as an outbreak progresses, so the larger networks become increasingly already infected, and the remaining networks for new infections will therefore tend to get smaller and smaller. As a direct result of this gradual process, R will naturally begin to reduce, even without imposing any extra social distancing policies. R is simply proportional to the size of any network (beta) that the average infected person belongs to, so as mean network size diminishes so does R. R is simply equal to beta/g where 1/g is the infection time in days (assumed constant). When R reaches 1 the epidemic peaks (herd immunity) and then falls to zero.

    Such a model seems to fit the Swedish data quite well, much better than say the UK data which has a stronger lockdown suppression.

  34. I think you’re full of crap. Look how the Chinese are dealing with this pandemic. They aren’t going for the herd immunity possibilty because there’s no indication that immunity is lasting. While the Chinese are taking this pandemic very seriously they are chuckling at our downplay and minimizing of the coronavirus. I find that a little disturbing.

    • It only needs to last long enough that the virus can’t successfully infect new hosts (eg, infectious people keep meeting only other infected or recovered people). If the antibodies had insufficient effect for that short duration, I wouldn’t have expected for instance even attempting use of blood plasma as a treatment in critical cases, since that relies on transferring the antibodies from recovered individuals, as has been reported to have effect, and initially by China.

  35. I’m pretty sure I am out of my depth here, but I am sure the denizens will have a better understanding, but has anybody thought about the millions and millions of discarded masks, the world over, many millions of which must be saturated with the virus, ending up where every discarded human waste ends up – in the sewage, drainage, and waste disposal sites. To my mind ideal, steaming “cooking” grounds of chemical and organic stews, frequented by rats, birds, bugs, and desperately poor human waste pickers. To me, unless I miss something, this is just a Pandora’s box of mutations on hold. Are my concerns unwarranted??

  36. Assume what you say is true. It’s been true for a long time with anything like a virus. It seems to be of the body. Our bodies.

  37. I don’t know who did more damage to the world, the guy that ate the bat or the guy that went to bat against Boris Johnson with self-written, 13-year-old code that he hid from prying eyes. I’m only half kidding. The power Neil Ferguson had over world leaders is quite astonishing. It’s because “SCIENCE!” — not to be confused with science — is the religion of this age led by its lab-coat-wearing Baals.

    Articles like this one and this excellent comment section gives me hope that science will defeat “SCIENCE!” ultimately.

    • Yep. “Scientism” has been & continues to be one of the banes of our “modern times” for at least 50 years or so.
      But, in this particular case & looking at the time-line of the NATIONAL lockdowns – I blame Conte-government’s hysterical decision (March 10th?) of #LetsLockThemALLup – that, I’d bet, had very little “scientific” and/or modelling input.
      This decision & the “falling dominoes” of other governments following the suit, within next couple of weeks, seems to have been driven by 2 factors:
      1/Global mass-media hysteria about “new deadly BAT-virus”
      2/Conte feeling pressure to do something that would LOOK BIG & “decisive”
      2B/All following “dominoes” governments feeling the same pressure + additional (“exponentially” increasing urgency of) “other countries are already doing it.”
      Only Swedish government had enough trust in the competence of their top HC-bureaucrat(s) (+ Belarusian-dictator Lukashenko – probably asking his favorite physicians) to withstand it.
      In this “act first – explain later” scenario – Ferguson’s model & other “scientific arguments” were (at most) supporting props.
      Once the national-lockdowns became “international norm” – a deadly combo of authorities’ & media’s hype about them being “necessary & ONLY practical solution” – eliminated from public debates & in most cases, from public action any consideration of (obvious from the go in Italy) vulnerability of the elderly – particularly in the nursing homes; contagion via subways, etc.
      We’re now in the later stages of this global mass-hysteria with an alliance of: HC-bureaucrats, authorities that won’t admit ANY mistakes and/or petty tyrants who don’t want to release absolute powers they got over their “subjects” as well Karen-types & in the US – “resistance” supporters who’d like the lockdowns to last until November 3rd – jointly fighting against any meaningful/substantial removal of lockdowns & return to normal.
      Meanwhile, the cumulative effects on the national (& global) economies & PREVENTABLE excess deaths (delays of treatment of cancer, heart-problems, strokes, etc.) continue to add up.
      In July & August of 1914 we had another case of “falling dominoes” of national governments following each other in taking most irrational & destructive possible actions – to address serious but manageable problem – leading to the government-made catastrophe of WW1.
      The scope of THAT disaster could have been hugely reduced if at least a few of these governments were willing to look at what became obvious in the Fall of 1914 & changed the course then & there.
      Let’s hope most of our governments will be (a little?) less stubbornly & suicidally stupid – this time.

  38. Pingback: Latest News – Lockdown Sceptics

  39. A Call for Honesty

    My son noticed how the projections of countries on https://covid19.healthdata.org/ conveniently only record the latest tweaking and not the comparative projections of each – say a week apart – for the past two months. This hides how far out the previous projections have been.

  40. Yes, I think this sort of analysis is along the correct lines.
    Sadly, this whole farce has demonstrated a bunch of people suddenly discovering the exponential and losing their minds.
    But nothing in nature is exponential. These 1D models assume everyone lives in the same room and that every potential is realized.
    A more accurate appraisal would have to account for spatial homogeneity and would look something like a stochastic reaction diffusion equation with random diffusivity. There are far more cases where the virus extinguishes and does not have access to its exponential potential as a result. This will lower any R0 that is determined concerning people in some glass jar.

  41. Too complicated. We are all drowning in this sort of analysis.. The simple reason why herd immunity threshold appears to be much lower than expected is that we are not counting enough of the asymptomatic cases.

  42. I posted a hypothesis some weeks ago based on the data from CVN71 (Teddy Roosevelt aircraft carrier). All crew was tested. Only about 16% positive despite ideal conditions for contagion spread.

    Low hospitalizations and only one fatality thanks to young age and lack of comorbidities obesity, hypertension, and diabetes.

    But why the low infection rate. There are four common cold corona viruses responsible for an estimated 25-30% of common colds. Two are beta coronas like Wuhan. It is plausible that a CVN71 common cold ‘epidemic’ conferred at least partial immunity to much the crew.

    In that case, NO herd immunity calculations work well because herd immunity is not exclusively specific to Wuhan. Just like Jenner’s famous vaccination discovery that mild cowpox protects against deadly smallpox.

    • thanks ristvan; some would say that innate immunity: (AMPs), anti-microbial peptides, destroy invading viruses in the nasal mucosa; if viruses get past the, the T-cells destroy; you could call it Level 3 where the viruses penetrate interstitial fluid or blood and provoke an antibody (IgG/IgM) response;

      so when folks do serological testing, they are missing what Ron Carlin calls “the asymptomatic” and a significant % of those have proven resilient; and yet their resilience cannot be measured by our current tests. We do have some understanding of innate immunity; it attacks the lipoproteins of the enveloped RNA viruses eg our friend the corona, and so destroys them.

    • Thanks for your comment.

      I agree that it is plausible that exposure to a common cold coronavirus may convey at least partial immunity to infection by the SARS-CoV-2 virus, and I was well aware of that point. Such quasi-immunity would imply that serological tests for antibodies specific to SARS-CoV-2 will undercount the proportion of the population that is immune to SARS-CoV-2.

      However, my modified SEIR model can allow for this, if somewhat crudely, by virtue of the variability in susceptibility that it provides for. Immunity has an identical effect to zero susceptibility, while partial immunity implies a very low susceptibility, and possibly also a low infectivity if infected.

      • Terry Wright

        “I agree that it is plausible that exposure to a common cold coronavirus may convey at least partial immunity to infection by the SARS-CoV-2 virus, and I was well aware of that point. ”

        who is saying that? The innate system has no “seen before” structure; it attacks new, not seen before pathogens;

        we feel we understand things according to our assumptions: eg this virus is highly contagious; highly infectious; spread is from sick to well; well get sick; they then spread on: all our assumptions;
        so how come from Ivor’s tweet, https://twitter.com/FatEmperor/status/1260903400734167040/photo/1 the peaks of Sweden and NJ are synchronous:

        viral respiratory illnesses (VRI) are seasonal; they relate to lack of sun; in the tropics, VRI are during the rainy season;

        they happened back in the 1600s ….. here from 1778 an English doctor writing .. “this epidemic [of 1775]. ..; for we hear of the same distemper having been in Italy, France and the Low Countries, and, I doubt not, in other parts of Europe, had we inquired.” quoted in Hope-Simpson

        simultaneous outbreaks; when you travelled by horse and cart ..

        one can rubbish this folks: no serology etc but doctors have described flu for ever;

        this virus is highly contagious; highly infectious; .. friends in NZ tell me they have had 1200 cases in 5 million: 0.02% positive: highly infectious in a hot summer there seemingly?

      • ‘who is saying that? The innate system has no “seen before” structure; it attacks new, not seen before pathogens’

        Read this article in Science journal, and the papers that it cites: https://www.sciencemag.org/news/2020/05/t-cells-found-covid-19-patients-bode-well-long-term-immunity

  43. Superb discussion. Thanks to Nic and all….

    • trying to rely to Ni: May15, 4.31pm
      https://www.sciencemag.org/news/2020/05/t-cells-found-covid-19-patients-bode-well-long-term-immunity
      thanks Nic: I agree T-cells are very important Nic;

      “Both studies also found some people never infected with SARS-CoV-2 have these cellular defenses,

      ……..most likely because they were previously infected with other coronaviruses.”

      That is an assumption; an attribution. ……

      “most likely” = I’m guessing, don’t know, but just humour me and agree …

      We have an innate immune system:
      level 1 would be the AMPs: stop the invader before the beach:
      level 2 would the T-cells: stop them as they land;
      …….. crucially no systemic antibodies: yes, memory now in the T-cells

      level 3 would be adaptive system kicking in; antibodies

      If one looks to Vit D, it up-regulates the innate system; paradoxically it to some extent down-regulates the adaptive system;
      so at our best of health; in summer in the sunshine; perhaps having spent a month in Greece … we have an upregulated innate, and down-regulated adaptive;

      a down-regulated adaptive means fewer cytokines produced; folks love to imply that they have a full grasp of intensive care medicine by casually dropping the phrase “cytokine storm” into their conversation; well, a down-regulated adaptive system does that.

      I worry I will anger you Nic; but I do feel we need to speak out each time about the assumptions that underlie so much of what we say/write;

      We crave certainty: currently, that is an antibody measurement; the other less tangible certainty is that all the history says respiratory viral epidemics are profoundly seasonal; and Hope-Simpson so patiently, and thoroughly demonstrated that; he took facts and evolved explanations, that came from empirical observations. we have an innate system. all best wishes Nic

  44. Great article. Not sure how relevant this might be, but don’t forget the curious fact that children don’t seem to get ill and may very well not even transmit the virus, a topic of hot debate at the moment. If this was true it would mean we effectively have a cohort of the population that are immediately a large component of the ‘immune herd’. In the U.K. 18% of the population are under the age of 15.

    It might also explain why Africa is so unscathed, contrary to the recent scientific scaremongering. As well as having a very young average age most countries have a huge percentage under 15. In Nigeria the average age is 18 and 43% are under 15.

    • Thanks. I agree that children don’t get ill, however, they certainly can become infected. It is however possible that infected children are not infectious, or have low infectivity. I think that there is evidence for that, but I’m not currently sure how robust it is.
      Either way, I think that the variability in susceptibility and in infectivity that my modified SEIR model includes can provide a crude representation of the impact of the cohort of children.
      A slightly more sophisticated model could allow separately for different age bands in the population having differing average susceptibility and infectivity levels.

      Your point about Africa is well made. I had had thoughts on similar lines but regarding the infection fatality rate in Africa, not the effect of children on the spread of the epidemic.

  45. Nic Lewis earns a mention in Lockdown Sceptics: https://lockdownsceptics.org/

  46. Alternate possibilities for low apparent HIT.
    1.We are not measuring the true I (infected) and R (recovered).
    a. Lack of randomized testing
    b. Poor test accuracy
    2. Seasonality
    a. Reduces R(t) independently of HI or intervention
    b. Reduces R(o) and R(t) independently of infectious period or contact rate

  47. Yes, great analysis.
    Missing from the discussion are.
    1 – whether the presence of Ab confers immunity
    2 – duration of immunity
    3 – On reinfection of a host with measurable titres of Ab will the subsequent infection be milder or enhanced? (ADE)

    In the case of influenza, immunity lasts about 9 (to 18) months. [If] protection from infection is conferred by Ab generated in a covid infection [and if] the duration of that immunity is less than the period required for R0 to drop below 1.0 [then] there will need to be a few more terms to deal with dependencies between compartments.

    We’ll see.

    • thanks pdcarey; also missing is that maybe immunity does not depend on the presence of IgG or IgM antibodies:

      .. all the clever modelling assumes that immunity=antibodies

      Underpining that belief is our ignorance; this lack of knowledge then supports the idea that immunity=antibodies

      We have an innate immunity system; please read this paper
      https://virologyj.biomedcentral.com/track/pdf/10.1186/1743-422X-5-29

      It may dawn on folks that things are more complicated; on flu, the above paper asks 7 questions during discussion
      Why is influenza both seasonal and ubiquitous and where is the virus between epidemics?
      Why are the epidemics so explosive?
      Why do epidemics end so abruptly?
      What explains the frequent coincidental timing of epidemics in countries of similar latitudes?
      Why is the serial interval obscure?
      Why is the secondary attack rate so low?
      Why did epidemics in previous ages spread so rapidly, despite the lack of modern transport?
      If you compared and contrasted what is happening now, and how many of these questions are relevant to what we are obsessing about now; the deepening thinking that might ensue, might enrich reflection; as we survey our ignorance of our bodies’ systems.

      • Thanks, Terry. I’m well aware that antibodies against SARS-CoV-2 are not the only possible reason for full or partial immunity against infection by it. I didn’t mention it here as I thought this article was aleady rather long and complex.
        Note that with a high variability given to susceptibility (and hence many never-infected individuals having near zero suscepibility), my SEIR model can mimic the effects of this phenomenon, in a simplified manner.

    • Thanks.
      SARS-Cov-2 seems to mutate more slowly than the influenza virus, IIRC, so immunity should last longer.

      • Terry Jones

        thanks Nic; glad to hear you may be well aware of innate immunity; Hope-Simpson in 1992 talked of DIPs; defective interfering particles.

        Von Magnus 6 first described incomplete virus particles that are produced early in influenzal infection and have the property of interfering with the replication of standard infectious virions.

        They are used in the laboratory to induce persistent noncytopathic infection of cell cultures,

        ……… and they are now known as defective interfering particles (DIPs)

        ………because even in very small numbers their presence can completely prevent the production of standard infectious virus.

        Because DIPs are produced early during natural infections, the new concept suggests that they may form a part of the mechanism that switches the virus from epidemicity to nonepidernicity by producing the interepidernic carrier state that explains the survival of the virus during its apparent absence between epidemics.

        The persistence of influenza virus and DIPs has frequently been demonstrated in cell cultures.

        Latent or persistent virus has not yet been found in human carriers, but is being sought by modem techniques of molecular virology. The new concept offers a credible, if tentative, alternative to the current concept

        Yet another thing to suggest why reality stubbornly refuses to conform to what modellers would wish.

  48. In the 60+ years I have been going to the Bruce Peninsula Ontario Canada, situated between Lake Huron and Georgian Bay, I have kept track of life on the Bruce as related to me by people who live there and the folks newspaper, the Wiarton Echo when I am not physically present.

    The Bruce has restricted travel enforced by the Ontario Provincial Police (OPP) whereby anyone coming up has to remain and anyone traveling from the Bruce can not return. The Mayor of the Municipality had ordered no one to come up to the Bruce. All these restrictions are a result of COVID-19. Essentially, the Peninsula has self quarantined.

    There had been no cases of COVID-19 on the Northern Bruce Peninsula Municipality (population 3600) until one was identified in a nursing home in Lion’s Head halfway up the Peninsula on Georgian Bay (population 600 counting all the nursing home residents).

    The curious issue for me, how did the nursing home resident, in an area quarantined from all of Southern Ontario acquire the novel coronavirus? During the summer, mostly July and August, Lion’s Head is a tourist Meca with 5000+, yet in the winter, the major employer is the nursing homes in the various small towns on the Peninsula, the rest is farming, construction and a scattering of machine shops along the central corridor road Highway 6. Lion’s Head has the only K-12 school on the Peninsula (children bussed from towns 50 miles away and they stay during the school year days with relatives or foster parents in the area. There is commercial fishing using small picturesque Great Lakes fishing boats, with one located in Wiarton on the Georgian Bay and one each in Howdenvale and Stoke’s Bay on the Lake Huron side.

    As the nursing home industry is a major employer, protecting these residents was foremost on the mind of the Mayor when he made is order. And yet, the virus got in and now jeopardizes those currently living in and acquiring more nursing home people. Case finding will identify how the virus traveled into the Bruce. In a region surrounded on three sides by water and an armed police presence stationed at the base of the Peninsula, is there any better quarantine situation? No need to invoke international air travel or interstate highways or mass gatherings of illegal concert goes, the virus does sneak in by a care worker, a visitor, a delivery person or a new resident from elsewhere.

    On the topic of early herd immunity, the Bruce Peninsula will be a case study in the evolution of this pandemic.

    • Thanks RiHo08; so this virus has been doing the rounds for a long time: 108 Canadians for example went to Wuhan and spent at least a fortnight there last October; https://en.wikipedia.org/wiki/2019_Military_World_Games with 172 from the US, etc etc. The US jets flew to and from Seattle. Have a read at this https://virologyj.biomedcentral.com/track/pdf/10.1186/1743-422X-5-29 .. it might interest that not all viruses obey the “sick to well” rule that we would wish them to obey: well, it would mean they then obey our models, wouldn’t it, and that should be the way the world runs, right? They have now recognised it was in Paris in December; it’s been everywhere man, it’s been up and down man; look at the way flu surfaces in winter; study flu: it’s revealing; flu does not obey the “sick to well” rule: how irritating.

  49. Pingback: Herd Immunity | Transterrestrial Musings

  50. As hindsight is 20/20 we will be able to check the numbers in a couple of months time. One of the worst cases will certainly be Brazil which is extremely non-herterogeneous in terms of income, genetics, health case, habitation and pretty much everything else.
    No real testing hsa been done and at best there will be some stats to check on the various factors. elderly, native Americans, blacks, community (favelas), low income, gender etc.Plus the response from both federal and local Gov.
    Good news for the folk who study this, but bad news for the thousands who are suffering now.

  51. But, I’ve also heard that herd immunity is impossible without vaccinations… as we have with the measles virus, for example. Also heard that as many as 95% of the people in this country or at least significant areas of this country are covid ‘virgins’ and that while we’re currently going on 60 to 70,000 deaths nationwide there could be as many as 600,000 deaths in the next 18 to 24 months… we just don’t know. But, we flattened the curve so medical facilities we’re not overrun, tra-la, and… It’s time to get back to work. Meanwhile, the death rate in the United States is much lower than Sweden and Sweden is climbing not falling.

    • “I’ve also heard that herd immunity is impossible without vaccinations”
      That’s just not so.

      • So what we don’t know even listening to the Senate hearing today is how many people here have already been infected but in any event, as a covid skeptic all you have to be is someone who doesn’t believe the models are right because so far they had never been right and also that anyone who does get it is probably not going to suffer dire consequences if they’re not over 70. It’s starting to look like, without a vaccine, reaching the age of 85 is the new centenarian.

  52. This reminds me of arguments/discussions about climate models….
    My model is correct even if it doesn’t reflect observations; your model is incorrect even if it does reflect observations. Why? Because observations are wrong; models are correct.

  53. Excerpted from my post on watsup,

    https://wattsupwiththat.com/2020/05/11/why-herd-immunity-to-covid-19-is-reached-much-earlier-than-thought/#comment-2991472
    [excerpt]

    The full lockdown was a huge error. I told you so 21Mar2020. So did Willis E, independently.

    Sweden was correct – no full lockdown. So were we.

    Nic Lewis is a very intelligent gentleman with a good track record of being correct. I don’t have the time to duplicate his work, but he is probably correct.

    Total mortality in Sweden peaked in Week 15 2020, the week of 6Apr2020 to 12 Apr2020. In Europe. It peaked in Week 14, on average.
    It could very well be true that herd immunity was reached ~2 weeks prior, circa Week 12 or 13, 16Mar2020 to 29Mar2020.
    https://www.euromomo.eu/graphs-and-maps/

    Herd immunity was probably also achieved by ~mid-to-late-March 2020 in most countries. The lockdowns has little effect, except to trash the economy and impoverish billions of low-wage earners, especially young people.

    The high death toll in London, New York and elsewhere was concentrated in old folk’s homes and similar – due to criminal incompetence by the authorities.

    The low-risk population was over-protected and the high-risk population was enormously under-protected.

    I repeat – what a grotesque, costly debacle!

  54. THE FULL LOCK-DOWN OF THE ECONOMY MADE “THE CURE WORSE THAN THE DISEASE”.

    As it becomes increasingly clear that the Covid-19 “pandemic” was similar in total fatalities to a bad winter flu season like 2017-2018 and less dangerous than the Hong Kong flu of 1968-69, rational voices have suggested that the full lock-down of the economy made “the cure worse than the disease”. While this was a tough call based on limited data, that was the conclusion I published early in the lockdown on 21March 2020 (below), and I was correct.

    https://wattsupwiththat.com/2020/03/21/to-save-our-economy-roll-out-antibody-testing-alongside-the-active-virus-testing/#comment-2943724
    [excerpt- posted 21Mar2020]
    LET’S CONSIDER AN ALTERNATIVE APPROACH, SUBJECT TO VERIFICATION OF THE ABOVE CONCLUSIONS:
    Isolate people over sixty-five and those with poor immune systems and return to business-as-usual for people under sixty-five.
    This will allow “herd immunity” to develop much sooner and older people will thus be more protected AND THE ECONOMY WON’T CRASH.

    https://rosebyanyothernameblog.wordpress.com/2020/03/21/end-the-american-lockdown/comment-page-1/#comment-12253
    [excerpt- posted 22Mar2020]
    This full-lockdown scenario is especially hurting service sector businesses and their minimum-wage employees – young people are telling me they are “financially under the bus”. The young are being destroyed to protect us over-65’s. A far better solution is to get them back to work and let us oldies keep our distance, and get “herd immunity” established ASAP – in months not years. Then we will all be safe again.
    ___________________

    It is notable that Sweden sensibly rejected the full Covid-19 lock-down, and that strategy has been far more successful in total than the “full-gulag” adopted by Canada and many other countries and states.
    https://www.euromomo.eu/graphs-and-maps/

    I wrote recently:
    https://wattsupwiththat.com/2020/05/06/using-excess-deaths-to-correct-chinese-virus-mortality-counts-coronavirus/#comment-2989783

    The global data for Covid-19 suggests that deaths/infections will total ~0.5% of the total population – not that different from other seasonal flu’s – but dangerous for the high-risk group – those over-65 or with serious existing health problems.

    Here in Alberta, the Covid-19 lock-down has resulted in a mis-managed debacle. Most of our deaths are in nursing homes – our policy seems to be “Lockdown the low-risk majority but fail to adequately protect the most vulnerable.” This was also true elsewhere in Canada (Montreal) and the USA (New York City) and in England (London).

    “Elective” surgeries in Alberta were cancelled about mid-March, in order to make space available for the “tsunami” of Covid-19 cases that never happened. Operating rooms were empty and medical facilities and medical teams are severely underutilized. The huge backlog of surgeries will only be cleared with extraordinary effort by medical teams, and the cooperation of patients who die awaiting surgery – patients who were impatient… Alberta started to re-open on 1May2020, exactly to the day as I predicted one week before. Elective surgeries re-started on 4May2020.

    Two doctors from Bakersfield California, Dr Dan Erickson and Dr Artin Massihi doctors reached similar conclusions, and were censored by YouTube for expressing their honest views. Here is the Bakersfield doctors’ ~1.1 hour video that was repeatedly banned by YouTube, preserved elsewhere:
    https://savedmag.com/dr-erickson-covid-19.mp4?id=0

    The Bakersfield doctors were telling the truth – they were saying that Covid-19 was not more severe than other major seasonal flu’s and less severe than some.

    In Europe, Total Deaths from All Causes peaked in week 14, the week of 30Mar2020-5Apr2020, suggesting that the lockdown was too late to be effective. The exception was England, which has the worst Covid-19 death rate in Europe. Here is why:

    Dr. Malcolm Kendrick, a Scottish physician, wrote:
    https://drmalcolmkendrick.org/2020/04/21/the-anti-lockdown-strategy/
    “Unfortunately, it seems that COVID-19 has infected everyone involved in healthcare management and turned their brains into useless mush.
    [In my view, if we had any sense, we would lockdown/protect the elderly, and let everyone else get on with their lives].
    However, the hospitals themselves have another policy. Which is to discharge the elderly unwell patients with COVID directly back into the community, and care homes. Where they can spread the virus widely amongst the most vulnerable.
    This, believe it or not, is NHS policy. Still.”
    ___________________________

    GOVERNOR ANDREW “CUOMO KILLED MY MOM”

    https://www.bizpacreview.com/2020/05/10/giant-cuomo-killed-my-mom-sign-erected-on-bridge-as-heartbroken-new-yorkers-grieve-on-mothers-day-919031

    Many New Yorkers are ushering in a grim Mother’s Day this year amid accusations that Governor Andrew “Cuomo killed my mom” thanks to his deadly policy that forced nursing homes to admit coronavirus patients.

    The bone-headed move resulted in the deaths of thousands of senior citizens living in nursing homes.

    Cuomo mandated that nursing homes must accept coronavirus patients even though older people are the most at-risk to die from COVID-19. Making matters worse was the fact that nursing homes did not have personal protective equipment or COVID testing capability.

    Shockingly, the mainstream media not only gave Cuomo a pass on the scandal, but lionized him as a hero.
    ___________________________

    In conclusion, the full-lockdown was a huge error – we should have followed the Swedish model and taken precautions but not shut down the economy, which harmed so many young people. We have over-protected the huge low-risk majority from a virus that typically does not harm them, and severely under-protected the high-risk elderly and infirm.

    This is not 2020 hindsight. I reached my conclusion in mid-March 2020 and published it on 21-22Mar2020, based on data from the Diamond Princess cruise ship, South Korea, and total mortality in Europe. Iceland data was examined later.
    _________________________

    THE BEARER OF GOOD CORONAVIRUS NEWS
    Stanford scientist John Ioannidis finds himself under attack for questioning the prevailing wisdom about lockdowns.
    By Allysia Finley, Wall Street Journal
    Updated April 24, 2020 5:14 pm ET
    https://www.wsj.com/articles/the-bearer-of-good-coronavirus-news-11587746176

    Stanford scientist John Ioannidis finds himself under attack for questioning the prevailing wisdom about lockdowns.
    _________________________

    EXCELLENT VIDEO BY CALIFORNIA DRS. DAN ERICKSON AND ARTIN MASSIHI
    https://savedmag.com/dr-erickson-covid-19.mp4?id=0
    _____________________

    SACRIFICED IN THE NAME OF COVID PATIENTS’: TENS OF THOUSANDS AFFECTED BY SURGERY CANCELLATIONS
    Almost 200,000 surgeries and other procedures were shelved indefinitely, as hospitals braced for a deluge that never quite materialized
    National Post, 9May2020, Tom Blackwell
    https://nationalpost.com/health/sacrificed-in-the-name-of-covid-patients-tens-of-thousands-affected-by-surgery-cancellations

  55. I’ve been looking into individual variations in susceptibility, as well as Sweden’s data. My thoughts:

    1) There have been lots of contact tracing studies, but Gangelt Germany’s is the only household study to my knowledge which used by PCR and antibody testing. It found a single infected in a two-person household was 44% likely to infect the other person. Three and four person households dropped this chance to 36 and 18%, respectively.

    Needless to say, this seems very low. The infection rate for people at Gangelt’s carnival was 21%, more than in a a house with 1 / 4 people infected. This implies some people do spread it much more efficaciously than others.

    However this study (and the other Asian contact tracing studies I’ve seen) was prior to the D614G mutation which may roughly double viral load (https://github.com/blab/ncov-D614G) and increase transmissibility (https://www.biorxiv.org/content/10.1101/2020.04.29.069054v1.full.pdf). None of the sequences I’ve seen from Gangelt have this mutation.

    2) In prisons we’ve seen up to 80% infected, and that is only using PCR tests which may miss past infections. The Greg Mortimer was a small cruise ship on which 59% of the people tested positive via PCR.

    3) If only a few people are highly infectious, crowded areas like ships and prisons may let them spread it easily. Meanwhile it would only spread easily in households if they were unlucky enough to have one of these super-spreaders. Ergo this is my current hypothesis: contagiousness is highly variable.

    4) Assuming a similar R0 figure between the UK, US and Sweden was simply ridiculous for many reasons. Many of these are obvious, like cars vs. public transport, small Swedish household sizes, or their trust in their government. These should have made US politicians question the Imperial College’s work.

    5) 0.24% of NYC has allegedly already died of covid. Similar figures have been found in other hard-hit areas. Given the drastic measures taken to limit covid’s spread, it is difficult for me to believe it has already done whatever it is going to do in these areas.

    Sweden’s death rate in particular seems to have plateaued, but has not yet dropped. ICU admissions have dropped more than cases, implying they’re simply intubating fewer people.

    6) I would think CV goes down as social distancing decreases. Some people have essential jobs where they must socialize. Some are taking this very seriously, while others are not. In a more normal society everyone socializes to some degree.

    However in places like NYC or much of the UK, driving oneself is often not an option. One must expose oneself to go anywhere, regardless of social distancing measures. CV in these cases is probably lower, are varies less than say suburban Florida (where everyone has their own car and drives everywhere).

    7) Everyone has an agenda in this ultra-polarized world, and population-level studies are easy to bias. All the accurate antibody tests I’m aware of require more than a pin prick of blood, which probably biases the test towards people who think they were exposed.

    I admit to being biased against these lockdowns. Certain wars aside, I believe they are the worst policies we’ve seen since the Great Depression.

  56. Pingback: COVID19, Lag Ba-Omer edition: active cases graphs around (mostly) Europe; more sophisticated model predicts much smaller herd immunity thresholds; Swedish healthcare problems; N-acetylcysteine | Spin, strangeness, and charm

  57. Excellent discussion w/r/t facile comparisons to Sweden:

    > (3) Concerning Sweden, Die Welt (in German) looks at what it calls the Swedish Sonderweg (“special road [taken or followed]”). Notably, it does not attribute the much higher mortality (compared to fellow Scandinavian countries) just to its not entering a lockdown (some voluntary social distancing measures are in place) — but to the “limping” Swedish healthcare system (marodes Gesundheitssystem).
    They are at pains to point out that this is not a matter of money — Sweden has the 2nd highest pro capita spending in the EU, after Germany — but of inefficiency, administrative bloat, and wastage. Once upon a time, Sweden had 49.5 ICU beds per 100,000 inhabitants, which today would be the highest in the world, above even the USA. Today? Just 5.8.
    Even before the COVID19 crisis, 12% of elective surgery patients has to wait 4 months or more, compared to 2% in France and none at all in Germany. One-fifth of Swedes have to wait more than 2 months for a specialist appointment, compared to only 3% in Germany.
    Much like Israel’s public system, rapid access for life-threatening emergencies in Sweden is maintained at the expense of ever greater delays for everything else. [But much unlike Israel, Sweden entered the present crisis without the benefit of a young population and a warm, sunny winter and spring climate…] Doctors in the public system are salaried employees of the state, with all that entails in terms of (lack of) incentives…

    https://spinstrangenesscharm.wordpress.com/2020/05/12/covid19-lag-ba-omer-edition-active-cases-graphs-around-mostly-europe-more-sophisticated-model-predicts-much-smaller-herd-immunity-thresholds-swedish-healthcare-problems-n-acetylcysteine/

  58. Just to do a sanity check.

    The figures seem to show herd immunity arises in about 120 days with peaks around 60-80 days. We are slightly past 60 days into this pandemic in the United States and over 70 days in Sweden. so is this a prediction we will now see a rapid fall off in number of cases so that by July this will be over? If not, why not.

    The estimated R0 for the 1918 pandemic is in the general range proposed here for COVID-19 yet it raged for almost two years with repeating waves. How would your analysis work if applied retroactively to the 1918 flu?

    • Your questions are good, but one correction- we are past 100 days into this pandemic in the US. The first known death in the US was in California on Feb. 6 – 92 days ago. And we know the person contracted the virus from community spread, it was not travel related. It’s reasonable to assume they were exposed at least 8 days before they died of it, and who knows how long the person they caught it from had it.

      We are ~60 days into lockdown plus or minus 7 days depending on location. But the virus was running unchecked in the nation for at least 40 days before that. The first (known and confirmed) death was in Santa Clara County- a local with 1.8 million people right outside San Francisco.
      That’s a long time for a highly infectious virus to be at work in major city with a massive international and national air and sea travel hub without even so much as voluntary social distancing.

      • I was using a more conservative approach to calculate the start – the time the epidemic reached 1/1M detected.

        But, if you move back the start (and I assume a more or less equivalent amount in Sweden), then the figures and model make even less sense. They seem to have little or no relation to the real world. Maybe they work in some ideal world of a corralled herd of Swedes.

        So this conclusion seems unlikely to be correct.

        “The HIT is 60% lower than for a homogeneous population, at 23.6% rather than 58.3% of the population. And 43% rather than 88% of the population ultimately becomes infected”.

        More likely there is simply a pool of uninfected who will become infected with the next wave or the data is simply wrong.

      • I don’t think treating the USA as a single population makes sense for these purposes. It seems clear that COVID-19 reached the west coast of the USA much earlier than it reached the east coast. And the strains of virus involved appear to differ.

      • Does it make sense for any real population of people?

        A single county in Sweden?

        Even that seems doubtful to me unless the real number of infected is closer to 70-80%. With a lower rate of infection unless Stockholm is isolated from the rest of the world, there will be too many people remaining who can become infected with new outbreaks.

    • James Cross

      Invoking Sweden’s approach to the pandemic and any suggestion that now or in the future Sweden is a model to be considered requires a deeper dive into the specifics.

      Sweden has 10 million people, 40% of all households are solitary. 25% are immigrants/ refugees from Iraq and Syria constituting almost half of the immigrant population. These families live in multigenerational housing in pockets just North of Stockholm. Concurrently, nursing homes are in these areas and have staffing, drivers, delivery personal employing immigrants. Working immigrants send money back to their war-torn countries of origin so living in relatively crowded conditions is another way to save money to provide remittances.

      Sweden’s pandemic strategy was in part constructed with the foreknowledge that 40% of the population was already self-isolating. In addition, the plan was to protect the vulnerable like nursing home residents. However, not in the calculus was an awareness that immigrants would be care providers in nursing homes. It was assumed that Sweden’s generous social safety net, universal health care and (almost) affordable housing (at least in some locations) would provide immigrants with benefits the same as other Swedes. Not accounted for by the Swedish pandemic plan, the vast cultural differences in behaviors, hygiene, and most importantly, voluntarily following authority’s recommendations as if they were orders. Social consciousness for the greater Swedish good by Swedes in general was an expected attitude by authorities and found to be, unfounded.

      The startling hodge-podge of responses on the part of the population derailed in part, the outcome and will require a re-think before developing plans for future pandemics or a resurgence of COVID-19.

  59. Ireneusz Palmowski

    “Interleukin 6 (IL-6) is a pleiotropic cytokine exerting multidirectional effects on the cells of both innate and acquired immune systems. This cytokine is recognized as a key factor regulating the defence mechanisms of organisms. Its ability to initiate and regulate acute inflammation as well as to facilitate and direct an acquired immune response are the major functions of this cytokine. Interleukin 6 also exerts systemic effects. Overproduction of IL-6 mediates a shift from acute to chronic inflammation and is critical for the development of some diseases. The structure of IL-6 and its receptors, the signal transduction pathways and biological activities, as well as the implications of this cytokine in animal models of both arthritis and rheumatoid arthritis (RA) are reviewed. Currently available data show that IL-6 blockade will be a useful therapeutic strategy for RA patients and has scientific support.”
    While there has been an obvious thrust toward developing antivirals and vaccines to counter the Covid-19 pandemic, companies are repurposing drugs originally intended for chronic autoimmune disorders that target cytokine storm syndrome (CSS), which is also associated with Covid-19 illness. In the absence of antiviral therapy, it is important to treat the overexuberant immune responses seen in Covid-19 patients, said Dr Randy Cron, professor of Pediatrics and Medicine, the University of Alabama at Birmingham.

    The protocols for Sanofi/Regeneron’s Phase II/III Kevzara (sarilumab) trial (NCT04315298), Roche’s Phase III COVACTA study (NCT04320615) of Actemra/RoActemra (tocilizumab) and Hemel Hempstead, UK-based Eusa’s Sylvant (siltuximab) trial (NCT04322188) indicate the inclusion of patients who may require oxygen through invasive ventilation, considered in critical cases.

    Yet, experts emphasised the need to use anti-IL-6 repurposed antibodies before hospitalised Covid-19 patients become critically ill or require mechanical ventilation to give the therapies the best chance to be effective mechanistically. Acute lung injury and acute respiratory distress syndrome (ARDS) are common consequences of CSS, which then necessitate interventions like mechanical ventilation to help a patient breathe.
    https://www.clinicaltrialsarena.com/comment/sanofi-partners-repurposed-antibodies-covid-19/

    • Hi Ireneusz; folks who eat a SAD (Standard American Diet) lead themselves towards diabetes: 64% of US population over age 45 is T2 diabetic, or prediabetic;

      eating a high carb load; and eating grains; promotes inflammation; RCTs of low-fat vs low-carb show clearly that all markers of inflammation go down markedly on a VLC (very low-carb) intake: so Il-6 and other interleukins decrease; hCRP, TNF etc etc

      so by following the very unwise guidelines of the ADA (its mission is to sell grains ……), we are setting up a high-inflammation population. It is clear those doing very badly at present have multiple co-morbidities: diabetes, hypertension, heart disease, obesity, fatty liver … all from carb loading.

      Virta Health has reversed T2 diabetes in up to 60% of its patients, by following their low-carb way; inflammatory markers are way down in their patients: we don’t need Big Phharma; eating real food will do fine.

      • Ireneusz Palmowski

        Well-known anti-cytokine storm drugs can save many people. Not everyone understands that the Cov-2 virus, by inactivating the ECE2 enzyme, causes a cytokine storm. To fight the virus you need to “calm down” your own immune system. If we don’t use these drugs, there will still be many deaths.

      • Terry Jones

        Hi Ireneusz

        “Well-known anti-cytokine storm drugs can save many people.”

        “To fight the virus you need to “calm down” your own immune system.”

        as Tom Sowell said

        “Oft-repeated claims can frequently be mistaken for facts”.

      • Ireneusz Palmowski

        Sorry.
        Not everyone understands that the Cov-2 virus, by inactivating the ACE2 enzyme, causes a cytokine storm. To fight the virus you need to “calm down” your own immune system. If we don’t use these drugs, there will still be many deaths.
        “When the immune system is fighting pathogens, cytokines signal immune cells such as T-cells and macrophages to travel to the site of infection. In addition, cytokines activate those cells, stimulating them to produce more cytokines. Normally this feedback loop is kept in check by the body. However, in some instances, the reaction becomes uncontrolled, and too many immune cells are activated in a single place. The precise reason for this is not entirely understood, but may be caused by an exaggerated response when the immune system encounters a new and highly pathogenic invader. Cytokine storms have potential to do significant damage to body tissues and organs. If a cytokine storm occurs in the lungs, for example, fluids and immune cells such as macrophages may accumulate and eventually block off the airways, potentially resulting in death.

        The cytokine storm (hypercytokinemia) is the systemic expression of a healthy and vigorous immune system resulting in the release of more than 150 inflammatory mediators (cytokines, oxygen free radicals, and coagulation factors). Both pro-inflammatory cytokines (such as Tumor necrosis factor-alpha, Interleukin-1, and Interleukin-6) and anti-inflammatory cytokines (such as interleukin 10, and interleukin 1 receptor antagonist) are elevated in the serum of patients experiencing a cytokine storm.

        Cytokine storms can occur in a number of infectious and non-infectious diseases including graft versus host disease (GVHD), adult respiratory distress syndrome (ARDS), sepsis, avian influenza, smallpox, and systemic inflammatory response syndrome (SIRS).”
        https://www.wikidoc.org/index.php/Cytokine_storm

    • “When the immune system is fighting pathogens, cytokines signal immune cells such as T-cells and macrophages to travel to the site of infection. In addition, cytokines activate those cells, stimulating them to produce more cytokines. Normally this feedback loop is kept in check by the body. However, in some instances, the reaction becomes uncontrolled, and too many immune cells are activated in a single place. The precise reason for this is not entirely understood, but may be caused by an exaggerated response when the immune system encounters a new and highly pathogenic invader. ”

      Not understood because…just like in this statistical analysis of infection subject, environmental influences on the state of individual and group immune systems is not being considered. How can Heme components of cytochrome oxidase not be altered/affected by heavy metal contamination.
      Furthermore, this system communicates through electron transfer. How can information be correctly transferred (i.e. the spin intergity of the iron atoms maintained) and thus have properly functioning mitochondria and metabolism/oxygen uptake in an environment filled with emf smog?

      • Terry Jones

        Hi Iren;

        this is all just simplistic rubbish: make believe; as you practice intensive care medicine, tell us which blood tests you are going to do on cases in your ICU to diagnose and exclude this storm that so fascinates; and how frequently will you monitor for this storm; and if it is an all or nothing phenomenon, as your noun seems to imply: big storm, little storm, quite a big storm, quite a little storm; quite a long storm; well, it’s just a bit breezy; well, a bit breezy now but calming later …….

        “Not everyone understands that the Cov-2 virus, by inactivating the ACE2 enzyme, causes a cytokine storm. To fight the virus you need to “calm down” your own immune system. ”

        This is all just hype and make-believe to try to scare everyone.

      • Ireneusz Palmowski

        According to New York health officials, 60% of the children with these symptoms statewide tested positive for COVID-19 and 40% tested positive for the antibodies. 14 percent tested positive for both.

        Experts believe the victims may have been exposed to the virus weeks before developing symptoms. They range in age from less than 1 year to 21 years old.
        https://abc7ny.com/coronavirus-new-york-reopen-ny-news-update/6179458/

  60. This link is making the rounds- a respectable researcher, on the faculty as a prestigious US university, great discussion of how the virus spread in a restaurant, a choir practice, and a call center. Also and interesting section on sneezes and coughs vs talking, singing, working out.

    The aim is to inform people of the risks.

    https://www.erinbromage.com/post/the-risks-know-them-avoid-them

    As you can imagine, she thinks the risks of reopening are significant, but manageable.

    She answers questions from many many readers in the comments section, scroll on down to where she writes this in response to a question about air travel:
    “There have been recorded incidents of infections occurring on planes, but for the volume of air traffic, the incidence is low. They have great air filtration on board most modern planes. Those immediately around you on the plane and fomite transfer from surfaces are your major concern. We travelled internationally recently, and just had wipes with us to clean our immediate contact surfaces and limited/were super cautious using the bathroom. ”

    Catch that?
    In the middle of a pandemic, under a lockdown, an expert on infectious diseases working at a university in hard-hit US city took an international flight. Not only exposing themselves on the plane, but in all the other places you have to patronize when you’re thousands of miles from home.

    Can’t workplaces and restaurants install “great air filtration?” I’m sure there is a lot of “volume of air traffic”- there is a higher “volume of” people at work or in a restaurant.
    If the experts are unconcerned about being on an airplane at 35,000 feet above the ocean, tell me again why CNN and the Washington Post claim the Governor of Florida is a murderer for letting people on the beach.

    The answer isn’t that her science is bunk- it really is a good article.

    IMO, what’s happening here is a few things- first, she weighed the risk against the opportunity to do something she wanted to do and chose to accept the risk. She’s a normal person.
    Secondly, subconsciously, she’s adopting an all-too common attitude among society’s elite- the rules don’t apply to me. As long as YOU sit idle at home, I can safely do whatever I want. Therefore, It is safe to be on an airplane as long as you kick the riff-raff off of it (and out of the hotel at the destination).
    Then there is herd mentality. All the cool kids in science academia hate Trump and are joining the effort to patiently explain to the fools just why it is so darn risky to go on the beach. Even if you write it while waiting for the airplane to board.
    Finally there is the selective amplification in the media. Everyone ignores the fact that the expert went flying in the middle of the pandemic and said it was fine with a few baby wipes. But they all noticed she said it was dangerous to eat a taco in an airy room with 20-foot ceilings- presumably on the basis of the impossibility to have either wipes or HVAC filters on the ground.

    • Actually, it’s a he.

    • “a respectable researcher, on the faculty as a prestigious US university”

      I agree Jeff; these folks are part of the elite; they love lecturing others on how to live their lives; they, the intellectuals, know best; what is best for others.

      They are like Ferguson: they are exempt from the rules; “do what I say, NOT do what I do …….”

      see them illustrate that; https://www.youtube.com/watch?v=rVYwPTE8B8g

      • I get the need for an elite, I just want it to take it’s role seriously. A university expert on infectious diseases is something we need right now. Her article is actually really good, very informative, pretty straight forward, and based on the response in the comments people really want it.
        Every response is awesome.
        Until she undermines everything she’s said by telling everyone she flew internationally in the middle of a pandemic, during lockdown order, from a city with a high rate of infection.
        It’s staggering to me. Our elite is so… bad is the only word… that they can’t even grasp that they look foolish. Part of it is that they simply don’t grasp that the common high school graduate these days can spot the BS

    • Jeff,

      Erin is a man.

      He writes: “I am not holding myself out as an expert on this virus or epidemiology”.

      He also writes: “So throughout most of the country we are going to add fuel to the viral fire by reopening”.

      Most airline flights hardly have any people on them so they are probably relatively safe.

      • You cannot fly internationally and stay locked down at home, and you cannot vacation and assume (and insist) that nothing be open at the destination.
        He (sorry about the gender) is in favor of a lockdown he wouldn’t follow himself and assumed he’d be able to ignore it at his destination as well.
        Either he made an educated decision that lockdown was unnecessary, or he weighed the risks informatively and chose to do what he wanted to do, or determined that it’s relatively safe for our elite to travel and eat out as long as only our elite are allowed to do so, and/or he doesn’t really believe we are adding fuel to anything, but all his friends are saying that and gosh it sure does make the Republicans squirm when academics write this stuff.

        There is an option where he believes everything he wrote- in which case he decided he didn’t care that as a resident of a city with an active outbreak he might unknowingly be a carrier of a highly infectious lethal disease and therefore his decision to travel with wipes could kill people on the plane and dozens if not hundreds more at his destination.

        I got the link from a friend- people are passing it around by text and social media saying “see, experts say we have to stay locked down!”

    • Hi Ireneusz; we are entirely in agreement!

      “Experts believe the victims may have been exposed to the virus weeks before developing symptoms. ”

      We are entirely in agreement: everyone thinks of the sick to well; well becomes sick; they spread to well; well becomes sick;

      Maybe we make too many assumptions; maybe we should write down all our assumptions about viruses; then think of those as we read facts;

      maybe we should read some of this https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2870528/pdf/S0950268806007175a.pdf

  61. Richard Gilbert

    Sunetra Gupta, Professor of Theoretical Epidemiology at the University of Oxford, was among the earliest critics of the covid-19 work of Neil Ferguson’s team. She believes that a large number of UK residents may have already been infected. Thus, the UK’s fatality rate upon infection may be very low, perhaps below 0.1%
    A recent interview in an Indian newspaper appears to set out her current position: that the virus dribbled into the UK in mid-December and escalated thereafter. It indicates that a report on her team’s latest results will be available in a few weeks. The interview is at:
    https://www.sundayguardianlive.com/news/death-rate-uk-will-not-increase-lockdown-lifted-prof-gupta-oxford

  62. Rob Johnson-Taylor

    I keep wondering why the health services or governments not recomending taking Vit D & Zinc suppliments as these two substances are known to reduce the severity of COVID-19, especially for those having dark skin. I think some lives would have bee saved if this had been done. The scientific litrature on this has not surfaced politically or in the public eye. True these substances do not cure COVID-19 but they do reduce severity. The vast majority of people in ICU with this virus have significantly reduced Vit D levels.
    Getting people out of lockdown, reducing infection severity will improve heard immunity

    https://www.bmj.com/content/369/bmj.m1548/rr-6

  63. Here is why quarantine of healthy people is a mistake:
    Sooner or later many, perhaps most, otherwise healthy people will get it, recover and for at least months be immune and cannot infect others. About half will not even have symptoms. The risk of them dying from it is negligible.

    Those with co-morbidities (obesity, diabetes, old (like me), etc.) need to take every precaution to avoid becoming infected because the consequences can be excruciating including a significant possibility of death. We cannot safely return to normal life style until herd immunity develops either the old fashioned way by getting the disease and recovering or by vaccination. Vaccination is not yet available.

    All that social spacing, masks, quarantine, etc. will do is slow the development of herd immunity the old fashioned way.

    • J Waldron, M.D.

      The risk of dying if you are young and healthy is like playing russian roulette. There is an incredible variance in how it attacks different patients. Case in point, the Kawasaki-like disease attacking children, when most case studies Jan-Apr described kids has having very few symptoms. And we have seen so many cases of the young otherwise healthy patients who end up on a ventilator, with this virus apparently attacking not only the lungs but the cardiovascular system, clotting cascade, and brain. We are still learning what the rehabilitation phase will look like for most.
      The best strategy would have been containment but no use crying over spilled milk. Now we are trying to flatten the curve. But the curve needs to be extremely flat to avoid excess fatalities in many parts of the U.S. I grew up in the NE corner of MT, the most remote place from a metro area in the continental US. doi:10.1038/nature25181 It’s 6 hours to the nearest pulmonologist and fully-staffed ICU. Our population is older and sicker than average. We have 8 reservations in Montana and luckily have had few cases associated with them. My heart breaks for the Navajo/Dine and Hopi Nations: If their reservations were a state, they would be 3rd highest fatality rate in the nation.
      Finally, I would argue that the more people infected the more likely for this virus to mutate, which may explain why the West Coast variety seems to be tamer than the East Coast virus. Mutations would likely make a vaccine even harder to develop, just as our influenza vaccine is an educated guess every year as to which strain will circulate.

      • Ireneusz Palmowski

        It is not the virus itself that causes the patient’s condition to deteriorate, but the cytokine storm it causes. And there are medicines for this.

      • Dan Pangburn

        One way to put things in perspective is to consider relative risk. According to the NY data on covid thru May 12, the risk of a person 64 years old or younger dying from covid-19 is about the same as the risk of dying in a traffic accident for driving 30,000 miles.

    • I was somewhat persuaded by this argument at one point but not any longer.

      First, there is a significant number of people in the 45-64 age group who die and even a good number in the 18-44. Almost 30% of the deaths are from those groups.

      https://www.worldometers.info/coronavirus/coronavirus-age-sex-demographics/

      Second, it is much harder to keep older people isolated than you imagine, particularly if we are talking about 1-2 years of isolation. They have relatives. They need to eat so somebody has to deliver. Some need regular medical care at their house. Things need repair so somebody has to come to their house. They still have to go out for some things – doctor and dentist visits, banking. Some are simply stubborn and want to leave the house.

      • James

        I don’t want to get bogged down in specific numbers or ages, etc, but you do realize those data are from NYC, which may or may not represent the US experience.

        But that is not my main point. Look further down your link at the fatality rate. Let’s average the 30-49 Age group. The average is .3. The 80 over is 14.8%. So, that older age group has a fatality rate nearly 45 times the younger cohort. The 70-79 age group is about 25 times the 30-49 group.
        A slightly out of date CDC report has 3,000 deaths in the approximate age group. A somewhat comparative age group from the Census is about 130 Million. I don’t want to quibble about specifics but assuming these are ballpark close numbers, having 3,000 deaths out of 130 Million does not seem material. Whether you consider the relatively low fatality rate or the number of deaths as a percentage of the total population,it’s insignificant.

        I’ve just read the Georgia report on the COVID19 impact on Long Term Health Facilities. It should be a model for all states since it tells what other states don’t include, even when they do a report. It includes Census (beds?, Patients?) at each facility, Patient cases, Patient Deaths, Staff Cases etc.

        What struck me was how many facilities had extremely high rates of cases and deaths for patients and high rates of staff cases at some locations. In a few locations the number of cases of staff and patients were HIGHER than the apparent patients or beds.

        The deaths in long term facilities in Georgia is about 50% of the state total deaths. If we want to get a real return on investment to reduce deaths with little negative impact on the economy, additional resources ought to be shifted to the really bad actors in the Long Term Health Care Facilities. Because other states don’t provide as much detail as the Georgia report, I don’t know if the statistics are representative of the US. If they are, shame on somebody.

      • ceresco

        Deaths are naturally going to be in long term care homes at first because you have a large contained population of vulnerable people. That doesn’t mean it is not going to affect the same age groups outside of the long term facilities eventually.

        We have had some people arguing the problem was a NY problem. But now, it spreading more rapidly in the heartland.

        There is a lot of trying to extrapolate short term experience to longer terms. That is learning yesterday’s lesson and trying to apply it to today’s problems.

        Barring some favorable mutation or a vaccine, the pandemic is going to touch everywhere. It has showed up first in large cities with a lot of reliance on mass transit, nursing homes, prisons, and meat packing plants, but it will end up in rural Mississippi and Kansas eventually.

        I don’t know what you mean about shifting resources to “bad actors in the Long Term Health Care Facilities”. It’s probably too late to do anything about most of them. Whether anything could have been done I doubt. These facilities are necessarily going to have medically compromised people packed into them like sardines with probably an underpaid, overworked staff to maximize their profits. That is going to turn these facilities into Petri dishes for any kind of highly contagious disease.

      • “We have had some people arguing the problem was a NY problem. But now, it spreading more rapidly in the heartland.”

        Los Angeles, San Diego and San Francisco had the virus for a long time before NYC (and before social distancing). Houston, Miami, San Antonio, Dallas, Tampa about the same time as NYC.
        New York has 4.8 times as many dead as California, Texas and Florida combined and less than a fourth of the population.

        There is no reason to believe we’re just waiting for this to spread everywhere and for people to eventually die in the heartland.

        There is direct evidence to the contrary.

        Tell people to stay in their own state and avoid old people. Use testing to quash outbreaks when and where they happen.

        I’d also urge you to find “event date” information. More than half the deaths reported in my state every day now actually happened days or weeks ago. They’re working through a massive backlog of testing samples.

      • James

        It seems the nursing homes, et al. are easily controlled with testing at the facility, closely monitoring entrance, social distancing and all that is being recommended for the public at large, yet they are under such control that best practices can be implemented more efficiently than throughout society. If as reported, these facilities have had 1/3 of the deaths, reduction of deaths could be effected without shutting down the economy and in fact could be a growth area for added jobs.

        I’m sorry to burst your bubble, but NYC and Detroit are still the hotspots. The so-called heartland is not getting close to the death rates in those 2 disaster areas. There are hundreds and hundreds of counties with 0 or single digit deaths. Major population centers like Harris County, Texas and Orange County, California are still a fraction of NYC. We would have several thousand fewer deaths if NYC and Detroit Metro areas had rates of deaths at levels comparable to those 2 counties.

      • Don Monfort

        No matter how much the pro virus crowd would wish it ain’t so, the trend is down:

        https://coronavirus.jhu.edu/data/new-cases

        High-risk states are seeing fewer new coronavirus cases

        https://www.axios.com/coronavirus-cases-map-high-risk-states-8ceeaa05-cc07-4e8b-b9f4-df3a3315f143.html

      • Jeff,

        NY waited about 10 days after California locked down. That time was critical particularly in a city with heavy mass transit usage. Time is of the essence, as they say.

        Most of the heartland has never locked down to any significant degree at all and almost everywhere is opening up again. Wishful thinking isn’t going to stop it.

      • No matter how much the pro-New Yorkers dead crowd might not like it, things are getting better in New York.

      • Yeah Don. Down to 20K a day. Let me know when you have some good news to report.

      • Don Monfort

        triggered

      • > It seems the nursing homes, et al. are easily controlled with testing at the facility, closely monitoring entrance, social distancing and all that is being recommended for the public at large, yet they are under such control that best practices can be implemented more efficiently than throughout society. If as reported, these facilities have had 1/3 of the deaths, reduction of deaths could be effected without shutting down the economy and in fact could be a growth area for added jobs.

        Yah. All we need to do is lift the mandates and the economy won’t be “shut down.”. People will just start going to restaurants and movie theaters and concerts again. The economy won’t be shut down.

        And with better control of nusing homes and the economy opening up, greater rate of infection without testing/tracing/isolating things will be just peachy keen. Sure, lots of people will die, but most of them won’t be in nursing homes and they’ll be dead anyway.

        Yup, the pro virus killing old people crowd will be very happy.

      • James

        New York City has 20,000 deaths.

        If NYC had death rate of Harris County (Houston) they would have 325 deaths instead of 20,000 deaths.

        If NYC had death rate of Orange County (next to Los Angeles) they would have 220 deaths instead of 20,000 deaths.

        The only places in America that have higher rates of death vs population than Detroit and New York City are some Georgia Nursing Homes who have more deaths than patients.

      • James: “NY waited about 10 days after California locked down.”

        California locked down two months after the outbreak started. Florida and Texas locked down after New York.
        There is some reason other than lockdown date for the huge disparity in death rates.

        And it’s not just in the US. The nation with the highest death toll – Belgium – shares a border with one of the lowest – Germany. No observer of this epidemic is assuming we’re just waiting for Germany to catch up to Belgium. Nor is anyone assuming it’s a matter of time before Finland out-dies Sweden or Portugal catches up to Spain.
        Why?
        One reason is these nations don’t have the bizarre groups that insist on politicizing a virus – there’s no political benefit to attacking a fellow who gets a beer in Germany, so nobody does it.

        So, for purely political reasons, we can’t talk about opening, much less how to open. I live a few miles from the beach in Virginia. The packed cars are arriving from New York, New Jersey, etc.
        They shouldn’t be.
        IMO, I should be able to go out to eat locally, but I shouldn’t go to NYC and NYC shouldn’t come here. According to the newspaper I subscribe to – The Washington Post – there is nothing to discuss. I couldn’t possibly have seen cars from New York and New Jersey packed with beach toys a few minutes ago because all the deep blue residents of those states are absolutely following the lockdown orders without the slightest complaint. Only snaggle-toothed rednecks in the “heartland” are defying lockdowns and as a result,, will be dropping dead any day now.

      • kevin roche

        you can’t take it as a percent of deaths, you have to take it as percent of cases, or better yet by population. There are a ton more people in the younger age groups and much fewer deaths per population unit. Last time I looked, 104 million people aged 24 and under in the country, 60 deaths. 22 million over 75, over 22,500 deaths (CDC data is lagged, but as deaths grow pattern holds) Ratio is around 250 times more deaths.

      • Dan Pangburn

        James,
        It is not a question of ‘if’ for employed people, it is only a question of ‘when’. The risk does not become negligible until herd immunity is established. I am way beyond the 45-64 age group so I don’t have to ‘imagine’. The prospect of spending the rest of my life under de facto ‘house arrest’ is abysmal…and not without risk.

  64. Another paper on the same theme, although funds heterogeneity returns a higher HIT than Nic calculated.

    https://arxiv.org/abs/2005.03085

  65. Stephen Anthony

    Nic,

    I am seriously impressed by your work here. I have not replicated a heterogenous model such as yours, which is what I would need to do to be absolutely sure.
    It explains why the peak infected totals of the Diamond Princess, Theodore Roosevellt aircraft carrier and the Italian town of Vo are so low.
    The classical idea that infected population increases until the HIT is equal to 1 – (1/Ro) as a proportion is now defunct.
    I would never have guessed that a heterogenous model could bring the HIT so far down. In my head I had been playing around with ideas like proportions of the popuiation as “Uninfectable”, “Resistant” and perhaps exercised immune systems as offering some explanation of what we have seen in the example locations mentioned above.

    What role do you see for changed behaviour in response to the virus if any?
    ot
    Would a heterogenous rat population produce the same results?

    Regards, Steve

    • Steve, thank you for your comment.

      It seems clear that people would change their behaviour as a result of an epidemic like COVID-19 even without any government restrictions. People would become more cautious about close interactions with others, particularly in enclosed settings – where almost all infections seem to be transmitted – and many of them might well wear face masks. Moreover, many of those people who were aged and/or had existing health issues would choose to self isolate once the importance of these factors in the infection fatality rate became publicly known. So I think that changed behaviour would have brought the reproduction rate down significantly even without any, or with only minor, government restrictions on behaviour.

      In principle a heterogenous rat population would produce similar results for a rat epidemic, I think, although the parameters involved would be different. And rats presumably wouldn’t be able to change their behaviour so readily, or have the knowledge to prompt them to do so.

      • Stephen Anthony

        Thanks for the reply. I am very grateful for the hope your post offered, that we likely won’t have to wait for 58.33% infected with an Ro of 2,4 to get to herd immunity. Your paper is also remarkable in that you have shown that the classical model of herd immunity is exaggerated for all pandemics that apply to genetically diverse populations. No mention of that before that I have heard of from anyone else. It looks like a paradigm shift.

        My questions were based on trying to tease out the relative importance of
        social distancing (which rats were unlikely to observe). Decreasing Ro by social distancing measures is not ideal & probably can’t be maintained for very long.
        You have mentioned that incorporating social distancing into your model is work in progress. I very much look forward to reading it.

    • The protections granted by genetic variability in the population, as bequeathed by evolution in part for the purpose, should work for rats as well as for humans. Plus, animals have many instinctive behaviours to help protect them against diseases (e.g. see https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3189355/). Come to that, much of the reaction of human publics is driven by instinct, albeit this is nuanced by virtue of intelligence. Given a huge dearth of knowledge at the beginning (and for instance the WHO were still touting no human-to-human transmission at mid-January), plus months later even the experts are still arguing about what behaviours are best, the strong voluntary reactions to isolate (plus public pressure upon some governments to formalise this), are surely more about instinctive fear than rationality. The pictures coming out of Italy certainly created fear in Europe.

  66. Nic,
    I’ve not yet come across social distancing emulations in SIR-SEIR modelings. The simplest would alter the infectious rate constant, k S(t)I(t) over finite intervals of an I(t) plot. When applied prior to the maximum, there is a pronounced effect – if too much, a secondary maximum subsequently appears. An intermediate reduction can halve the maximum while flattening the curve. When applied after the maximum, effects are minuscule.

    You might be interested in the IHME down-loadable csv files. These are apparently the basis for CDC prognostication. Of particular interest are the two columns beds_occupied(t) and admissions(t). The former appears to be a good proxy for I(t) and the latter allows calculation of R(t) and S(t). While rather noisy, asymptotic analysis yields rate constants not inconsistent with current ballpark estimates. The death rate for this select group of the most vulnerable is unfortunately ca. 25%. The four states I’ve so far looked at, FL, MI, NJ, PA, all share a mid-April maximum. (In May, IHME changed algorithms and some prior values in these files.)

    • Thanks, Quondam.
      I have now carried out some simulations with social distancing interventions included, but I haven’t completed this work yet.

      Noted re the IHME data files, thanks.

  67. Very nice work. But simple ‘SEIR’ epidemiological model does not take correctly into account a reaction of people to the disease such as social distancing, masks, self-isolation and so on even no official quarantine is imposed. As population inhomogeneity, it has huge impact on ‘herd immunity’, while population keeps social distancing. However it is difficult to estimate this influence and correctly include into standard compartmental epidemic models. Therefore estimation of her immunity on base of R0 for current stage of epidemic is not correct. Therefore, other approach based on other parameter is more flexible and therefore forecasts more exactly:

    https://www.medrxiv.org/content/10.1101/2020.04.28.20083428v2

    This paper considers the population heterogeneity too and proposes that separate clusters should be simulated separately. Some additional discussions about this approach:

    https://sciencefiles.org/2020/05/04/war-die-quarantane-in-deutschland-effizient-oder-unnotig-neue-studie/

    Best regards

    Hans

    • Thanks, Hans. I will look at that paper. I had not spotted it – there are so many preprints coming out on COVID-19 now!

      I agree that people would have changed their behaviour even if no lockdown had been imposed, particularly with governments and others advising them to do so. One of the major benefits of allowing people to make their own decisions tabout what degree of social distancing to undertake is that young, healthy people would be likely to social distance less.
      Therefore COVID-19 infections would be skewed towards that group, for which the hospitalisation rate and death rate are far lower than for the population as a whole. And, once they have recovered, the average transmission efficiency and hence R of the virus will be much lower, since the most socially connected people are neither infectious nor susceptible.

      So the HIT would be reached both more quickly and at a far lower human cost than if everyone is made to social distance equally.

      • Your scenario is based on a notion that the population can effectively be segregated by age. That isn’t realistic for any particular demographic, but it’s easy for someone of yours to be completely out of touch with how totally unrealistic your segregated scenario is among lower SES communities.

        Meanwhile, for communities where that segregation isn’t realistic, your prescribing a disaster. You’re suggesting a massive increase in an infectious vector that is likely to mix with older demographics, increasing the rate at which older people will get infected.

        You’re also effectively ignoring the impact of increased morbidity among a highly infected younger demographic. And you’re ignoring the potential of long-term health effects in younger people who get infected and sick but don’t die. We don’t know yet what such long term effects might be., so rolling the dice may not be a great idea.

        And what is the benefit? Highly uncertain. Perhaps the same number of people will be infected either way, but perhaps millions of infections can be avoided through a vaccine should the rate is spread be slowed down. And perhaps a lower mortality rate via better therapeutics will save many lives should the rate of spread be slowed and the same total reached over a longer period of time.

        Perhaps there are economic advantages to a faster/shorter spread than a slower/longer spread. Again, we don’t know – but these decisions should not be made through a facile treatment of the huge and multi-factoral uncertainties involved.

      • > Many people think COVID-19 kills 1% of patients, and the rest get away with some flulike symptoms. But the story gets more complicated. Many people will be left with chronic kidney and heart problems. Even their neural system is disrupted. There will be hundreds of thousands of people worldwide, possibly more, who will need treatments such as renal dialysis for the rest of their lives. The more we learn about the coronavirus, the more questions arise. We are learning while we are sailing.

        https://www.sciencemag.org/news/2020/05/finally-virus-got-me-scientist-who-fought-ebola-and-hiv-reflects-facing-death-covid-19

      • “Your scenario is based on a notion that the population can effectively be segregated by age. That isn’t realistic for any particular demographic, but it’s easy for someone of yours to be completely out of touch with how totally unrealistic your segregated scenario is among lower SES communities.”

        I didn’t see Lewis advocating for segregation but rather describing reality before the virus. What happened is other people imposed segregation. Old people are segregated. School children are segregated. A whole host of lessor citizens made that way under emergency impositions.

        Here’s what I am hearing from you. Poor people are going to die because they can’t socially distance. Yes. And they are going to come out on the other side sooner. While the rich people die later like Howard Hughes hiding from germs.

      • I don’t think the population needs to be segregated by age to protect those vulnerable. Among those still in the work force, the more important factor is that those with serious health issues need to be segregated and that should not be a huge mission for states to take on. In any case, most people over 70 do not work and so its easy to isolate them.

        I just don’t see Josh that you are thinking of innovative ways to do things.

        Those who are poor are always “hardest hit” by every stress. This is no different. But perhaps governors can help them differentially by providing protective gear for their seniors.

  68. Pingback: Why Herd Immunity to COVID-19 Is Reached Much Earlier Than Thought – Anti-Empire

  69. Pingback: Nothing New Under The Sun 2016

  70. Stephen Anthony

    Nic,
    Another paper on herd immunity being lower than the classic herd immunity level. Not as optimistic as yours but in the same direction.

    Click to access 2005.03085.pdf

    • Stephen
      Thanks. I read that paper after writing my article. I think that their, the Gomes et al and my range of assumptions as to the degree of population inhomogeneity should in the first instance be taken as illustrative.

      It is only by calibrating model assumptions by real data, either directly or as regards the model output, that their realism can be judged. That is why I brought in the case of Stockholm County, and an estimate of the apparent herd immunity threshold there (it may be higher or lower in other regions, of course).

      • Nic Lewis: . I think that their, the Gomes et al and my range of assumptions as to the degree of population inhomogeneity should in the first instance be taken as illustrative.

        Thank you for this reply to Stephen Anthony’s post, and your replies to the other commenters.

    • Stephen Anthony: Another paper on herd immunity being lower than the classic herd immunity level.

      Thank you for the link.

  71. What is lacking in this discussion is a performance metric that looks at both the actions to mitigate COVID and the reactions to those actions. I have simplified the problem into jobs and COVID 19 deaths. Job loses are a huge destructive force that lead to many health issues including deaths. Job losses also reflect fear – from dying from COVID and from the consequences of COVID. My performance metric is called #conquer-cv. It is simply number of increased jobs divided by number of new COVID-19 deaths x (times) 350. This can be for any country, state, county, City, Business. This index puts the focus where it belongs – minimize damage to lives.

    Mike

  72. Nic, I have quickly read through your post here with great interest. I can see where your model results could have dramatic implications for government policy going forward. If allowing the economy to proceed requires sufficient relaxations of the measures that shut it down, in turn, produces an Rt reproductive rate of significantly over 1, estimating the herd immunity threshold (HIT) would be critical for decision makers. In my view keeping the economies shut down has or soon will make the medice much worse than the disease. There are a number of those familiar with epidemiology who predict that mitigation efforts to lower the number of cases and deaths (or flatten the curve) will merely postpone the ultimate spread of the disease that produces (HIT). Of course, this assumes that in the meantime no effective vaccine or prophylactic are available.
    I have been using the Annan Bayesian model (see link below) to track the Ro and Rt values for various nations, US states and cities. That model is based on a 6 box SEIR model described by Thomas House in next link down. I believe the 4 and 6 box models would yield essentially the same Ro and Rt values. The Annan model resultant Ro and Rt values appear on initial testing to be uninfluenced by the selected priors.
    From this model most nations have Ro values in the range of 3.0 to 3.5 while states in the US and NY City can have Ro values in the 4 to 5 range. The value you use for Sweden is much the same as the Annan model yields, which is 2.5.

    I believe that your model accounting for inhomogeneity in a given population for infectivity, susceptibility and social connectivity can stand on its own from an a prior basis and to be empirically tested in a manner to be determined. Sweden is probably the closest condition to test your model if the voluntary mitigation actions of the citizens there can be accounted for.
    I plan to run your model with other parameters and steal/borrow code for building my own model.

    Click to access operational.pdf

    https://personalpages.manchester.ac.uk/staff/thomas.house/blog/modelling-herd-immunity.html

    • As far I can tell, his model doesn’t apply to the US and I assume it wouldn’t apply to the UK either. It doesn’t even apply to Sweden. It only applies to Stockholm County.

      • It doesn’t even apply to Stockholm necessarily. As I point out upstream, there is strong reason to believe that Stockholm prevalence is sub-10%, and unlikely to be anywhere close to herd immunity. Mobility data shows that Sweden is effectively under lockdown by its own citizens’ actions.

        There is no forecasting power behind the speculation that the corona virus can hit herd immunity at these low prevalence levels even lower than for the seasonal flu. It already fails with the evidence on hand from NYC and Italy. Further, herd immunity is only the point at which the R drops below 1. The spread in the population continues beyond that point.

      • Don Monfort

        I suspect that Mr. RB is likely correct.

      • RB
        You say, re Nashville vs Stockholm, that “per Apple data, iPhone users in these cities have nearly the exact same adjustment in driving, walking, and transit use”.
        But the linked graphs actually show that the mid-March (when goverment action was taken) to end-April average declines in driving, walking, and transit use were far greater in Nashville than in Stockholm. Driving was down about 3x as much, walking 2x as much, and transit use about 20-25% more.
        Since walking and driving involve very little risk of infection, while transit use involves a much higher risk, this shows that in the absence of a lockdown in Sweden the inhabitants of Stockholm were able to modify their behaviour in a much more intelligent way, achieving a much higher “bang for the buck”.

        I think that, even in Stockholm, Swedish people naturally behave in a way that is somewhat more socially distanced than in a city like NYC, not least because the population density is lower in Stockholm. However, when I was in Stockholm fairly recently I didn’t find social behaviour to be very much different from that elsewhere in Europe, excluding very crowded cities.

      • “But the linked graphs actually show that the mid-March (when goverment action was taken) to end-April average declines in driving, walking, and transit use were far greater in Nashville than in Stockholm. ”

        Sweden, IMO, is politely saying the truth- you actually can’t “lockdown” or “quarantine” a major western city. Millions of people in a small space, all living right on top of each other, and all presumably allowed to avoid starving to death.
        The best you can do is tell people some precautions that will help- stay home as much as you can, keep your distance, wash hands, if you’re old or have underlying health concerns self-quarantine.

        This was an urban pandemic. It was Brussels, not Belgium. London and Paris, not UK and France. New York, Chicago, and Detroit, not the United States. Lockdowns were largely theater in those cities though they probably slowed hospital use to some extent.

        Outside of those cities the Swedish model was fine. In other words, people lost their jobs and their life’s work in many places where they didn’t need to and, because politics, we can’t acknowledge that and adjust.

      • Based on the forecasts of the Swedish Riksbank , the Swedish GDP is expected to contract by 6.9%-9.7%. Neighboring Finland and Denmark are expected to contract by under 7% also, but with a lot fewer population-adjusted deaths. It is too early to say if a strategy that gave 10% higher mobility in Sweden was a successful one. The original report that Swedish health authorities issued gave a 95% CI for infection was larger than the population of Stockholm. After questioning by a journalist, they issued a revision bringing down the upper bound by a factor of 10. Britton predicted half the population would be infected by April, then it was May, later it is June. Now, he says that if only 10% have been infected, it might be time to change strategy.

      • Nic –

        > Since walking and driving involve very little risk of infection, while transit use involves a much higher risk, this shows that in the absence of a lockdown in Sweden the inhabitants of Stockholm were able to modify their behaviour in a much more intelligent way, achieving a much higher “bang for the buck”.

        Really? You make that comparison without accounting for the much greater typical use of cars in Nashville?

        > I didn’t find social behaviour to be very much different from that elsewhere in Europe, excluding very crowded cities.

        I’ll compare your anecdote-based science to someone who presumably has more expertise from actually being Swedish:

        > It may seem that Sweden (where I live) is closer to the approach suggested by Lewis. However, one should bear in mind that the restrictions taken in Sweden is what the country can manage. We simply cannot put out the 100000 police and military necessary to enforce a lockdown. We don’t have these numbers available. Also, the social distancing policy is not a problem in Sweden, because that is how it works normally. It is more than a joke when quoting the swedish reaction to the distancing rule of 2m: “that close?!!”. We don’t adress or greet strangers. Chit-chatting about nothing in public is not heard of except from the large immigrant minorities and the occasional “boomer” missing the good old days of demonstrations for some obscure communist guerilla, made up of three letters…We are fullfilling the demands of social distancing without effort.

        https://judithcurry.com/2020/04/26/a-sensible-covid-19-exit-strategy-for-the-uk/#comment-915893

    • Ken, thanks for your comment. Please do use my code, which is posted on my own web pages. If you have any queries or comments on it, please either raise them in a comment on the version of this post there or email me directly. I put the code up in haste and there are one or two rough edges in it.
      I’ve found no real difference between Annan’s 6 box SEIR model and my standard 4 box one. And the chosen latent and infectious periods only have a scaling effect on the growth rate.

  73. Update 14 May. I have replaced the words “antibodies to” by “infections by” in the 5th paragraph. A reader pointed out that the Stockholm survey tested for the prevalence of (current) infection by COVID-19, not the prevalance of antibodies to the virus. I had misread/misunderstood what the (Swedish language) report said. There are no implications for anything else written in my article.

  74. Question about your script:

    The following instruction occurs just before you call runSEIR():

    R0timeline= data.frame(dy = c(intervention_day, period), R0.I = c(R0e / mean(Sy * Iy), RIe))

    Why wouldn’t “mean(Sy * Iy)” instead be “mean(Sy %*% Iy)” (which I think would end up as unity)? That is, each population bin will infect every population bin, not just the same population, so at first blush it seems that the average rate should depend on the outer product, not the dot product.

    What am I missing?

    • Joe, thanks for raising a good technical question. The reason is that, early in the epidemic, the number of people infected reflects Sy (the total ‘force of infection’ is an average that applies to all population bins, but people in bins with greater susceptibilty are preferentially infected). And the infectees who were most susceptible are also the most infective, assuming correlation between susceptibility and infectivity through the common social connectivity factor. Hence the dot product Sy * Iy applying to determine the total force of infection.
      In the case where all the variability in Sy and Iy arise from the common social connectivity factor, my factor simplifies to mean(Sy^2), which agrees with the modification to the basic reproduction number given by equation (3) of the Gomes et al.paper.

      • Thanks very much for taking the time to respond. But I’m afraid I’m still in the dark. Perhaps I can impose upon you further to consider the problem in more detail.

        Let’s consider a four-bin calculation with the following susceptibility and infectivity vectors:

        Sy = c(1.37, 2.39, 0.54, 2.63)
        Iy = c(1.64, 2.39, 1.93, 0.96)

        as well as the following initial-population and infectiousness-duration values:

        N = 100
        infectious_p = 4

        The question before the house is how to calculate beta, the coefficient by which the rate dSL of new infections is calculated from the product of (1) the scalar product sum(Iy * I) of the infectivity vector Iy and the infectious-population vector I and (2) the vector Sy * S / N of bin-specific susceptibilities:

        dsL = beta * sum(Iy * I) * Sy * S / N

        What we want is the value that should initially produce a desired R0 value:

        R0 = 2.7

        Your approach is to scale beta in accordance with the dot product of the susceptibility and infectivity vectors:

        beta = R0 / infectious_p / mean(Sy * Iy)
        beta
        # [1] 0.234255

        But let’s see what happens when we use that value on an initial state that includes the following susceptible- and infectious-population vectors

        S0 = c(25, 25, 25, 25)
        I0 = c(0.25, 0.25, 0.25, 0.25)

        (For the sake of exposition I’ve cheated and made the susceptibles add up to the total population even though there are some infecteds.)

        Here’s the result:

        dSL = beta * Sy * S0 / N * sum(Iy * I0)
        sum(dSL * infectious_p)
        # [1] 2.80846

        As you can see, that’s not quite the R0 value we wanted.

        Now let’s try an alternative:

        beta = R0 / infectious_p / mean(Sy %*% t(Iy))
        dSL = beta * Sy * S0 / N * sum(Iy * I0)
        sum(dSL * infectious_p)
        # [1] 2.7
        To me, that makes more sense.

        Sorry to belabor the point, but any further light you could shed would be appreciated.

      • Joe,
        I haven’t had time to look at your examples in detail, but I accept that in a general case it may be that using the outer product is required for accuracy. However, I have checked and satisfied myself that, for the type of correlated and non-correlated randomness in Sy and Iy that I am employing, the inner product method produces the correct R0 value, ignoring sampling error.
        A practical reason for not using the outer product is that it would involve creating a matrix with 100,000,000 elements in my case, which would be computationally demanding.

      • While I’m currently of the opinion that you do get the wrong R0, your assurance otherwise certainly gives me pause, so I’ll have to go back and find out where I’ve erred.

        In the interim, I’ll mention that, although I explained my view in terms of the mean of the outer product because that seemed more straightforward conceptually, the calculation would in practice of course just be mean(Iy) * mean(Sy).

        Indeed, in your script’s current version you could dispense with that calculation altogether; the script normalizes Iy and Sy to unity mean values.

      • Your example doesn’t reflect the point I was making, other than in the very first generation.

        It would have perhaps been better if I had set Io to have the same distribution as Sy, rather than be uniform, but since it moves to reflect Sy over the first generation or two the Io distribution makes a negligible difference.

        If you want to pursue this matter further, may I suggest you study the Gomes et al paper, focussing on the section ‘Variation in eexposure to infection’.

      • Since I need to start on my taxes without having figured this out, I’ll mention that I’ve determined that that you do get the right answer, whereas I wouldn’t have–but I haven’t yet figured out why.

        Specifically, the equation coefficients (beta, delta, gamma) should be (2.4/4, 1/3, 1/4) for R0 = 2.4, latent period = 3, and infectious period = 4. That makes the early days’ higher eigenvalue about 0.157: after the first few days, the infection should increase by 17% per day until the susceptible-population change becomes significant.

        And that’s the increase that your script’s output does indeed exhibit.

        But I don’t see why it does; the way I read your script the value you use for beta is 0.303, not 2.4/4 = 0.6, when CV = 1, SDs = 0.4, SDi = 0, and alpha = 1, so I would have thought the early rate of growth you’d get would be only 3%.

        Obviously I’m wrong here, but, again, I’m going to have to put off figuring out why, so I thought I’d make the concession while it’s more likely to be read by someone whom my earlier comments might have led astray.

      • Don Monfort

        Joe is a scholar and honorable gentleman.

      • Joe Born:
        “I thought I’d make the concession while it’s more likely to be read by someone whom my earlier comments might have led astray”

        Thanks, Joe. Appreciated.

      • Don Monfort:

        Thank you for the kind words, which were particularly charitable in light of the mess I made upthread.

      • To clean up the mess I made above, I’ll briefly describe how I went wrong:

        In the early days the distribution of the susceptibles vector S barely changes, and all components of the susceptibility-times-susceptibles vector Sy*S are multiplied by a common sum of the infectivity-times-infectious Iy*I vector’s components. From that I mistakenly inferred that any correlation between Iy and Sy would be irrelevant, and I therefore thought that the normalizing factor mean(Sy * Iy) Mr. Lewis used in the script line

        R0timeline= data.frame(dy = c(intervention_day, period), R0.I = c(R0e / mean(Sy * Iy), RIe))

        should instead have been mean(Sy %*% t(Iy)).

        What I (blush) failed to take into account was that the infectious vector I itself results from, and in the early days thereby quickly becomes proportional to, the susceptibility vector Sy, so a component-by-component multiplication effectively occurs between Iy and Sy.

        The correlation that as a result almost immediately develops between I and Iy increases the effective value of beta over what I had taken it to be, and that’s why the simulation exhibits the correct eigenvalue I mentioned above.

  75. Ireneusz Palmowski

    There is further evidence that Cov-2 inactivates the ACE 2 enzyme, whose role is to prevent the narrowing of blood vessels. It turns out that the role of ACE 2 in the body is much more important than we think.
    Abstract
    The Covid-19 pandemic revealed that there is a loss of smell in many patients, including in infected, but otherwise asymptomatic individuals. The underlying mechanisms for the olfactory symptoms are unclear. Using a mouse model, we determined whether cells in the olfactory epithelium express the obligatory receptors for entry of the SARS-CoV-2 virus by using RNAseq, RT-PCR, in situ hybridization, Western blot, and immunocytochemistry. We show that the cell surface protein ACE2 and the protease TMPRSS2 are expressed in sustentacular cells of the olfactory epithelium, but not, or much less, in most olfactory receptor neurons. These data suggest that sustentacular cells are involved in SARS-CoV-2 virus entry and impairment of the sense of smell in COVID-19 patients. We also show that expression of the entry proteins increases in animals of old age. This may explain – if true also in humans – why individuals of older age are more susceptible to the SARS-CoV-2 infection.

    https://pubs.acs.org/doi/abs/10.1021/acschemneuro.0c00210

  76. Hello Judith

    I have made a simple model for the epidemic with Excel:

    https://drive.google.com/file/d/1RVsgm1LFLx3TPlEylYIXajnxEuI1QTev/view?usp=sharing

    You can enter some kind of lockdown for a certain time. It gives more or less the same graphs and data like world-odometer. So we can easily adapt the parameters of the model so that it fits the actual data.

    It clearly shows that the graph for the spreading (new cases) looks totally different than those for herd immunity. With reaching herd immunity the number for new cases drops very steep when it is reached. But without herd immunity but slowing though a lockdown (i.e. reduction of R) you have a slow decrease – exactly what we have in most countries. I think we are far away from herd immunity….

  77. Hello Judith

    I have made a simple model for the epidemic with Excel:

    https://drive.google.com/file/d/1RVsgm1LFLx3TPlEylYIXajnxEuI1QTev/view?usp=sharing

    You can enter some kind of lockdown for a certain time. It gives more or less the same graphs and data like world-odometer. So we can easily adapt the parameters of the model so that it fits the actual data.

    It clearly shows that the graph for the spreading (new cases) looks totally different than those for herd immunity. With reaching herd immunity the number for new cases drops very steep when it is reached. But without herd immunity but slowing though a lockdown (i.e. reduction of R) you have a slow decrease – exactly what we have in most countries. I think we are far away from herd immunity….

  78. Calling the policies “draconian” as Lewis did, tips his hand by showing the per-determined perspective he brings to this topic. The idea of lockdowns didn’t start with Ferguson’s model, despite what I’ve heard a lot of anti-lockdown right-wing people say. Instead the public health community discussed lockdowns for years, in the context of an insufficiently restricted pathogen with a large enough R0 and infection fatality ratio. In fact, Sierra Leone instituted a nationwide lockdown twice in response to an ebolavirus epidemic. So there’s prior experience with understanding how this works, not just reliance on a model:

    “Rites of mobility and epidemic control: Ebola virus disease in the Mano River Basin”
    “Global emergency legal responses to the 2014 ebola outbreak”

    With respect to Lewis’ discussion of Sweden: Tamino (Grant Foster) made a nice post recently comparing Sweden to Switzerland. Early on Switzerland had an epidemic of cases much larger than that of Sweden. So Switzerland initiated a lockdown and stuck with it. That helped bring Switzerland’s number of COVID cases per day to below Sweden’s by about mid-April. Thus, as Tamino notes, Switzerland effectively addressed the problem; Sweden instead largely contained it, while remaining near the edge of an outbreak occurring if their government eases its recommendations on voluntary social distancing. In addition to Switzerland, France is another country in which lockdown worked:

    https://tamino.wordpress.com/2020/05/14/covid-19-a-tale-of-two-countries/
    “Estimating the burden of SARS-CoV-2 in France”
    Non-peer-reviewed: “Effect of a one-month lockdown on the epidemic dynamics of COVID-19 in France”
    Non-peer-reviewed: “COVID-19: One-month impact of the French lockdown on the epidemic burden”

    So even Sweden is now beginning to accumulate excess COVID-19 cases in comparison to a country (Switzerland) that stuck with a lockdown. And that’s not even factoring in the risk of Sweden’s cases increasing further if they ease their recommendations. Sweden therefore is not a great example helping Lewis’ case.

    Lewis also cites a non-peer-reviewed article from Gomes et al. on factors that can, in principle, reduce the HIT from its typical value of {1 – 1/R0}. But there are also factors that can, in principle, increase HIT. This is where it pays to have biologists and/or medical experts involved in the evaluation of these subjects, instead of just doing it on climate blogs for politically-motivated non-experts.

    For instance, many people act as if the presence of higher virus-specific antibody titers is necessarily equivalent to immunity, including herd immunity. Antibody titers are good, rough metric to start with for immunity, but they’re not the sole determining factor of immunity. Take the following 2 examples:

    1) Vaccinations can result in the production of memory CD8+ T cells that kill virus-infected cells, without necessarily needing antibody production [possibly with indirect help from other immune cell populations, such as iNKT cells].
    2) Antibodies can fail to work by being non-neutralizing. Classic examples are antibodies for dengue viruses and HIV. In some cases the antibodies can make the condition worse, but I highly doubt that will apply for SARS-CoV-2, since it doesn’t seem to preferentially infect immune cells. Or the virus mutates, causing different variants of the virus in the population that are more resistant to the antibody.

    A typical layman response at this point is that ‘if antibodies don’t always entail immunity, then vaccines then wouldn’t be useful’. But this response fails. As per point 1 above, vaccines can work by antibody-independent mechanisms. And as per point 2, an imperfect antibody can still save lives, such as the antibodies generated in response to seasonal flu vaccines. Vaccine-induced antibodies need not protect against all variants of a pathogen all the time in order to be helpful.

    Applying the above points to HIT means that one can have a scenario in which HIT is higher than expected because:

    – antibodies are less effective at preventing disease than expected;
    – or vaccination / infection uses non-antibody, memory mechanisms to improve subsequent responses to the pathogen, and these mechanisms are less effective than expected;
    – or the virus mutates to a form previously infected people are not immune to, and that mutated virus begins to make up a larger proportion of the viruses infecting people;
    – or…

    So it’s cherry-picking to just focus on the factors that can make HIT lower than expected, while ignoring the factors that can make it larger. That looks like working backward from anti-lockdown conclusion to premises for reaching that conclusion. With respect to the viral mutation discussed above, there’s already some peer-reviewed + non-peer-reviewed research on SARS-CoV-2 mutating in relevant ways. And we already know it needs to have mutated in order to become as dangerous as it now is in humans (possibly including evolving to better evade the immune system):

    “The proximal origin of SARS-CoV-2”
    “SARS-CoV-2 and ORF3a: Nonsynonymous mutations, functional domains, and viral pathogenesis”
    “Evolutionary analysis of SARS-CoV-2: how mutation of Non-Structural Protein 6 (NSP6) could affect viral autophagy”
    Non-peer-reviewed: “Patient-derived mutations impact pathogenicity of SARS-CoV-2”
    Non-peer-reviewed: “Spike mutation pipeline reveals the emergence of a more transmissible form of SARS-CoV-2”
    Non-peer-reviewed: “Mutation patterns of human SARS-COV-2 and bat RaTG13 coronaviruses genomes are strongly biased towards C>U indicating rapid evolution in their hosts”

    • Re: “Lewis also cites a non-peer-reviewed article from Gomes et al. on factors that can, in principle, reduce the HIT from its typical value of {1 – 1/R0}. But there are also factors that can, in principle, increase HIT.
      […]
      This is where it pays to have biologists and/or medical experts involved in the evaluation of these subjects, instead of just doing it on climate blogs for politically-motivated non-experts.
      […]
      So it’s cherry-picking to just focus on the factors that can make HIT lower than expected, while ignoring the factors that can make it larger. That looks like working backward from anti-lockdown conclusion to premises for reaching that conclusion.”

      Apparently one of the co-authors of Gomes et al. spoke out about Lewis’ blogpost:

      • The first tweet that you cite predates my article. The second tweet is inaccurate. As I am simply using the same model as Gomes et al. devised, rather than replying on the the results of that study, I cannot be said to misrepresent it. I didn’t claim that their study endorsed any particular level of inhomogenity, rather that “It shows that variation between individuals in their susceptibility to infection and their propensity to infect others can cause the HIT to be much lower than it is in a homogeneous population.” That is an accurate statement.

        I have tried to go beyond their study by calibrating the degree of inhomogeneity so that the herd immunity threshold is consistent with developments in Stockholm County. Whether that attempt produces a reasonable result or not remains to be seen. I didn’t present any of my results as being defnitive, merey saying that “In my view, the true herd immunity threshold probably lies somewhere between the 7% and 24% implied by the cases illustrated in Figures 4 and 5”. Why shouldn’t I be free to express my considered view?

        It is also not true that Gomes et al .say that the relevant parameters are “essentially unknown”. They use illustrative examples based on CV=1 and CV=3, show that for other infectious diseases CV varies between 1.8 and 3.3 and say, referring to a SARS-CoV study:
        “but the way authors describe superspreaders is suggestive that higher infectiousness stems from higher connectivity with other individuals, who may be susceptible. This would support the scenarios displayed in Figure 2, with CV = 3 for exposure to infection.”
        They then in their concluding discussion say:
        “Popular models based on contact matrices use a coefficient of variation around 0.9 and perform similarly to our scenarios for CV = 1. Supported by existing estimates across infectious diseases, we argue that CV is generally higher and prognostics more optimistic than currently assumed. However plausible, this needs to be confirmed for the current COVID-19 pandemic.”

      • Compare and contrast:

        > I didn’t present any of my results as being defnitive

        And

        > Why herd immunity to COVID-19 is reached much earlier than thought

      • “This is where it pays to have biologists and/or medical experts involved in the evaluation of these subjects, instead of just doing it on climate blogs for politically-motivated non-experts.”
        What they’ve done has contributed to a trainwreck. Point to a trainwreck. You can do it. You are still a funtioning human being.
        We live in a democracy. Let’s keep it that way.

      • @niclewis

        Re: “Whether that attempt produces a reasonable result or not remains to be seen. I didn’t present any of my results as being defnitive, merey saying that “In my view, the true herd immunity threshold probably lies somewhere between the 7% and 24% implied by the cases illustrated in Figures 4 and 5”. Why shouldn’t I be free to express my considered view?”

        I’m not attacking your legal freedom of speech, anymore than you were attacking Resplandy et al.’s freedom of speech when you criticized their work (free speech =/= freeze peach). Moreover, as Joshua aptly noted above, your current comments differ from the more confident stance taken in your post’s title. One issue here is that many right-wing / conservative people online cite your blogpost as if it’s a definitive scientific study, since it confirms their preconceived, politically-motivated dislike of government intervention such as lockdowns. They leave out the fact that your article is not peer-reviewed, nor written by an expert in this topic.

        Hence my point that some informed biologists / medical experts ought to have looked at your blog article before it was posted, especially given the (possibly very detrimental) impact your article could have if it’s wrong and more widely accepted. To give an example closer to your field: it would be like if someone told you the transient climate response was 0.4K and equilibrium climate sensitivity was 0.6K. That conflicts with so much evidence (ex: observed industrial-era surface warming, paleoclimate data, temperature response to volcanic eruptions, climate models with observed emergent constraints applied, evidence on positive feedbacks [ex: water vapor, ice-albedo], etc.) that showing it to most informed climate scientists would cause them to immediately suspect an error was made in the analysis that led to such low values. Similarly so for how many informed immunologists / medical experts would respond to your claim on low HIT.

        For instance, your position implies that we could get away with using a SARS-CoV-2 vaccine that is way less effective than we reasonably expect, or that we could get away with vaccinating a much lower proportion of the population than we reasonably expect based on centuries of vaccination research. There’s a reason vaccines are given to so many people from a young age into adulthood. There’s a reason the WHO and other organizations push for massive global vaccination initiatives on measles, tuberculosis (not as much in the US), etc. It’s because the relationship between R0 and HIT tends not be what you claim it is for SARS-CoV-2 when we look at other pathogens; with a high enough R0, we simply need to vaccinate that many more people with an effective vaccine in order to get herd immunity.

        That extends to your points on individual variation in susceptibility to infection and their propensity to infect others, since other pathogens have those same issues apply to them, yet we still need to vaccinate a large proportion of the population against them, consistent with a higher HIT. Take the example of the 2009 H1N1 influenza pandemic (swine flu). That had an IFR and R0 lower than SARS-CoV-2 induced COVID-19 (on average), but still with skewing towards killing a larger proportion of the elderly population vs. younger people:

        Extended data figure 3 of: “Estimating clinical severity of COVID-19 from the transmission dynamics in Wuhan, China”
        “Early characterization of the severity and transmissibility of pandemic influenza using clinical episode data from multiple populations”
        “Epidemiological characteristics of 2009 (H1N1) pandemic influenza based on paired sera from a longitudinal community cohort study”
        “Case fatality risk of influenza A(H1N1pdm09): a systematic review”
        “Global mortality estimates for the 2009 Influenza Pandemic from the GLaMOR project: a modeling study”

        Yet even given it’s preferential mortality in the elderly and lower R0, that 2009 swine flu pandemic would have still required vaccination at a higher rate than your position implies in order to achieve herd immunity. Also, the same concerns I mentioned in my previous comment applied, such as mutation of the virus increasing HIT and a second wave occurring for the pandemic. Interestingly, there was research on this with respect to Sweden, so they’ve clearly been thinking for a long while about how to factor vaccination into their pandemic strategy:

        “The vaccination coverage required to establish herd immunity against influenza viruses”
        “The impact of antigenic drift of influenza A virus on human herd immunity: Sero-epidemiological study of H1N1 in healthy Thai population in 2009”
        “Critical immune and vaccination thresholds for determining multiple influenza epidemic waves”
        “The 2009 H1N1 pandemic influenza virus: what next?”
        “Economic consequences to society of pandemic H1N1 influenza 2009 – preliminary results for Sweden”

        So it’d be great if you were right about HIT being low; I don’t want to see more people die and lockdowns are painful for many people. Also, it would be politically-convenient for a lot of right-wing people if you were correct, just as it would be convenient for ECS to be 0.6K so they can avoid climate policies they dislike. But there’s every reason to think you’re wrong, just as there’s every reason to think ECS is not as low as 0.6K.

      • “One issue here is that many right-wing / conservative people online cite your blogpost as if it’s a definitive scientific study, since it confirms their preconceived, politically-motivated dislike of government intervention such as lockdowns. They leave out the fact that your article is not peer-reviewed, nor written by an expert in this topic.”

        And the stuff you quote confirms your preconceived, politically motivated desire for a technocracy of supposed superior people telling everybody what they can and can’t do. There is no such thing in a democracy.

        The other name for peer review is “GroupThink”. Peer review stopped being useful when people with alternative points of view were expelled from the peer group and researchers stopped being tenured so they could say what they really thought without fear of sanction.

        “Peer review” is like the old Catholic priest demand that the Bible remain in Latin and only they can be trusted to interpret it properly. No. Publish on the Internet and let all people make up their own mind. Trust that democracy will sort out the correct average view.

        And who says an expert is an expert? Their peers in their peer group? That’s little more than truth by repeated assertion. If you can’t persuade by argument from first principles but have to rely on reputation and credentials then you’re not worth listening to.

        In any scientific field where the hypothesis cannot be eliminated by double-blind experimentation there are no experts and there are no facts. There are just people with differing opinions and different interpretations trying to reach a political consensus. Likely they won’t and then we’ll have to vote on the differing choices.

        Scientism and veneration of supposed experts as the new priesthood is just another form of Woo. Stop it. It doesn’t persuade anybody outside your Cult.

    • Atomsk’s Sanakan: Calling the policies “draconian” as Lewis did, tips his hand by showing the per-determined perspective he brings to this topic.

      In California a man surfing alone was taken into custody. Examples have been in the news from other states. In Michigan gardeners were prohibited from buying seeds and other gardening supplies.

      “Draconian” is an appropriate epithet for these petty tyrannical idiocies.

      Much social distancing was carried out voluntarily before the decrees were announced: citizens cancelled vacation plans; companies cancelled travel plans; scientific and other organizations cancelled or virtualized their annual, semi-annual and quarterly meetings; resorts closed down. The lockdown decrees (variously named) did not accomplish much of additional value.

      • this might be “draconian”

        https://www.sfgate.com/bayarea/article/While-South-Lake-Tahoe-welcomes-back-second-15272363.php

        Prohibiting all surfing I think is draconian. But it wasn’t just surfing, it was all water activities, all beach activities, and all skate-boarding. Municipalities even wasted their tax money putting sand in the skate-board parks. Low density outdoor events engaged in by mostly young people not at risk. All while some prisoners were released.

        Not that I am totally oblivious. At age 73, with Afib and overweight, I am in a high risk group. Not that I am worried, but before the lockdown was ordered I started to say away from the rink where I ice skate, from the pool where I swim, and from the fitness center where I work out on weights. I don’t want to harm other people in case I get an infection and might carry it to them. The lockdown was totally unnecessary: healthy young figure skaters were never at risk

      • Re: “Just on a point of detail, Sint Maarten is not in Europe, but rather the Caribbean, though under Netherlands jurisdiction in some way (I’m not familiar with the exact constitutional arrangement)”

        You’re right, my mistake. I mixed up jurisdiction with geography.

    • Atomsk’s Sanakan: With respect to Lewis’ discussion of Sweden: Tamino (Grant Foster) made a nice post recently comparing Sweden to Switzerland. Early on Switzerland had an epidemic of cases much larger than that of Sweden. So Switzerland initiated a lockdown and stuck with it. That helped bring Switzerland’s number of COVID cases per day to below Sweden’s by about mid-April.

      So 1 or 2 countries in the EU did better than Sweden and most of the rest did worse. If you are going to select 1 country for comparison to Sweden, shouldn’t you at least select 1 with a seaport?

      • Matthew –

        Why not compare to the rest of the Scandanavian countries, ones with relatively similar comorbidity rates, ICU beds per capita, access to healthcare, % of citizenry living in single person households, etc?

        And then compare the state of their economic status across government mandate/no mandate policies. Any differences?

        It’s too early to tell anything. And cherry picking isolated factors on wither side of the divide only serve to confirm biases.

      • verytallguy

        “1 or 2 countries in the EU did better than Sweden and most of the rest did worse.”

        In terms of deaths per capita, most European countries have done better than Sweden

        Sweden is currently #6 in the table on total deaths per capita in the EU.

        https://ourworldindata.org/coronavirus-data-explorer?zoomToSelection=true&time=2020-03-06..&country=GBR+DEU+FRA+AUT+BEL+BGR+CZE+DNK+EST+HUN+IRL+ITA+LTU+NLD+POL+ROU+SVK+SVN+ESP+SWE+FIN+GRC+LUX+PRT+HRV&deathsMetric=true&totalFreq=true&perCapita=true&smoothing=0

        Based on current daily deaths per capita, Sweden is now the very highest in Europe (7 day smooth applied as the data is noisy)

        https://ourworldindata.org/coronavirus-data-explorer?zoomToSelection=true&time=2020-03-06..&country=GBR+DEU+FRA+AUT+BEL+BGR+CZE+DNK+EST+HUN+IRL+ITA+LTU+NLD+POL+ROU+SVK+SVN+ESP+SWE+FIN+GRC+LUX+PRT+HRV&deathsMetric=true&dailyFreq=true&perCapita=true&smoothing=7

      • Re: “In California a man surfing alone was taken into custody. Examples have been in the news from other states. In Michigan gardeners were prohibited from buying seeds and other gardening supplies.
        “Draconian” is an appropriate epithet for these petty tyrannical idiocies.”

        Please let me know when you have some evidence for this; I know better than to take your word on it. And selecting isolated incidents doesn’t show a whole policy is “draconian”, just like cherry-picking isolated incidents of police misbehaving doesn’t mean the entire practice of policing is bad. I already cited evidence that lockdowns saved lives. If you’re going to claim the lockdowns were still “draconian” (i.e. excessively harsh or severe), then you’re going to do better than a couple of unsourced anecdotes, given those lives saved.

        Re: “So 1 or 2 countries in the EU did better than Sweden and most of the rest did worse. If you are going to select 1 country for comparison to Sweden, shouldn’t you at least select 1 with a seaport?”

        Feel free to share evidence that the others did worse, and how that related to the effectiveness of lockdowns. Again, I know better than to just take your word on this.

      • verytallguy: Sweden is currently #6 in the table on total deaths per capita in the EU.

        https://ourworldindata.org/coronavirus-data-explorer?zoomToSelection=true&time=2020-03-06..&country=GBR+DEU+FRA+AUT+BEL+BGR+CZE+DNK+EST+HUN+IRL+ITA+LTU+NLD+POL+ROU+SVK+SVN+ESP+SWE+FIN+GRC+LUX+PRT+HRV&deathsMetric=true&totalFreq=true&perCapita=true&smoothing=0

        Based on current daily deaths per capita, Sweden is now the very highest in Europe (7 day smooth applied as the data is noisy)

        https://ourworldindata.org/coronavirus-data-explorer?zoomToSelection=true&time=2020-03-

        thank you for the links. I think the most relevant for evaluating policy is the total deaths per million, which I’ll keep following. But it is also pertinent that daily deaths per million is now high; Sweden has moved up in deaths per million since I last reviewed the data.

      • Re: “So 1 or 2 countries in the EU did better than Sweden and most of the rest did worse. If you are going to select 1 country for comparison to Sweden, shouldn’t you at least select 1 with a seaport?”

        So you didn’t have a shred of evidence for your insinuation, as usual. As per verytallguy’s source ( https://ourworldindata.org/coronavirus-data-explorer?zoomToSelection=true&time=2020-03-06..2020-05-14&casesMetric=true&dailyFreq=true&perCapita=true&smoothing=0&country=SWE ), the Switzerland and France examples I went over would not be the only two examples. Both had a pattern in which their confirmed cases per day per capita (cdc) was larger than Sweden earlier in the pandemic (March / April), they instituted a lockdown, and their cdc plummeted to beneath Sweden so far. Since you want to insinuate that that’s just for “1 or 2 countries in the EU” without a “seaport”, here are other European states that followed a similar pattern:

        with seaports:
        Norway, Netherlands, Iceland, Belgium, Germany, Spain, Portugal, Italy, Monaco, Ireland (also: Isle of Man, Guernsey, Jersey), Sint Maarten, Estonia ( https://www.reuters.com/article/us-health-coronavirus-estonia-restrictio/estonia-opens-healthcare-schools-to-follow-in-easing-of-lockdown-idUSKCN2242MR )

        without seaports:
        Austria, Luxembourg, Andorra

        Other European countries followed another pattern in which they had about as much cdc as Sweden earlier in the pandemic (instead of a cdc that spiked higher above Sweden), instituted lockdown measures, and then had their cdc remain below Sweden’s so far:

        with seaports:
        Slovenia, Denmark, Finland, Croatia, Lithuania, Latvia, Turkey, Malta, Montenegro, Cyprus

        without seaports:
        Czech Republic, Serbia

        Also, though Liechtenstein’s cdc was above Sweden’s early on and eventually came down to below Sweden’s so far, I can’t find clear evidence on whether they had a lockdown. But their government did institute one of the more impressive electronic contact tracing setups. I’m not sure if many people in the US or UK would like it though, given their concerns about privacy and paranoia about the government:

        https://inews.co.uk/news/health/coronavirus-testing-latest-liechtenstein-pioneering-biometric-bracelets-2540911

        And, of course, there are other European countries beyond those I listed. But many of those countries didn’t have a significant cdc anytime during the pandemic so far, so they’re not as pertinent to this topic of limiting cdc once it rises.

        Another interesting case is Armenia. Armenia’s cdc remained below Sweden for March and April. They then prematurely ended their lockdown on May 1, at which point Armenia’s cdc promptly rose to the level of Sweden’s. Belarus, in contrast, didn’t have a lockdown and avoided social distancing measures. It’s cdc is now above Sweden’s, and has been since late April.

        (Note: I excluded San Marino due to poor data quality, such as a negative cdc value)

        Two non-EU European outliers are Russia and the United Kingdom. Russia’s cdc steadily increased to levels that are now slightly above Sweden, despite Russia having a lockdown. Similarly so for the UK, though their cdc very recently dipped below Sweden’s (this might be temporary, however). In Russia’s case, part of the issue might be the massive size of the country, or their proximity to China as the source of the outbreak. In the UK’s case, there are numerous reports on how much of the population didn’t follow the lockdown. It likely didn’t help that there were people like Nic Lewis incorrectly insinuating that non-vaccine-mediated herd immunity was a better strategy:

        https://www.thetimes.co.uk/article/more-than-200-000-report-neighbours-to-police-for-breaking-virus-lockdown-rules-jlzn3b5vv
        https://www.sheffield.ac.uk/news/nr/young-men-most-likely-break-coronavirus-lockdown-rules-psychology-mental-health-study-1.888316

        Are you starting to see a pattern, Matthew? Numerous European countries, not just “1 or 2 countries in the EU” as you insinuated, instituted lockdowns that helped bring their cdc to below that of Sweden. That included numerous countries with seaports (a goalpost you randomly introduced), along with land-locked countries, different ethnic make-ups across the countries, different forms of government across the countries, etc. Lockdowns worked across Europe, for the most part. Thus Sweden looks like an outlier. So like many other political conservatives / right-wingers, your pre-determined bias against lockdowns caused you to not cogently evaluate the evidence on them. Please stop doing that.

        Looking at the cdc in those European countries, it makes sense why many say a Sweden-inspired herd-immunity-based strategy is dubious at best. For instance:

        “The WHO director added: “So I do think this idea that ‘maybe countries who had lax measures and haven’t done anything will all of a sudden magically reach some herd immunity, and so what if we lose a few old people along the way?’ This is a really dangerous, dangerous calculation.””
        https://www.independent.co.uk/news/health/coronavirus-herd-immunity-who-uk-matt-hancock-a9510231.html

        “Is gradual and controlled approach to herd protection a valid strategy to curb the COVID-19 pandemic?”
        “Herd immunity – estimating the level required to halt the COVID-19 epidemics in affected countries”
        Non-peer-reviewed research: “Mitigation and herd immunity strategy for COVID-19 is likely to fail”
        Non-peer-reviewed research: “COVID-19 herd immunity strategies: walking an elusive and dangerous tightrope”
        Non-peer-reviewed research: “Suppression and mitigation strategies for control of COVID-19 in New Zealand”

        https://fivethirtyeight.com/features/without-a-vaccine-herd-immunity-wont-save-us/

        As far am I’m concerned, lockdowns greatly hurt a lot of people, especially economically. So a competent government should not use them indefinitely. Instead lockdowns should be used to mitigate COVID-19 deaths and new confirmed cases, while buying time for other interventions to be developed, such as:

        – building the capacity of the healthcare system to take care of more patients
        – some form of contact tracing
        – developing and validating treatments, such as antivirals ( https://judithcurry.com/2020/03/14/coronavirus-discussion-thread/#comment-916797 )
        – increasing testing capacity

        That way society is better equipped to address the disease after the lockdown is lifted. But let’s not kid ourselves that we’ll reach some low herd immunity threshold as a means for avoiding a lockdown; achieving herd immunity in a short time without a vaccine would require massive loss of life (as per the higher IFR for COVID-19: https://judithcurry.com/2020/05/06/covid-discussion-thread-vi/#comment-916987 ), and opponents of lockdowns should honestly own up to that fact.

      • Atomsk’s Sanakan: As far am I’m concerned, lockdowns greatly hurt a lot of people, especially economically. So a competent government should not use them indefinitely. Instead lockdowns should be used to mitigate COVID-19 deaths and new confirmed cases, while buying time for other interventions to be developed, such as

        That was a very fine post.

        Have I advocated against lockdowns? I self-isolated before California and San Diego county instituted their lockdowns, and I supported those lockdowns when they began. Not that my support mattered, but there it was.

        But continuing? All auto factories shut down? in South Carolina, Alabama and N. California same as Michigan and Ohio? Beaches and oceans? Garden supplies? Elective surgeries? Costing somewhere in the range of 1/6 -1/3 workers to be thrown out of work? Those have been Draconian absurdities.

      • When Willis wrote a post comparing Switzerland and Sweden, he look at the per capita death rate and noted they were about the same # and concluded that “lockdowns don’t work.”

        Since that time Sweden has risen to a much higher per capital death rate, and will probably soon be double that of Switzerland.

        What is the reason? Well, that’s very complicated. A lot of it has to do with variability in how the metrics are applied (i.e., the call cause excess death rate in Sweden seems lower, relatively, then the # for per capita death rate from COVID)..

        Probably best to wait until we have decent data, and have waited for the trends to actually stabilize, before trying to draw conclusions. Drawing conclusions now is more than likely just basically confirming ideological biases – a trap that rather obviously Willis fell into.

      • Matthew –

        > That was a very fine post.

        And that’s a fine thing to say – particularly since the tone of Atomsk’s post was less than magnanimous. Maybe some reasonably productive dialog could become a more regular event here at some point.

      • Re: “Both had a pattern in which their confirmed cases per day per capita (cdc) was larger than Sweden earlier in the pandemic (March / April), they instituted a lockdown, and their cdc plummeted to beneath Sweden so far.”

        I’ve repeated the same process, but using confirmed deaths per day per capita (ddc ; https://ourworldindata.org/coronavirus-data-explorer?zoomToSelection=true&time=2020-03-06..2020-05-14&deathsMetric=true&dailyFreq=true&perCapita=true&smoothing=0&country=SWE ) instead of cdc. Ddc goes through a roughly weekly cycle, possibly tied to differences in behavior, reporting, hospital workloads, etc. on weekends vs. weekdays. So I’ve also looked at a 7-day rolling average to take account of that ( https://ourworldindata.org/coronavirus-data-explorer?zoomToSelection=true&time=2020-03-03..2020-05-14&deathsMetric=true&dailyFreq=true&perCapita=true&smoothing=7&country=SWE ).

        The states below had a ddc larger than Sweden’s earlier in the pandemic (March / April), instituted a lockdown, and then their ddc plummeted to beneath Sweden’s so far. Given Matthew’s previous insinuation that it was just “1 or 2 countries in the EU” without a “seaport”, I’ll list those states with seaports as well:

        with seaports:
        Netherlands, France, Spain, Italy, Ireland (also: Isle of Man, Guernsey, Jersey), Sint Maarten

        without seaports:
        Switzerland, Luxembourg, Andorra (just recently dipped below Sweden)

        [Note: I again excluded San Marino, though it lacked negative ddc value, in contrast to some of its negative cdc values]

        The following states had about as large a ddc as Sweden earlier in the pandemic (instead of a ddc that spiked higher above Sweden), instituted lockdown measures, and then their ddc remained below Sweden’s so far:

        with seaports:
        Denmark, Iceland, Portugal, Monaco

        without seaports:
        Austria

        The following states had a ddc larger than Sweden earlier in the pandemic (March / April), instituted a lockdown, and then their ddc plummeted to near where Sweden’s is now, with a substantial chance of their ddc heading to below Sweden’s in the future:

        with seaports:
        Belgium, United Kingdom

        There are other European states beyond those listed above. But many of those states didn’t have a significant ddc anytime during the pandemic so far, so they’re not as pertinent to this topic of limiting ddc once it rises.

        So once again: numerous European states with a higher relative death toll instituted lockdowns that helped bring their confirmed deaths per day per capita to below that of Sweden. That includes numerous countries with seaports (the goalpost Matthew randomly introduced), along with land-locked countries, different ethnic make-ups across the countries, different forms of government across the countries, etc. Lockdowns therefore worked across Europe, for the most part, not only in terms of limiting confirmed cases, but also in terms of limiting confirmed deaths. Thus Sweden looks like an outlier in terms of it avoiding lockdown, while maintaining a higher number of confirmed deaths per day per capita.

        Moreover, out of 52 European states listed, Sweden has the 8th highest number of total confirmed deaths per capita, as of May 14, 2020 ( https://ourworldindata.org/coronavirus-data-explorer?zoomToSelection=true&time=2020-03-04..2020-05-14&deathsMetric=true&totalFreq=true&perCapita=true&smoothing=0&country=PRT+CYP+AUT+ALB+AND+ARM+BLR+BEL+BIH+BGR+HRV+CZE+DNK+FIN+FRA+GEO+DEU+GRC+GGY+HUN+ISL+IRL+IMN+JEY+RKS+LVA+LIE+LTU+LUX+MKD+MLT+MDA+MCO+MNE+NLD+NCL+NOR+POL+ROU+RUS+SMR+SRB+SXM+SVK+SVN+CHE+ESP+TUR+UKR+GBR+VAT+SWE ). Of the 7 states with a total confirmed number of deaths greater than that of Sweden:

        5 now have a ddc lower than Sweden’s:
        San Marino, Andorra, Spain, France, Sint Maarten

        2 now have a ddc around Sweden’s, and trending downwards to soon possibly be consistently below Sweden’s:
        Belgium, United Kingdom

        So not only does Sweden have one of the largest total deaths per capita in Europe, it’s likely going to accumulate even more deaths in comparison to other European states. The same point applies when you compare total deaths per capita and confirms deaths per day per capita between Sweden, the United States, and Canada: Sweden is worse, and continuing to get worse in comparison. That makes it all the more ridiculous when various right-wingers in the US claim they want to “be like Sweden”:

        “Conservative Americans see coronavirus hope in progressive Sweden
        […]
        But Swedes are quick to note their hands-off coronavirus approach relies on a concept antithetical to American conservative philosophy: extreme trust in government.”

        https://www.politico.com/news/2020/04/30/conservative-coronavirus-sweden-225184

        “Lockdown protesters shout ‘be like Sweden’ — but Swedes say they are missing the point
        “The Swedish strategy is very much relying on the individual’s trust in the state,” one Swede told NBC News.”

        https://www.nbcnews.com/news/world/lockdown-protesters-shout-be-sweden-swedes-say-they-are-missing-n1207566

      • verytallguy

        Atomsk,

        Just on a point of detail, Sint Maarten is not in Europe, but rather the Caribbean, though under Netherlands jurisdiction in some way (I’m not familiar with the exact constitutional arrangement)

      • Matthew R Marler

        Joshua: And that’s a fine thing to say – particularly since the tone of Atomsk’s post was less than magnanimous.

        It was tough medicine to swallow, and I need another day to recover from the aggravating side effects. But he made a good case. He and VTG showed that I had clearly fallen behind on the Sweden comparisons.

      • Atomsk’s Sanakan: (the goalpost Matthew randomly introduced),

        It was only one of the obvious geographic/cultural differences between those two countries that make it hard to draw conclusions from cross-country comparisons.

        Tamino shows that the infection rate and infection total rose much more rapidly in Switzerland than in Sweden, and in fact Sweden never had peak rates as high as Switzerland’s, and now looks like it is in a sort of approximate steady state. Why the rapid rise and high peak in Switzerland compared to Sweden?

        What is one to make of the fact that Switzerland has had a larger total number of cases per million than Sweden, but a lower number of deaths per million? Inadequacy of the Swedish health care system has been mentioned, but the total case load was much higher in Switzerland for a while than it ever was in Sweden — is there information on that?

        If the lockdown is ended in Switzerland, will the new infection and new death rates rise?

        More cross country and cross state comparisons will be coming soon, I hope.

      • Matthew, the death rate per reported case ranges from 16.3% in Belgium to 4.5% in Germany.
        Britain, Italy, France are 14 or 15%
        Sweden is 12.2% and Switzerland is 6.2%
        There isn’t any evidence that economic activity makes the virus more lethal, so either case counts are completely wrong or there are other reasons why you are more likely to die in some places than in others.

        What’s the number for the US? 6%. Because the US is so incompetent compared to Europe, of course, and has a callous private health system. But of course even within the US there is a big disparity.
        In New York, where the media says the governor performed perfectly with his progressive and compassionate bureaucracy and modern health care system, 7.8% of cases resulted in death.
        On the other hand is South Dakota, where the media says the governor displayed murderous disregard for the virus in state with Dickensian bureaucracy and health care system. In the cesspit that is South Dakota 1% of reported cases ended in death.

        What’s it all mean? Sweden did better than most, worse than some. The US as a whole did about middle of the pack of western democracies and is down that far entirely because of New York City. The political hatred of Swedish policy and the handling of the virus in the US is baseless (which means it will get louder).

      • Josh has a point I think. These comparisons may not tell us much. However eventually we can use comparisons to learn. For example New York and Florida have about the same number of people. New York has at least 10 times more fatalities. And DeSantos seems to have done a better job at nursing homes. That could be a critical difference to learn from.

      • I’ll say this again because a lot of what is said here is beside the point. For people under 60 in good health, this virus is not very dangerous. IFR’s are very low according to Ferguson for those under 40. If everyone under 40 was infected, less that 30K would die. If you think Ferguson’s numbers are too high by a factor of 2, its 15K.

        The lockdowns are draconian in many states and illegal. Oregon’s lockdown order was just struck down by a court. When the full impact is felt, many governors will not be reelected.

        There are many many smarter policies such as trying to isolate the most vulnerable and letting everyone else get on with their lives. I’m really really surprised noone among our brilliant governors has tried to do this. Focusing testing on hospitals and nursing homes makes tremendous sense. Roughly 40% of all US fatalities were among residents of nursing homes. This simple expedient would have had a huge impact on the death toll. Cuomo appears to have had a bad policy on this one and De Santis had a better policy.

      • @dpy6629 I agree 100% with your points.

        One could argue that Asian countries were possibly justified in lockdown since the characteristics of the “novel” virus were unknown. But in February we knew from Chinese data that most victims were elderly and that there were virtually no deaths in children.

        Italian data confirmed the Chinese data, and this was before any state in the US locked down. We knew before then that 81% of Covid deaths were in those over age 65.

        From Covid age stratification data from the CDC on April 18 https://www.cdc.gov/nchs/nvss/vsrr/covid_weekly/index.htm, we now have a good idea of mortality per age cohort, and we also have a good idea of the overall infection fatality rate from the Cambridge Center for Evidence Based Medicine (CEBM), which gave an IFR range of 02.% to 0.41%.

        If we take the stratification categories from the CDC and use US population records to find the percentage of the population in each age group, and we take an overall IFR of 0.41%, then my initial calculations show that for those over 65, the IFR is about 2%, which is reason to be concerned or even alarmed. However, even given the higher IFR estimate from CEBM, the age cohort of 35-64 has an IFR of about 0.2% and that’s slightly worse than a normal flu (IFR of about 0.1%.) Below age 35, the IFR comes out to 0.007%, or virtually zero.

        It looks like we have a path forward that doesn’t warrant blanket lockdown, neither now nor when we have our hypothesized second surge which, if/when it comes, will allow 84% of the population (those aged 0-65) to acquire Covid and thereby presumably acquire herd immunity. By this time we will also have refined our means of treating and/or protecting the most vulnerable cohort.

        The lockdown and the huge destruction it’s causing are unnecessary.

      • Thanks Don, In retrospect this will look like the biggest panic in history since the 19th Century when financial panics were common and had severe consequences.

    • Re: “For instance, many people act as if the presence of higher virus-specific antibody titers is necessarily equivalent to immunity, including herd immunity. Antibody titers are good, rough metric to start with for immunity, but they’re not the sole determining factor of immunity.”

      Some related possibilities to consider:

      1) Recurrence of COVID-19: People who recover from COVID-19 might suffer from COVID-19 again, [ex: a mutated form of SARS-CoV-2 that’s more virulent than the strain they were initially exposed to]. That would undermine immunity and increase HIT.
      2) Recurrence of SARS-CoV-2 infection: People who recover from COVID-19 and have no detectable SARS-CoV-2 viral load, might then have their viral load increase again later. If that happens and even if these people were immune, they could still have enough virus to infect vulnerable people, undermining herd immunity and increasing HIT.

      Will be interesting to see how the results below on point 1 are followed up on. Hopefully it will be with a larger sample size to make sure the recurrence phenomenon is real and substantial:

      “Recurrence of COVID-19 after recovery: a case report from Italy
      […]
      After 14 days the patients became afebrile and his respiratory symptoms disappeared.
      […]
      The two nasopharyngeal swabs collected on March 30 and 31 were both negative for SARS-CoV-2 infection. The patient was therefore discharged and encouraged to maintain home quarantine for at least 14 days. The molecular test was also negative at his follow-up visit on April 15, suggesting that the patient was cured from COVID-19. In addition, two serological assays […] revealed the presence of IgM and IgG anti-SARS-CoV-2. However, on April 30, he developed new symptoms, i.e., dyspnea and chest pain. […] Because of his recent clinical history, a SARS-CoV-2 molecular test was performed and proved to be positive. Moreover, serological assay revealed the presence of only IgG anti-SARS-CoV-2. To date, the patient is well, on anticoagulant therapy and does not require O2 supplementation.
      To the best of our knowledge, this is the first published report describing a reactivation of COVID-19 in an apparently cured patient in Italy.”

      Click to access s15010-020-01444-1.pdf

      https://www.independent.co.uk/life-style/health-and-families/coronavirus-immunity-reinfection-get-covid-19-twice-sick-spread-relapse-a9400691.html

      Related to point 2, and the unclear evidence on it:

      “COVID-19 and postinfection immunity: Limited evidence, many remaining questions”
      “Does immune privilege result in recovered patients testing positive for COVID-19 again?”
      “Recurrence of positive SARS-CoV-2 RNA in COVID-19: A case report”
      “False‐negative of RT‐PCR and prolonged nucleic acid conversion in COVID‐19: Rather than recurrence”
      Non-peer-reviewed: “Reinfection could not occur in SARS-CoV-2 infected rhesus macaques” (with: https://www.nature.com/articles/s41577-020-0316-3 )

  79. UK-Weather Lass-In-Earnest

    Interesting paper predicting that there are as many as 237 community cases in England for every case officially reported. It cites the wide variations in clusters of the disease. The work was headed by Dr Adrian Heald, Salford Royal Hospital, and conducted by members of the University of Manchester and others. It concludes that 29% of the population may have already had the disease and therefore have increased immunity.

    https://onlinelibrary.wiley.com/doi/abs/10.1111/ijcp.13528

    • Thanks for bring this up. I will read the paper.

    • This is indeed an interesting paper. If correct, it confirms the findings in the US that infections are 10-80 times higher than reported cases. Nic do you agree with the paper’s findings?

    • It’s an interesting paper. Its key finding is that the current average infection rate (new/existing infections) across 149 local authorities is negatively related to the total reported cases per thousand population, very significantly so (p < 0.0001) although the relationship is noisy (R^2=0.22) and not that steep. This is certainly consistent with growing herd immunity reducing the infection rate, but there may be other factors involved as well.

      • Nic: It should be obvious today that the conclusions reached by this paper are wrong. The authors EXTRAPOLATED that 29% of England had been infected as of the date this paper was written (4/19/20). However, the number of confirmed cases in the UK has more than doubled since then and the rate of new cases/day has remained approximately constant. There isn’t a robust sign that England has moved from 29% to more than 60% of the infections needed to produce herd immunity. The linear extrapolation in Figure 4 projects that the rate of new cases should have fallen by a factor of at least 2. That linear projection didn’t come with confidence intervals for the slope – and the authors admitted they had no reason to believe the relationship was linear.

        Figure 4 extrapolates from a relatively narrow range (3-fold) of infection rates and y values that have wide confidence intervals sub-national population is involved. (One plot of R for US states came with a wide confidence interval for all but the largest US states that left no significant difference between the vast majority of states. The confidence interval for California, roughly the same size as England, showed that R was unambiguously below 1, but not for any other state). Extrapolation from a narrow baseline on the x-axis and highly uncertain values on the y-axis is an inherently risky proposition.

        The antibody data showing that there are many more (40-80X?) silent infections that haven’t been detect by PCR tests was obtained in the early days before anyone had any idea of the false positive rate of the test used and whether there was any cross-reactivity detecting antibodies from coronaviruses that cause the common cold. When you test large number of people with a low incidence of infection with a test that produces large numbers of false positive, most of the positives reported will be false positives. After the CDC withheld PCR tests that hadn’t been been checked for reliability in February, they approved the sale of antibody tests without quality control checks.

        “Under normal circumstances, CTK Biotech would have to collect data for FDA approval of a novel diagnostic at three different sites, but under the emergency use authorisation issued by the agency in mid-March, this is no longer necessary. “Basically [the FDA authorisation] says, ‘You can start selling right away and then send us your data, and if we don’t like it, you have to take your product back’”, says Sam Lewis, CTK Biotech’s director of research and development.” (Lancet April 4, https://doi.org/10.1016/S0140-6736(20)30788-1 )

        Does anyone know of an article that reviews the interpretation of these early antibody results in light of the best information that is available today? IIRC, the FDA has withdrawn marketing approval for some tests.

    • Matthew R Marler

      UK-Weather Lass-In-Earnest: It cites the wide variations in clusters of the disease.

      Some days after you posted the link, I finally read it in a different context. To me the most interesting finding was that the rate of decline in R0 was unrelated to any of the covariates except the total fraction of the people already exposed; it suggests that the widespread acquisition immunity might have been more important in stemming the spread of SARS CoV-2 than anything else.

  80. Nic, not sure how to contact you other than through the post. I sent you the Gomes et al. paper. I live in Minnesota and the state has actually been very transparent. They just put up the new version of their model including the full code. You can find it here through links at the bottom of the page. The technical paper and presentation are useful and their is a youtube of the briefing they gave. I wrote a long critique of the original model and am writing one of this one. But I am not a math person. Be really good to see what you think of the work. It is an interesting example of how screwed up a model can be despite one’s best efforts. They tried to fit the model to Minnesota’s experience to date and claim to have done so, but the model predicts a number of deaths for the rest of May that simply can’t be achieved. And on and on. Anyway, hope you will take a look. https://mn.gov/covid19/data/modeling/index.jsp

    • Thanks, Kevin, I recall that it was you who helpfully drew my attention to the Gomes et al. paper.
      Thanks for the link to the Minnesota model. I’ll take a look when I get a chance.

  81. nobodysknowledge

    A new Spanish study shows that about 5% of the population is infected, much less than has been expected from other studies. The conclusion from this is that Spain is far from herd immunity.
    What is shown from most European countries now, is that the COVID-19 outbreak comes under control, and the countries can open up again. It seems that social distancing has been very effective. By testing and tracking the countries have a realistic hope of avoiding new outbreaks. The virus is less contagious than feared, as the infections stop in many areas. So perhaps the virus will die out locally many places, long before herd immunity is reached. It would be interesting to have some calculations on this.
    Restrictions have to be maintained, but they need not be economically devastating.

    • nobodysknowledge

      One hypothesis could be that social distancing has an effect on how the population inhomogeneity is working, so that different kinds of distancing have different outcomes.

    • “It seems that social distancing has been very effective.”

      could it not be; the silly hats we did wear; or not wear; or blowing tiger horns?

      How easy it is for us to make confident statements:

      “Oft-repeated claims are frequently mistaken for facts”

      Tom Sowell

  82. God morgon:

    • Bernie Sanders Dreams Of ‘Scandinavian Socialism.’
      Is there anything else we can do to get rid of Sanders?

      • Don Monfort

        ‘Scandinavian Socialism’ is just the bait. The hook is that for socialism to sustain itself for any length of time it has to be totalitarian socialism. I am sure that’s the message that this pointy head is trying to get over with the connivance of the NYslimes. Sweden socialism too soft.

        We are having an infestation of these pompous pointy heads, who drop in to abuse Judith’s hospitality solely to annoy the denier denizens and to denigrate the blog proprietor. They rejoice in and exploit bad news, because all bad news is “Trump’s fault.” They are going to be beaten, again.

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  84. Richard Gilbert

    In my May 12 contribution to this thread, I noted the possibility that the overall IFR for covid-19 will eventually be found to be below 0.1% – building on the work of Sunetra Gupta and her team at Oxford University.

    Calculations by Terence Corcoran in today’s Financial Post (Canada) suggest that with an overall IFR of 0.1% the economic benefits of Canada’s lockdown policy would be in the order of $50 billion.

    The economic costs would be about $660 billion, i.e., more than 10 times greater during 2020 alone (see https://business.financialpost.com/opinion/terence-corcoran-the-price-of-life-lockdown-costs-are-real-but-are-the-benefits).

    According to Corcoran, the economic benefits outweigh the costs only when the overall IFR rises above 0.5%.

    Given that the overall IFR is likely to be well below 0.5%, it’s becoming apparent that we are living through a travesty of public policy that sacrifices the young and the poor for the questionable benefit of the old and the rich.

    • > First the costs. The ultimate dollar value of costs will eventually be relatively easy to calculate. Until then, rough estimates are the best numbers available.

      How absurd to attribute all GDP loss to the “Lockdowns” as distinguished from a raging pandemic. Of course, by doing that you make confirming a bias “easy” indeed.

  85. a fan of irony – some thoughts for consideration:

    Trump supporters rail about the “lockdowns” as tyranny, yet ignore his pivotal role them being institited.

    Trump supporters rail against the Imperial College projections, yet ignore Trump’s constant reference to them to promote his greatness.

    Trump supporters say testing isn’t really necessary, uett ignore the wall to wall testing at the Whitehouse.

    Trump supporters praise a “herd immunity” approach AND support Trump who days we’ll have a vaccine very, very soon. But to the extent that a herd immunity approach will work, it relies on the logic of trading off a lot of people dying and getting sick quickly (even assuming the idea that protecting everyone vulnerable, which is highly unlikely) for a slower rate of infection. If a vaccine is developed and distributed quickly, it may well mean that many people will get sick and die needlessly in comparison to a long and slow approach to infection.

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  92. Nic: If I understand correctly, you and other have devised a hypothesis that says epidemics should be modeled using equations that contain terms describing a population composed of individuals a range of infectivity and susceptibility. The next step in the scientific method is to devise an experiment that can distinguish between accepted theory and a hypothesis that modifies that theory. Allowing a serious pandemic to spread until stopped by “herd immunity” on the basis of an untested “hypothesis” isn’t an attractive option for responsible policymakers being advised by experienced public health officials who have dealt with Ebola, HIV, Polio, influenza, small pox and other pandemics without recognizing a need to modify the equations that model these phenomena. Since we can’t experiment upon humans, we need to use natural experiments that nature has provided for us. Sweden is a natural experiment in government policy, but Swedes are likely to have changed their behavior.

    Question 1: Given that transmissibility changes because of changing human behavior (fear) and changing government policy (R(0) becomes R(t)?) will it ever possible to conclusively distinguish between pandemic slowing because of: a) inhomogeneity in susceptibility and infectivity and b) changes behavior and policy? I presume the data from Stockholm be explained by changing behavior and policy. (I’m sure you are familiar with the saying that an elephant shape can be modeled with four parameters and his trunk wiggled with five. And Occam’s razor recommends the simplest model capable of explaining the data, but doesn’t PROVE anything.)

    When I looked at data from the US, I found almost perfectly exponential growth (R^ = 0.998) in cumulative cases with a 2.5 day doubling time from 3/4 through 3/25. An obvious discontinuity between 3/3 and 3/4, suggests the trend started at least as early as 3/1, when there were only 40 cumulative cases. I don’t think I’ve ever seen data showing a change of nearly three orders of magnitude (10 doublings) that fit a theory so well. The viral transmission that produced these cases presumably occurred about a week earlier. So this period of exponential growth ended when US policies to slow transmission were implemented and people became more fearful. For the last month, a doubling time of 20-35 days provided a good fit (but isn’t distinguishable for linear growth). The change in the transmission of the disease occurred when only about 0.1% of Americans with confirmed infections (and an unknown number having undetected infections), so it was not due development of “national herd immunity”, but this doesn’t conclusively prove that “local herd immunity” wasn’t developing in some places.

    Cruise ships and prisons are great natural experiments. About a week ago, 86% of the prisoners in Ohio prison had tested positive. Superficially, that means that only a small fraction of the population can have very low susceptibility. However, I would expect R0 in a prison population to be much higher than R0 in the normal population, so you wouldn’t expect herd immunity in a prison at the same level as in the general population.

    The annual seasonal influenza epidemic may provide some information. Does it die out every spring because the annual 30 million Americans infected each winter plus the 50% of the people vaccinated each year, plus the existing, but fading, resistance from previous influenza seasons produce “herd immunity”. Obviously seasonal differences in transmissibility also play a role in the timing of seasonal influenza. Pandemic influenza (due to a new strain) has ignored season because few in the population are resistant.

    Another natural experiment occurred when Europeans first arrived in North American bringing new viral pandemics. In New England, I’ve read that 90% of Native Americans died. The Pilgrims planted their first crops on fields that had been cleared by a Native American community who died out after European fisherman stopped there for fresh water a few years earlier. This ancedotal evidence could be inconsistent with herd immunity developing well below 1-1/R0.

    The most useful natural experiments may be vaccination campaigns. If the traditional equations for modeling pandemics were adequate, the incidence and spread of outbreaks should diminish as vaccination rates approach 1-1/R0. Since it takes time for behavior and public policy to change in response to an outbreak, the spontaneous disappearance of pandemic disease around 1-1/R0 may be the clearest proof that current equations adequately model the population.

    Respectfully, Frank

    • > Allowing a serious pandemic to spread until stopped by “herd immunity” on the basis of an untested “hypothesis” isn’t an attractive option for responsible policymakers being advised by experienced public health officials who have dealt with Ebola, HIV, Polio, influenza, small pox and other pandemics without recognizing a need to modify the equations that model these phenomena. Since we can’t experiment upon humans, we need to use natural experiments that nature has provided for us. Sweden is a natural experiment in government policy, but Swedes are likely to have changed their behavior.

      +1

      • Crippling our economy and restricting personal freedom is not an attractive option either, of course. We can’t test the hypothesis Nic is promoting without risk, so we need to analyze existing natural experiments.

        There are some interesting parallels with climate sensitivity in climate science. The ice ages and earlier geological eras with changed climate are poorly-controlled natural experiments with poor data. The last few decades of apparently-forced warming provide increasingly compelling evidence that existing climate models can’t reliably determine ECS. (Work with ensembles of models with perturbed parameters suggests that the higher ECS of models is not due to bias in parameterization.)

      • Frank –

        > Crippling our economy and restricting personal freedom is not an attractive option either, of course.

        No doubt. But we’ll never actually know how much of that has been due to the government interventions vs. normal reactions to a raging epidemic.

        Just as we’ll never know how much reduction in transmission/deaths was due to normal reactions and social distance vs. government interventions.

        Even cross country comparisons are so riddled with confounds they’re virtually worthless.

    • franktoo,
      On your final point, your argument is wrong. In a natural epidemic, the most susceptible people (who probably also have the highest infectivity) are selectively infected and thus become immune. That reduces the average susceptibility of the remaining uninfected population. That doesn’t happen with vaccination, which is at random with respect to susceptibility. So the (1 – 1/R0) classical HIT value remains correct for vaccination even in an inhomogeneous population.

      On the native population point, remember that the HIT depends on R0, and for some viruses RO is far higher than for SARS-Cov-2 – over 10 in some cases. And the immune systems of native people may never have experienced similar viruses, whereas humans have experienced viruses that are not greatly dissimilar to SARS-CoV-2 and many of them may have some degree of resistance to it.

      To my mind, the value of the Stockholm data is that it indicates that the epidemic peaked and then started shrinking a considerable time after the government policy and unforced behavioural changes occurred about 2/3 of the way through March. That would be consistent with herd immunity having now been achieved, for the recent levels of social distancing, although I accept that it does not prove definitively that it has been.

      • Terry Jones

        and Nic a lot of these assumptions ignore previously well described features like DIPs: defective interfering particles; so Hope-Simpson in his 1992 book drew folks’ attention to them; as a flu epidemic ramps up, the number of DIPs being produced rockets; and the epidemic falls away as rapidly as it started; a bell-curve;

        I fear we are profoundly ignorant of the subtleties of what is happening; we say herd immunity as the infection rate fall; I commend

        Hope-Simpson RE: The transmission of epidemic influenza New York:
        Plenum Press; 1992

        to everyone; a must read before confidently opinioning: lest I be accused of that heinous crime, I would say I just urge “hesitate” and “reflect” and “pause” as verbs. all best wishes to all.

      • > I would say I just urge “hesitate” and “reflect” and “pause” as verbs. all best wishes to all.

        +1

      • NIc: Agreed: If there are significant differences in susceptibility, then vaccination if not an appropriate “natural experiment” for learning about development of herd immunity during a pandemic.

      • Nic: In addition to the prison in Ohio with an 86% infection rate I mentioned several weeks ago linked article in the Atlantic (with links to CDC reports) cites several super-spreader events where researchers have produced extremely high infection rates:
        1) 53/61 (87%) singers became ill after a SINGLE 2.5 h choir practice in Washington.
        2) 78/137 (57%) of workers in one room of a Korean call center tested positive.
        These appear to be natural experiments where a large group of people were exposed to an aerosol-infected virus and a large percentage of the people were susceptible to getting the disease. (It would be hard for one person to infect so many people by droplets, so I assume the bulk of these events were aerosol mediated.) As best I can tell, these experiments demonstrate that your hypothesis is incorrect, at least for transmission by super-spreaders. And I have read elsewhere that most transmission in this pandemic is done by super-spreaders: R_0 has been reported to be 3-6, but the median infected person infects ZERO others. (Sorry, I don’t have a citation for that.)

        Respectfully, Frank

      • Frank –

        Bergamo, Italy has been reported to have a very high population infection rate – and Lombardy in general as well. I already gave Nic a reference.

        https://judithcurry.com/2020/05/10/why-herd-immunity-to-covid-19-is-reached-much-earlier-than-thought/#comment-916652

        And Chelsea, MA.

        As for superspreaders, a preprint – taken with a grain of salt

        > A comparison between reported and model-estimated case numbers indicated high levels of transmission heterogeneity in SARS-CoV-2 spread, with between 1-10% of infected individuals resulting in 80% of secondary infections.

        https://www.medrxiv.org/content/10.1101/2020.05.21.20104521v1

      • That said, I think that the infection rates determined by seroprevalence studies are highly suspect. All the studies I’ve seen have big problems with sampling.

        This is a good explication of the problems with sampling – in particular with the convenience sampling seen with many of those studies.

      • Joshua
        Thanks for the link to the superspreader paper.
        I agree with you that non-random sampling (and varying test characteristics) means one has to be a bit cautious in interpreting seroprevalence study results, some more so than others.

  93. Nic: I think it is unlikely that humans differ GREATLY in their susceptibility to viral infections because our immune systems were carefully tuned by evolution to produce an optimum balance for preventing infection and cancer without causing auto-immune disease. If some fraction of the population had superior ability to prevent viral infection, when half of children died before reproducing, survival of the fittest would ensured that this ability was found in everyone. The hemoglobin mutation that causes sickle cell disease is only found in areas where it provides resistance to malaria.

    There are several exceptions to the above generalization. The adaptive immune system (antibodies) provides resistance to infections we have experienced before and closely related infections (cow pox and small pox). Mutations in the ACE receptor used for viral entry obviously could protect people with that mutation. Mutations in the major receptor used by HIV (there are two) provides resistance to AIDS.) Both of these phenomena provide major resistance one type of virus, but not to all viruses.

    Other differences reduce the susceptibility to all viruses. Differences in personal hygiene (health care workers and children, for example) provide resistance to transmission and number of interpersonal contacts (politicians vs hermits, high vs low density communities?) create the appearance of varying susceptibility. During pandemics, government policies and fear try to make us behave like doctors and hermits. To prevent an immune response during pregnancy, the mother’s immune system is suppressed during pregnancy and the baby’s immune system slowly matures after birth. And the immune system of the elderly is limited as more cells in the immune system reach their pre-programmed limits on division (that exist to prevent cancer).

    Once past these differences (which should be understood by traditional epidemiology), everyone is fighting off SARS using the same biological machinery. Individual cells have no defense against viruses; in a cell culture experiment all of the cells eventually die from viral infection. White blood cells kill human cells recognized as foreign as foreign viral proteins begin to be found on the surface as viruses assemble using lipid bilayer from the host cell. Interferons suppress protein synthesis in nearby cells so that they are less useful when a virus invades and viruses make proteins to count both of these responses. Our bodies are designed to that the early battlegrounds in the nose and throat don’t carry out essential functions. In the case of COVID-19, children and adults usually build up large loads of viral RNA in nasal tissues, but few children and more than half(?) of adults are asymptomatic or mildly symptomatic despite the raging infection. (AIDS takes about a year to develop after infection, because the war between the immune system and HIV, which replicates in T-cells, goes on for a year before T-cell count begins to diminish.) Life-threatening COVID-19 disease is trigger when the infection moves elsewhere in the body before enough antibodies have developed (after about week). Antibodies normally bind to specific viral antigens and therefore don’t poses as great a threat of auto-immune disease as the rest of the immune system. Antibodies are created by recombination of genes followed by cell division, a process that takes most of a week. I read somewhere (but didn’t properly research) that super-spreaders are people who fail to mount an antibody response to a viral infection and probably don’t develop serious symptoms that immobilize people who get desperately ill as the infection spreads. Since I assume everyone infected with enough SARS-CoV-2 will produce large amounts of (infectious) viral RNA, for me the mystery is why some people develop life threatening infections in their lungs or elsewhere and others (including most children) do not.

    One big variable between people is the number of viruses that cause the initial infection. Experiments with animals show that a single virus or ten viruses don’t cause viral disease. You need to breathe in one sizable drop infected with virus or a large number of smaller aerosol droplets with viruses to establish an infection. The initial dose of virus (multiplicity of infection) or the site of infection may be responsible for the different course of disease in different people.

    In conclusion, because we all fight viral infections with the same biological machinery, I’d guess that everyone is similarly susceptible to developing a viral infection that can be passed on to others – but not necessarily equally susceptible to that infection becoming life-threatening or debilitating enough to stay home or in bed. In the case of COVID-19, limited evidence shows that life-threating problems usually develop after RNA levels have begun to fall in response to antibodies.

    • It’s quite clear that the susceptibility to covid varies dramatically by age cohort. Virtually all young people have a very mild and short coarse. A brother of a colleague of mine is an MD and us 30. He had a mild sore throat and fever for e days. When he volunteered at a NY hospital he was tested and was positive. This is typical.

      • dpy6629: From the epidemiology point of view, one only needs to be susceptible enough to pass the infection on to others. That requires high levels of viral RNA in the upper respiratory. People with mild symptoms or no symptoms including children can have high levels of viral RNA and presumably be infectious. And viral RNA levels in the upper respiratory symptom begin to drop before severe illness develops and sometimes before symptoms develop – but few people without symptoms are tested and tested multiple times, so you can find contradictory opinions on this subject.

      • I’m not sure we know that for sure Frank. It makes sense to me that very mild illness would be associated with much lower viral load.

      • Susceptibility in younger age groups is actually quite high. The risk of serious infection is lower. The converse is true for older age groups. This makes sense because ACE2 is the target, ACE2 is important for BP regulation, and ACE2 levels drop with age.

      • dpy6629 wrote: “It makes sense to me that very mild illness would be associated with much lower viral load.”

        However, this generalization isn’t always or perhaps not even usually correct. See Lancet and especially reference #1 therein. DOI:https://doi.org/10.1016/S1473-3099(20)30237-1

        Infectiousness clearly depends on the amount of RNA in the upper respiratory tract that can be ejected into the air by an infected patient. (Patients coughing and blowing their nose more often may eject more contaminated fluid into the air, but by the time a patient is severely ill they are less mobile and can transmit to fewer people.) An infection never starts with a single virus; thousands may be need. They can to be present in one large droplet or many tiny aerosol droplets, so concentration (viral titer) is critical to infectiousness. This is what nasal swabs measure. No one dies from having a viral infection in their nasal tract – that infection must migrate to a critical organ. We can’t easily sample virus in deep lung tissue or other critical organs. There is relatively little SARS virus in the blood (viremia), but that isn’t always the case for other infections. The immune system can win the battle in the upper respiratory tract and leave no detectable viral RNA there, and lose the battle in the lungs. Actually many patients die drowning from the residue left by that battle in the lungs. Some drowning patients are given immuno-supressive drugs to dampen down the immune response and prevent such drowning. During the 1918 influenza pandemic, an unusually large fraction of the victims were 20-40 year olds who died quickly from the fluid that built up in the lungs because of a robust immune response. So RNA is a better measure of infectiousness than of severity of illness.

        There is a difference between the detection of viral RNA by PCR – where only a short segment of viral RNA must be intact – and the much more laborious detection of infectious virus (full length 30,000 base pairs of viral RNA plus viral proteins plus host cell lipid bilayer) by adding a diluted sample to a culture of susceptible human cells and counting the number of spots with localized cell death a day or two later. Viral RNA is detected in patients by PCR long after infectious virus can be verified by laborious cell culture experiments.

    • Stephen Anthony

      Franktoo,
      Black And Minority Ethnic groups seem to suffer much more and die more frequently than natives in the UK. Could be that it’s not due to being more infectious or susceptible but the fact remains that there is a difference.
      You seem to be also ignoring the evidence for super-spreaders.
      Some people have very wide social networks, these are likely to infect others first and be among the first to be infected.

      All that is required for Nic’s hypothesis to work is for these differences to exist, as I understand it.

      If you want to continue with believing in the classical herd immunity threshold, how can you explain the Diamond Princess infection rate of only 20% or the Theodore Roosevelt aircraft carrier with an infection rate of 1/6 or Nic’s example of the Stockholm data?

      • > If you want to continue with believing in the classical herd immunity threshold, how can you explain the Diamond Princess infection rate of only 20% or the Theodore Roosevelt aircraft carrier with an infection rate of 1/6 or Nic’s example of the Stockholm data?

        The same way you’d explain 60% + infection rates in Bergamo Italy, or 30%+ in Chelsea, MA, or very high rates in various prisons or long term care facilities, or among meat packing workers.

      • Terry Jones

        “If you want to continue with believing in the classical herd immunity threshold, how can you explain the Diamond Princess infection rate of only 20%”

        We have an innate immune system Stephen; no-one tells us this; it produces AMPs (anti-microbial peptides) under the stimulus of Vit D: cathelicidin and beta-defensins are two more words I can use to impress;
        so rather like a rugby player who fends off would-be tacklers, with a push of hand, an AMP does not need to “know” the invader, to kill it. So no record of the kill; AMP is the silent assassin.

        The adaptive immunity; that amongst other things creates antibodies; is actually quietened by Vit D: so in the height of sun, when we have had plenty of sun exposure, we have a heightened innate system; and a dampened adaptive system; yet we are at our best.

        Blessed is the depth of our ignorance; we have these unstated assumptions about viruses: they are out to destroy us; we can only defeat them by adaptive immunity: antibodies are what kills them; blessed be our ignorance.

        If one googles on DIPs: defective interfering particles: folks will find that as an flu epidemic ramps up, there are more and more of these DIPs being produced; so they are like dud cartridges; they not propagate; so the epidemic winds down as quickly as possible.

        All this talk of “vaccines”: implies adaptive immunity. We are healthiest out in the sun; all these respiratory viral epidemics are profoundly seasonal; in the northern european late winter; gone by summer; we need to repel invaders “on the beaches” and let our innate system do its work. Get sun; get your Vit D up; avoid sunblocker for 15 mins at midday: it has worked for thousands of years.

      • Steven Anthony: 86% and growing or 2000 prisoners in one Ohio facility have tested positive for COVID-19. Why isn’t it logical to assume that the same thing failed to happen of the Theodore Roosevelt because the ship was evacuated in time, and on the Diamond Princess because individual cabins allowed for effective social distancing?

        Yes, this pandemic has slowed with cumulative cases far too low for herd immunity. Is the reason fear and policy? Or depletion of the most susceptible members of the community, leaving the rest with herd immunity? I asked Nic if there were a way to distinguish between these two hypotheses, but didn’t receive an answer.

        In the US, the number of cases doubled every 2.5 days in March except for a slight reduction during the last week. That 5000-fold exponential increase in cases slowed dramatically in the next two weeks. Given a period of about one week between infection and detection of infection, it seems clear to me that the timing was about right for policy and fear to have been responsible for the end of doubling every two days. At the end of March, fewer than 0.1% of the US population had been infected. It seems unlikely that the slowdown was caused by approaching herd immunity at such a low percentage – unless there were about 100 undetected cases for every confirmed infection. Hopefully antibody tests are now or will soon be producing a small enough number of false positives so that we have a better understanding of this problem.

        The two countries with the lowest cumulative cases per capita are Taiwan, China, and South Korea (recently 18, 58 and 212 per million), precisely those countries that have taken the most stringent measure to protect public health. In Wuhan, they eventually resorted to mandatory quarantine away from home of everyone who was in contact with newly diagnosed patients and they had a team of 9,000 contact tracers identifying those contacts and following up daily to be sure they remained in quarantine. In South Korea, the vast majority of all purchases are made with credit cards. When you test positive, health officials immediately access the location of your purchaser and publish the places and times and identify who else was in the same location at the same time. South Korea, like many densely populated places in Asia, were badly scared by SARS and MERS and very critical of the response of their public health system. They were ready to implement measures the West hasn’t adopted. Hong Kong began taking the temperature of every passenger arriving from the rest of China about January 1, 2020, immediately after they learned that the Wuhan city website was warning citizens to wear masks because a new and deadly pneumonia (like SARS). At the same time I wrote down the above cases per million for these three Asian countries, the US had about 4,000 cases per million and most of the EU had 2,000-4000 cases per million. Clearly government policy and fear have brought the pandemic under control in these Asian countries with cases per million far below whatever herd immunity might be developing in the West.

        I listened to a talk discussing the 1832 cholera pandemic in Paris, which caused the highest per capita death rate since before the French Revolution. France had an estate tax with no exemption (paid on the first franc), so economic historians know wealth distribution of those who died in the 1832 pandemic and in normal years. The cholera epidemic caused more deaths among the less affluent then also. The suggested explanation for this general phenomena was that poorer people are in poorer health in general (poorer nutrition, do heavy work for longer hours, poorer heating) and therefore have poorer outcomes when they get ill. Heart disease, diabetes, obesity and other factors associated with greater lethality in COVID-19 are more common in minorities and the poor. Blacks are also genetically more susceptible to high blood pressure. I’m talking here about differences in lethality, not differences in an infection being established in the upper respiratory tract (where it can be passed on to others). Clearly living in more densely populated areas and closer together inside also makes it more likely that the poor with transmit disease to other poor.

    • “Nic: I think it is unlikely that humans differ GREATLY in their susceptibility to viral infections”

      thanks franktoo;

      Actually; humans and primates have Vit D receptors; and our innate system is strongly controlled by Vit D: so mice, rats etc do NOT have this Vit D factor; so we are, it would seem, quite different to lab animals we test on.

      It should cheer us: get out in the sun; make Vit D: or in a winter, consume it;
      https://virologyj.biomedcentral.com/track/pdf/10.1186/1743-422X-5-29

      I am sorry if that seems glib; but there is great truth in it: I too have only realised this recently.

      https://www.ncbi.nlm.nih.gov/pubmed/16959053 please even just read the abstract of this paper; to see if it can pique your interest to read the whole paper. This is all more complicated than we might wish it to be: we need to be overawed by how much we don’t know.

      • Interesting information on Vitamin D. I heard Vitamin D mentioned at a talk yesterday. Unfortunately, most papers say that its mechanism of action is to release more antimicrobial peptidees (AMPs). Antimicrobial peptides are amphiphilic peptides that exploit differences between the cell membranes of mammalian cells and those of bacteria and fungi. Unfortunately, enveloped viruses (like influenza and SARS) get their cell membrane (lipid bilayer) from the host cell it effects. So it isn’t obvious why AMPs should selectively damage the lipid bilayer of viruses at a lower concentration than they damage the lipid bilayer of host cells. You can get an antiviral effect by damaging the bilayer of the virus or the bilayer of the host cells. This doesn’t mean that Vitamin D can’t be involved in the seasonality of influenza; it just suggests that AMPs don’t mediate the effect of VItamin D. I didn’t look into this subject long enough to be confident of the my suspicions.

  94. Does this remind anyone of anything?:

    • Joshua: Does this remind anyone of anything?:

      What did you have in mind?

      Bergstrom: https://onlinelibrary.wiley.com/doi/epdf/10.1111/ijcp.13528

      The paper is interesting. It tries to relate changes in R0 across time to demographic differences between regions..

      Abstract: This article is protected by copyright. All rights reservedAbstractBackgroundThe COVID-19 pandemic has led to radical political control of social behaviour. The purpose of this paper is to explore data trends from the pandemic regarding infection rates/policy impact, and draw learning points for informing the unlocking process. MethodsThe daily published cases in England in each of 149 Upper Tier Local Authority (UTLA) areas were converted to Average Daily Infection Rate(ADIR), an R-value – the number of further people infected by one infected person during their infectious phase with Rate of Change of Infection Rate(RCIR) also calculated. Stepwise regression was carried out to see what local factors could be linked to differences in local infection rates.FindingsBy the 19th April 2020 the infection R has fallen over the from 2.8 on 23rd March before the lockdown and has stabilised at about 0.8 sufficient for suppression. However there remain significant variations between England regions.Regression analysis across UTLAs found that the only factor relating to reduction in ADIR was the historic number of confirmed number infection/000 population, There is however wide variation between Upper Tier Local Authorities (UTLA) areas. Extrapolation of these results showed that unreported community infection may be >200 times higher than reported cases, providing evidence that by the end of the second week in April, 29% of the population may already have had the disease and so have increased immunity

      It would be a good method to repeat in other data sets, and eventually to make cross-country comparisons. Like everything else we read, it ought not be regarded as definitive.

  95. Pingback: Only about 1.7 percent of Danes had Covid-19 antibodies back in April – Philip Greenspun’s Weblog

  96. John Daschbach

    I have some questions about the SEIR model used here. (I have the R code Nic supplied). I write an SEIR model (without population changes) as S^\dot = -\beta S I; E^\dot = \beta S I – \kappa E;I^\dot = \kappa E – \gamma I;R^\dot = \gamma I so that R0 = \beta/\gamma. The code Nic uses for the ODE’s has (for \rho = 0 as supplied) S^\dot = -\beta Sy S (\sum I * Iy)/N . At every point in time during the ODE calculation he is using an average \lamba = \beta \sum(I * Iy) /N for every set of ODEs. I do not think this is correct. Consider that instead of running m sets of ODEs in a single call to ode() you ran m separate ODE calculations. Then each set of ODEs would use it’s own value of I*Iy, not the sum(I*Iy)/N. Further it is unclear why when the sum() is over N/m equations the normalization for the sum is not N/m but N. Nevertheless, it should be clear that the calculation using a common value for \lamba for all sets of ODEs is not the same as the SEIR model. It’s not clear to me there is any mathematics to justify using a single value of \lamba for every independent set of ODEs. I will code up the more standard approach of calculating each set of ODEs independently and check. While a different calculation, calculating a SIR model with \beta chosen from a distribution changing every \tau time units, (in run heterogeneity) shows very little difference from one using a constant \beta.

    • I think Mr. Lewis is right on that point.

      The susceptible folks in any population bin are according to the model exposed to the infectious folks in every bin. So they’re all exposed to the same, common “infection power” sum(I*Iy).

  97. John Daschbach

    No, that is not the mathematics in the Nic Lewis code. As he notes above the CV factor “However, since COVID-19 transmission is very largely person-to-person, much of the inhomogeneity in transmission rates will reflect how socially connected individuals are, and how close and prolonged their interactions with other individuals are.” is directly dependent on social connections. When every channel is connected to the same mean infection pool you have explicitly removed social connection from part of every channel. Think about the resulting mathematics. What are we learning? Holding the primary distribution of I uniform is not a CV model, in fact it’s the opposite having nulled the social connection channel on I.

    • John Daschbach, may I suggest that you study the Gomes et al. paper. I think you will find that the mathematics of my code reflects the modified SEIR equations in that paper, save for my further modification to allow for not all variability in susceptibility and in infectivity being in common.

      The social connection variability factor affects the average “force of infection” both via more susceptible people being overpresented in the infected pool (since they are more likely to have been in contact with an infected person) and in those same people being more infective (since they are more likely to meet a susceptible person). Hence my mean(Sy * Iy) multiplier (recall that Sy and Iy both reflect the common social connectivity factor, as well as any unconnected variability).

      That common average “force of infection” then applies to all susceptible people, but infects them probabilistically according to how susceptible they are.

  98. from here https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2870528/

    “Volunteers inoculated with live attenuated influenza virus are more likely to develop fever and serological evidence of an immune response in the winter.” https://www.ncbi.nlm.nih.gov/pubmed/562369

    So in summer, with Vit D, the innate system is up-regulating; so AMPs and T-cells “repel the invaders” and the adaptive system is down-regulated

    In winter, with low Vit D levels, the innate system is depleted; more invaders so adaptive up-regulates and “fever and serological evidence of an immune response in the winter” …..

    I saw all this because folks seem to me; to have this concept: of antigen-antibody as a very fixed thing; like 2 lego bricks sticking together; and that the adaptive system (producing antibodies) is the only system we have; and that it is fixed;

    I am suggesting strongly that respiratory viral infections are profoundly seasonal; check on the data: late winter is when they hit; you don’t get flu (and other respiratory viral epidemics in the UK summer);

    In down-regulating the adaptive system, Vit D “acts as an immune system modulator, preventing excessive expression of inflammatory cytokines”;

    which is what it is very fashionable to talk about; thank you for listening; my best wishes to all

  99. John Daschbach

    I will read the Gomes paper but your last paragraph causes some worry. What you are doing is not “all susceptible people, but infects them probabilistically according to how susceptible they are.”. What you are doing is holding I at the average value for all time during the integration in every channel. Calling it the “force of infection” is a bit misleading. I is only the number of infections at time t.

    So what are the physics required to satisfy this model? That’s very simple. It is the limit of infinite human mobility for Infected people. In the view of the model given here Infections are perfectly mixed at all times. (for now lets ignore the apparent high transmission rate in the late Incubation, early Infected period).

    At this stage in the pandemic infinite mixing of Infected people is so far from reality I question why it’s considered.

    • “What you are doing is not “all susceptible people, but infects them probabilistically according to how susceptible they are.”. What you are doing is holding I at the average value for all time during the integration in every channel.”

      No, the “force of infection” is recalculated at each time step by averaging the infectivity of the currently infected individuals, and susceptible individuals then become infected probabilistically according to that average force of infection and their own susceptibility.

      “At this stage in the pandemic infinite mixing of Infected people is so far from reality I question why it’s considered.”

      I am using a standard, simplified model of epidemic progression, that has been found in much previous epidemiological work to provide reasonable results despite its simplifying assumtions being of questionable reality.

  100. John Daschbach

    I have some experience with coupled ODEs in other contexts.

    https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.92.198306

  101. talking of defective interfering particles, that are produced in viral replication
    https://en.wikipedia.org/wiki/Defective_interfering_particle

    where “blanks” are produced;

    “when defective particles increase, the amount of replicated non-defective virus is decreased. The extent of interference depends on the type and size of defection in the genome; large deletions of genomic data allow rapid replication of the defective genome.”

    So they interfere with what should be happy, unlimited viral replication: why? Defective production? ……… possibly …… but …………

    Alternatively, they may be produced for evolutionary reasons, such as the stimulation of innate immunity (8–10), that could favor survival of the host species and hence perpetuation of the virus population itself”

    Click to access zjv5217.pdf

    So many seem to see the goal of a virus as an external invader; intent on destroying the host it invades; but if we reflect; the virus only lives in its host: there must surely be a symbiotic relationship; no host = no virus; do our models see that?

    should we not contemplate that a virus is like the mafia: it just wants its cut:it just wants to stay around; it just wants to be “Mr 10%”:each and every year; it needs its host to continue surviving, so that next year it again gets its cut, and continues to be around …

    so by producing DIPs, it self-limits its own otherwise destructive powers: we know surely each of these respiratory viruses show a bell-curve of on and quickly off;

    in the ways plants throw out seeds, viruses self-replicate in what to them are good times: winter; the respiratory virus makes gains; but not too many; when Vit D levels are low; and innate immunity is depressed;

    As this paper said https://virologyj.biomedcentral.com/track/pdf/10.1186/1743-422X-5-29

    Why do epidemics end so abruptly?

    Could the virus be controlling this by its DIPs:

    As this paper https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3185524/pdf/viruses-01-00895.pdf is entitled

    “Defective Interfering particles (DIPs): Foes of Viruses and Friends of
    Virologists “

  102. Stephen Anthony

    franktoo,

    Thanks for your detailed reply.

    I was unaware of very highly infected populations until I started reading this thread. It does blow a hole in my argument based on the ship examples. I don’t think that it affects Nic et al’s hypothesis in the same way.
    Prisons seem to be an extremely disease friendly & unnatural environment.

    In an earlier comment you stated “I think it is unlikely that humans differ GREATLY in their susceptibility to viral infections because our immune systems were carefully tuned by evolution to produce an optimum balance for preventing infection and cancer without causing auto-immune disease.”

    I have always thought the opposite, evolution favours diversity, it has selected sexual reproduction in plants and animals. What’s the point of sexual reproduction if not to create more diversity? In humans males have wider variation than females in attributes like IQ. Arguably this gives females a wider range of many different attributes from which to select a mate. Since the more varied males can and often will impregnate many different females, mate selection by the sexes also has a role.

    Thus it would be no suprise to find that susceptibility to infection and also infectiousness is also varied especially if such variation brings benefits to the herd as Nic’s hypothesis/model shows (reduced HITs).

    “Yes, this pandemic has slowed with cumulative cases far too low for herd immunity. Is the reason fear and policy? Or depletion of the most susceptible members of the community, leaving the rest with herd immunity? I asked Nic if there were a way to distinguish between these two hypotheses, but didn’t receive an answer.”

    There might be a way to distinguish with animal experiments, heterogenous groups versus homogenous groups. Best if the animals are prone to Covid-19. Could even use humans if they were volunteers, I have heard of people who want to catch it, “to get on with the rest of their life” as they put it.

    It’s possible we will find out as Stockholm County progresses.

    • Anthony: Random mutation and exchange of genetic material produce diversity, but survival of the fittest results in the fittest genes dominating within a single species.

      More than 99% of species that have ever existed have died out, so evolution doesn’t necessary promote diversity.

      Within the human species, the odds of a child surviving from birth to reproduction – the thing evolution really cares about – were less than 50% due mostly to childhood illnesses. If some fraction of the population had an immune system that increased these odds, that trait would quickly dominate the population.

      Does it make sense for survival of a species for part of the population to take greater risk of getting auto-immune disease and the other part to take greater risk of infection? Sure, but evolution selects usually for traits in INDIVIDUALS that make individuals more likely to reproduce, not traits that are best for the species. (The big exception here may be genetic recombination via sex and related processes that vastly increases the diversity of combinations of traits that already useful that might be found in progeny. Genetic recombination allows two traits that evolved separately to find their way into one superior individual.)

      For this reason, I don’t expect to find large differences in genetic susceptibility to infection and viral reproduction in the upper respiratory system so that the virus can be transmitted to another individual. Better nourished and healthy people are likelier to survive if the infection spreads to vital organs.

      Viruses are most successful when they infect their host without causing any problems. Killing your host and having to find a new one isn’t the best strategy. Most viruses that cause disease tend to evolve into less deadly variations. Coronaviruses have an ecological niche in bats, which aren’t harmed by them.

      Although the adaptive immune system is apparently unique to mammals, the innate immune system has been around much longer. In the case of humans, however, we did make a big change less than 10,000 years ago when we began living in closer contact with other humans and farm animals, and eating a different diet. 500 generations isn’t a lot of time for evolution to adapt to new circumstances and the biggest changes have occurred in the last 50 and 10 generations. We are vulnerable to swine and avian influenzas and small pox, because we live amid pigs, chickens and cows. So evolution hasn’t had enough time to select immunological traits capable of handling the pandemics that are new to agricultural society. When Europeans came to the Americans, they brought epidemic viral diseases from farm animals into a human populations that had never lived among these farm animals. If these native populations were genetically innately less capable preventing establishment of a viral infection, you can see how quickly evolution eliminated this weakness in some places – but the problem may have been environmental – lack of exposure to childhood diseases that are more dangerous for adults.

      We have the ability to study the genomes and immune systems of humans who have experienced asymptomatic, mild and severe SARS infections and find out what they have in common. Perhaps I’ll discover I was wrong.

      • Terry Jones

        Thanks franktoo; “we began living in closer contact with other humans and farm animals, and eating a different diet.”

        You may emphasise the former: I would highlight the latter;

        we have an epidemic of diabetes around the world; it affects some groups more: eg UK data: “SA communities have a four-to-six-fold greater
        rate of people with T2DM than White British communities”

        SA= South Asian

        It seems clear that many of those ill and dying have diabetes, hypertension, heart disease, obesity: all deeply interwoven with high carbohydrate consumption; eat carbs, get diabetes; cancer, bacteria, viruses and fungi all delight in profuse sugar.

  103. John Daschbach

    In my modeling and mathematical experience I have had to question many things. And in chemical physics the concept of detailed balance has always been important in my science career. Using mean(I) for S^\dot on dSL and not on R^\dot means that detailed balance is not maintained. You can use I (infections) in different models in different ways, but you can’t use different models between the core values in coupled ODE calculations.

  104. Carlos R Rabaca

    Very interesting analysis, and I agree that the factors introduced are important and can explain why many countries have experienced a much lower number of infected and deseased people than earlier predictions. But I don’t understand how this can explain the number for Sweden, since the population is that country is very, very homegeneous. There is almost no ethnic mix to explain genetic factors of inhomogeneity in susceptibility and infectivity. I am from Brazil and down here we have that! Someone has mentioned in the comments that there is a large number of Swedish people living alone in their house. My question to you is: is it possible that this housing condition can be used to somehow explain these factors of inhomogeneity in susceptibility and infectivity?

    • Although the Swedes may be homogeneous genetically, apart from their now sizeable immigrant community, the important variability in social connectivity factor still applies. Having many single person households will affect that, but it is not obvious to me whether people living in them will lower social connectivity (as there is no one else in the household) or higher social connectivity (as they may go out to meet other people more often). Probably some are less, and some more, socially connected.

      • > Having many single person households will affect that, but it is not obvious to me whether people living in them will lower social connectivity (as there is no one else in the household) or higher social connectivity (as they may go out to meet other people more often).

        ?

        We know that the most likely method of transmission is sustained, close contact. Meeting people in a bar is clearly not as “connected” as living in the same house with someone.

      • “Meeting people in a bar is clearly not as “connected” as living in the same house with someone.”

        No, that’s not clear at all. Many early clusters of infections seem to have occured in noisy social situations, such as bars.

      • > Many early clusters of infections seem to have occured in noisy social situations, such as bars

        There are clusters – that represent a small number to total infections. 60 people in a church choir get infected. And then they go home and infect thousands of family members.

        From Korea contact tracing:

        54% of cases are family to family
        33 % were friends
        24% were co workers
        8% were from a common place visited.

      • I don’t think that’s believed to be typical for western countries.

        Regarding the Ferguson / Imperial College model, the US NBER working paper 27007 (http://www.nber.org/papers/w27007) says:

        “The model is parameterized so that initial transmission events occur approximately equally at home, at school/work, or in the community, matching a stylized fact from previous studies suggesting that approximately one-third of transmissions occur in each of these places.”

      • We have observational data for this virus.

        What’s your proposed mechanism for why it would be different in Korea?

        Without a tested mechanism, for all you know it could be even more the case in Western countries, or it could be idiosyncratic with this virus.

    • nobodysknowledge

      The social distancing in Sweden has been effective against the spreading of the virus. When Swedes answer questionnaires about habits and behaviour, 99% answer that they have changed their behaviour. They have stopped inviting people home, and a lots of other things.

  105. Dr. Jay Bhattacharya: His new MLB COVID-19 Study and the Dilemma of the Lockdown

  106. Pingback: Dr. med. Martin Hirte | Kinderarztpraxis München – Coronavirus

  107. Pingback: Dr. med. Martin Hirte | Kinderarztpraxis München – Corona virus

  108. “Still, keep in mind that there’s currently no evidence that taking any supplement, including vitamin D, reduces your risk of developing COVID-19 as a result of contracting the SARS-CoV-2 coronavirus.”
    https://www.healthline.com/nutrition/vitamin-d-coronavirus#bottom-line
    No regrets answer: Eat foods rich in vitamin D. Pickled herring is your best bet.
    People have suggested poor people are dying more from this and that proves we’re racists. It may mean poor people have vitamin D deficiencies at a greater than average rate. Also suggests an answer for the NY CA difference.

  109. “However, the Ferguson20 report estimated that relying on herd immunity would result in 81% of the UK and US populations becoming infected during the epidemic..”

    Actual infection rates in contained environments such as ships have a much lower infection rate. Suggesting the majority are not at risk from infection at all.

    • Actually that’s a good point. Particularly on the early ship outbreaks, the vast majority of people never tested positive for the virus, although they didn’t do serological testing I think.

  110. > Actual infection rates in contained environments such as ships have a much lower infection rate.

    Respect uncertainty.

    There are plenty of contained environments where there have been very high levels of infection. Many of them less adaptable to interventions focused on reducing infections.

    • Prisons are one example, care homes another. There may be immunological reasons why high levels of infection can occur in those places.

      • Ulric Lyons

        In UK care homes and prisons there is extensive use of drugs which retard the immune system, such as benzodiazapines and gabapetins. Also death rates in care homes would be raised by drugs which harm the heart, such as anti-inflammatories. Interestingly the death rates with UK hospital staff is not above the national mean, but it is well above the mean with care and social workers.
        Countries where millions of tests have been conducted are beginning to reveal the general infection rates, which range from 4% to 12.5%. So Ferguson20 is looking backwards and some, in most regions more than 81% are not getting infected. The early guesstimates before Imperial College bolted the Gates was for around 30% of the population to potentially be infected.

      • Terry Wright

        “In UK care homes .. there is extensive use of drugs which retard the immune system”

        and the statins are extensively prescribed; and statins are well recognised to increase the risk of infections; those with low LDL levels are at greater risk of infections and cancers; statins are given with the express aim of lowering LDL, thus opening up those who take them to increased infection risk.

  111. Meanwhile…in Sweden…

    I’m not particularly critical of Sweden’s approach. It’s one of the variety of bad choices.

    But when you look at the metric of deaths per capita, you will note that the rate of decline is Sweden considerably lower than in many other countries, such as Switzerland, the Netherlands, even France, and many, many other countries. Sweden is rising up the chart at a consistent pace.

    In fact, Sweden has had the higher per capita deaths in Europe over the last seven days. Even higher than the UK.

    Cross-country comparisons are of limited value. And the reasons for Sweden’s relatively slower decline than elsewhere are complicated. And there are necessarily tradeoffs in all of this, but you can’t even evaluate the tradeoffs if your vision is limited by your ideological blinders.

  112. Oops.

    > STOCKHOLM (Reuters) – A Swedish study found that just 7.3 percent of Stockholmers developed COVID-19 antibodies by late April, which could fuel concern that a decision not to lock down Sweden against the pandemic may bring little herd immunity in the near future.

    https://www.reuters.com/article/us-health-coronavirus-sweden-strategy/swedish-antibody-study-shows-long-road-to-immunity-as-covid-19-toll-mounts-idUSKBN22W2YC

  113. I have not gone through the article in detail or the myriad of comments, so I apologize if I am reiterating previously discussed issues.

    The sensitivity of the PCR test is in practice only 63%, so that the actual prevalence of infection is likely 50% higher than the test positivity rates you are using. Thus the apparent HIT is lower than the true HIT. Thus your calculated numbers would lead to very low test positivity determined HITs which do not appear to correlate well with the data.

    In New York City, the current per capita fatality rate is .26%. The estimated case fatality rate for COVID-19 is estimated in the range of .3%, which fits the available data well in the U.S. and the rest of the world. Recent data in NYC does show rapidly dropping cases, hospitalizations and deaths, consistent with reaching HIT, but empirically that level would be around 80%.

    No where else in the US do we see any real decreases suggesting that lower HITs are being reached. Rather we see areas with better physical distancing with slower growth rates, and areas with poor distancing racing upward. Sweden had a per capita fatality rate of .04% on 4/5/20, it is now .38%.

    • RTW –

      > The estimated case fatality rate for COVID-19 is estimated in the range of .3%,

      What are you talking about? Did you mean infection fatality rate?

    • RTW, I agree that the false negative rate for PCR tests can be very high – I’ve seen estimates between single % figures and 30%. Most of that is probably because they are difficult to administer properly, and unpleasant for the patient when administered properly.

      However, the PCR-test-based estimate that by 11 April 17% of people had been infected by COVID-19 in Stockholm is supported by subsequent serological antibody sampling, which indicates that 10% had been infected by late March.

      I would expect the HIT to be considerably higher in NYC than in Stockholm, because it has a much higher propulation density, New Yorkers are probably naturally less socially distanced than Stockholm residents, and quite possibly on average have higher susceptibility to infection.

      I’ve seen no evidence that COVID-19 prevalence in NYC is anything like 80%.

    • RTW: Rather we see areas with better physical distancing with slower growth rates, and areas with poor distancing racing upward.

      Where in the US is daily incidence “racing upwards”?

      • Look at the fatality rates in the Midwest and South which are now climbing more rapidly. Confirmed case rates mean very little because they are entirely bounded by testing rates which are very limited.

        The testing which is not being accessed is for voluntary antibody or PCR surveys which asymptomatic individuals are unlikely to want to take because of time constraints, requirement for prior scheduling, limited sites and potential exposure risks.

        Testing for ill individuals occurs at hospitals. Turnaround time in skilled nursing facilities remains variable 2-7 days. Many doctors’ offices do not offer testing because the investment in personnel time, PPE, and logistics is not worth the trouble. So there remains a significant hurdle in most areas for an ambulatory individual, symptomatic or not to access PCR testing. Antibody testing is just a blood draw and is readily available.

    • These numbers could be reconciled if in fact most of the vulnerable in New York had already been infected. The remaining healthy and young population could get infected with few fatalities.

      It is frustrating that we don’t have better visibility of the demographics of the serologic testing results.

  114. nobodysknowledge

    Why COVID-19 virus is burning out much earlier then thought?
    In many countries in Europe there are lots of municipalities that never got the virus, and places that was infected have now been clean of the virus for the last month. Even countries, like Iceland and Faeroe Islands have had no spreading of the virus for weeks. It looks like the virus is burning out, like SARS. I would like to see some mathematics of the extinction of the virus.

  115. Jasper van Loon

    Hi Nic, Was age a consideration in your model? In the Daimond Princess the percentage of people below 60 that were infected (about 10%) was much lower than the percentage of people infected above 60 (about 21,5%).
    An extra twist is that most of the cases in the older group were asymptomatic, while in the younger group very few cases were asymptomatic. (1)

    (1) https://cmmid.github.io/topics/covid19/diamond_cruise_cfr_estimates.html

    • Age wasn’t explicity considered in my modified SEIR model, but its effects in generating inhomogeneity in susceptibility and infectivity are implicitly included.

      In the Diamond Princess case, there were very few (6) infected people under age 20; only 2 of them were symptomatic, but the sample size is too small to read anything into that. It’s true that for ages 20-49 around 9% were infected, of which 80% were symptomatic, whereas for ages 50+ approaching 25% were infected but only 40-50% were symptomatic. But the younger age groups will have largely consisted of crew members, and the older age groups of passengers, so I’m not sure one can generalise from this case.

  116. Antibody tests end of April show that 7.3% of people in Stockholm had covid-19. But strangely enough the numbers at the hospitals keep going down. https://www.reuters.com/article/us-health-coronavirus-sweden-strategy/swedish-antibody-study-shows-long-road-to-immunity-as-covid-19-toll-mounts-idUSKBN22W2YC

    • “Antibody tests end of April show that 7.3% of people in Stockholm had covid-19.”

      I suspect that figure is incorrect. It was based on a small sample – there were 1104 tests covering 9 regions, so maybe of the order of 100 for the Stockholm area. So the uncertainty range will be large.

      Previous results showed higher prevalence, and prevalence cannot decrease over time. A study based on blood donors showed about 11% had developed antibodies in mid-April, although the sample size was only 100.

      More importantly, a study that sought response from a random sample of households in the Stockholm area obtained 446 valid results from tests on an average date of 11 April, reflecting infections up to late March. It found 10% prevalence. https://www.kth.se/aktuellt/nyheter/10-procent-av-stockholmarna-smittade-1.980727 As the sample size is much larger than for the end April tests, the uncertainty range will be much smaller – perhaps half as wide.

      Moreover, the antibody tests used appear to have a sensitivity of only 70-80 percent, so 20-30% will test negative even though they have been infected. But the tests have 100% specificity – no one will test false positively. https://www.svt.se/nyheter/inrikes/11-procent-av-stockholmarna-har-antikroppar-mot-covid-19

      There is no indication that any of these seroprevalence results have been adjusted for the relatively low sensitivity of the test used. So it seems likely that in all cases the true prevalence was 25-43% higher than that reported.

      Of course, if the true prevalence was only 7.3% for infections up to mid-April (resulting in antibodies developing by end April) then the herd immunity threshold must have been even lower than I suggest in my article, as recorded new cases and net hospital admissions had peaked by then, implying (given the infection to testing delay) that the HIT had been reached a week earlier. Moreover, COVID-19 deaths in Stockholm county peaked around 6 May, which is consistent with a mid-April peak in new cases, as the average time from cases being recorded to death is about 20 days.

      • > I suspect that figure is incorrect. It was based on a small sample – there were 1104 tests covering 9 regions, so maybe of the order of 100 for the Stockholm area. So the uncertainty range will be large.

        It’s the official announcement of the Swedish government.

      • They’re saying it’s up to 20% now.

        I’m skeptical. The Swedish government says it went from zero to 7.3% from January 1 to the last week in April, and then from 7.3% to 20% in 4 weeks since. Even if we think that the rapid growth didn’t begin until well into February, given that the fasted growth was likely earlier (before social distancing got momentum), I doubt that it would have grown that much faster since the end of April (when social distancing is happening in earnest).

      • > As the sample size is much larger than for the end April tests, the uncertainty range will be much smaller – perhaps half as wide.

        The uncertainty range depends on far more than just the size of the sample. For example, what was the non-response rate of the different surveys? In fact, what were the sampling methods? Have you dug into that to assess the uncertainty ranges?

        > as recorded new cases and net hospital admissions had peaked by then,

        Recorded new cases is a bad measure. They aren’t testing much, and have likely reduced their testing. As for hospitalization, it could very well be that the reduction comes from the LTCFs, where you’re likely to get the sickest people even as the infection rate among the general public is increasing.

      • Nic –

        It’s interesting which numbers you have confidence in. Seems to me that there isn’t much reason to have any confidence in any of them.

        On April 21 they said: “Around one-third of Stockholm’s 1 million people will have had the novel coronavirus by the start of May and the disease may have already passed its peak in the capital, Sweden’s public health agency said on Tuesday.“

        On April 22nd, “Tegnell said sampling and modeling data indicated that 20% of Stockholm’s population is already immune to the virus, and that “in a few weeks’ time we might reach herd immunity and we believe that is why we’re seeing a slow decline in cases, in spite of sampling (testing for the coronavirus) more and more.”

        On May 20th, “Sweden’s state epidemiologist, Anders Tegnell, said the antibodies figure was “a bit lower than we’d thought”, but added that it reflected the situation some weeks ago and he believed that by now “a little more than 20%” of the capital’s population had probably contracted the virus.”

        “is a little bit lower (than expected) but not remarkably lower, maybe one or a couple of percent,” Tegnell told a Stockholm news conference. “It squares pretty well with the models we have.”

        Maybe you should allow for a bit more uncertainty.

      • Actually, now that I think about it the timeline from 7.3% to 20% seems more plausible.

        The number for late May reflects infections for two weeks earlier. And the 20% estimate now isn’t seroprevalence but actual number. So that makes it more like 7 weeks to go from 7% to 20%. Makes more sense.

      • oops:

        Number for late *April* reflects infections for two weeks earlier (Maybe *April* 7th?). And the 20% now isn’t seroprevalence but actual number. So that makes it more like 7 weeks to go from 7% to 20%.

      • I have not looked at numbers for Stockholm, but for Sweden as a whole, the fatality totals, assuming a .3% case fatality rate, would imply a 12% infection rate as of 2-4 weeks ago.

    • All data about case prevalence rate around the world is biased because of several major issues. The first is sensitivity. The tests are only about 63% sensitive, so actual prevalence may be 50% greater than “confirmed cases”.

      Secondly, there is tremendous selection bias, especially in a non-isolation setting, like Sweden, since there is no incentive to be tested unless there are significant symptoms, so test positivity percentages are artificial elevated everywhere in the world.

      Finally, antibody persistence is not known, but usually IgG will persistent for months to years, so the cadre infected so far in this pandemic should remain positive till next year, if this infection is similar to other similar viruses.

      • When you get prevalence estimates from antibody tests, they adjust for both sensitivity and specificity. So the confidence intervals you see in those reports incorporate a distribution associated with both. And usually, like Nic, they are too optimistic about specificity which with time doesn’t stand up to scrutiny.

  117. I must be missing something with this “mistake” If you ramp up testing to identify old cases that weren’t reported and then combined that with tests to discover current, active cases, you should be inflating the number of “new” cases reported each day.
    Yet the Atlantic writes: “The upshot is that the government’s disease-fighting agency is overstating the country’s ability to test people who are sick with COVID-19.”

    Two things are correct- you shouldn’t mix the results, and The Atlantic’s argument about the “upshot” of the mistake makes no sense. The article even concedes that the number of tests for active cases is up considerably.
    Other news organizations – notably the Washington Post – are reporting that they have more testing capacity than they have people willing to be tested to see if they are currently infected. The Post even ran a column this week urging the government to pay people to be tested.

    https://www.google.com/amp/s/www.washingtonpost.com/health/as-coronavirus-testing-expands-a-new-problem-arises-not-enough-people-to-test/2020/05/17/3f3297de-8bcd-11ea-8ac1-bfb250876b7a_story.html%3foutputType=amp

    By the way, knowing how many people have been AND are infected is important information. Knowing how many are currently infected is important information and has been inaccurate from the start of this due to the fact that it can take days and even weeks for text results to come back .

    • jeffnsails850: Other news organizations – notably the Washington Post – are reporting that they have more testing capacity than they have people willing to be tested to see if they are currently infected.

      I have read that elsewhere as well.

  118. “Antibody tests end of April show that 7.3% of people in Stockholm had covid-19.”

    I suspect that figure is incorrect. It was based on a small sample – there were 1104 tests covering 9 regions, so maybe of the order of 100 for the Stockholm area. So the uncertainty range will be large.

    Previous results showed higher prevalence, and prevalence cannot decrease over time. A study based on blood donors showed about 11% had developed antibodies in mid-April, although the sample size was only 100.

    More importantly, a study that sought response from a random sample of households in the Stockholm area obtained 446 valid results from tests on an average date of 11 April, reflecting infections up to late March. It found 10% prevalence. https://www.kth.se/aktuellt/nyheter/10-procent-av-stockholmarna-smittade-1.980727 As the sample size is much larger than for the end April tests, the uncertainty range will be much smaller – perhaps half as wide.

    Moreover, the antibody tests used appear to have a sensitivity of only 70-80 percent, so 20-30% will test negative even though they have been infected. But the tests have 100% specificity – no one will test false positively. https://www.svt.se/nyheter/inrikes/11-procent-av-stockholmarna-har-antikroppar-mot-covid-19

    There is no indication that any of these seroprevalence results have been adjusted for the relatively low sensitivity of the test used. So it seems likely that in all cases the true prevalence was 25-43% higher than that reported.

    Of course, if the true prevalence was only 7.3% for infections up to mid-April (resulting in antibodies developing by end April) then the herd immunity threshold must have been even lower than I suggest in my article, as recorded new cases and net hospital admissions had peaked by then, implying (given the infection to testing delay) that the HIT had been reached a week earlier. Moreover, COVID-19 deaths in Stockholm county peaked around 6 May, which is consistent with a mid-April peak in new cases, as the average time from cases being recorded to death is about 20 days.

    • Nic here is conflating sensitivity and specificity from another test conducted with 100 people that confirms his biases to dispute seroprevalence numbers from a test with 1100 people that contradicts them. The test showing 7% prevalence had 98.3% sensitivity and 97.7% specificity . And of course if infections have peaked, it must be because of the imagined herd immunity thresholds and not because of the documented fall in economic activity. It’s a shoddy attempt at doing science.

      • The 1100 people were from throughout Sweden, not from Stockholm, so your comparison is invalid, and highly misleading.
        I discussed the existence of moderate social distancing in Sweden, which no doubt is one factor involved in the spread of the virus.

      • OK, the 1100 people are from nine regions. However, that was not really my main point. The test sensitivity is much better than you indicated and specificity is worse. So, the adjustment is likely to be more skewed toward false positives than false negatives. There may be other reasons for the prevalence finding though since per this test Sweden was 5% and Stockholm had 7.3%. By my estimates, Stockholm prevalence should be roughly twice that of Sweden as a whole.

  119. John Daschbach

    This work and the Gomes paper would not make it through peer review in the journals I am used to in Physical Chemistry and Chemical Physics. The reason is the introduction of the “force of infection” in the dSL term. You can’t consider different connectivity as one of the reasons for varying infectivity and then connect every Susceptible to the mean of the pool of Infected. Physically the model here is assuming an infinite mixing rate between Susceptible and Infected at all times but then unmixed Infected in the dIR term. But in coupled ODEs the conditions for any dependent variable are identical because it is the same variable. There is no physical model in which Infected people are perfectly mixed with Susceptible people at all times but Infected people are completely unmixed with themselves with respect to Recovery at all times. The mixing in Infected has to be identical everywhere to be valid physics because it is the same variable.

    • That seems logical and you are probably correct. However, it may not matter.
      Epidemiology we have seen lately seems to be only nominally based on physical science.

    • A single common force of infection is the standard assumption in compartmental epidemiological models, which has been published very many times in peer reviewed journals.

      • John Daschbach

        Using the term force of infection is clearly confusing too many people. Infection transmission is an apparently non-linear, above some discriminator (with some distribution function) function. I think that is supported by the data from around the world.

      • John Daschbach

        Ok I can’t figure out how to edit a post. The bottom line is that you can’t do what you (and Gomes) have done. Two ways to understand this are through Detailed Balance (which your model violates) or finding an ensemble that better represents reality. But you (and Gomes) have adopted a model that is not just not physically impossible it, in the end, violates Thermodynamics. You can’t have an infinite mixing rate for Infection with Susceptible and a zero mixing rate for Infection with itself. As I said my experience is in Physical Chemistry and Chemical Physics. These models likely wouldn’t make the cut to go out for peer review in the best journals in these fields.

      • John Daschbach:

        Whatever shortcomings the model may have, it doesn’t seem to me to suffer from the problem attributed to it in your statement that “Physically the model here is assuming an infinite mixing rate between Susceptible and Infected at all times but then unmixed Infected in the dIR term.”

        Why would mixing be a consideration in the dIR term? That term is merely the rate at which infectious folks get well; according to the model, the infectious in all population segments are equally likely to recover over the next day, so each segment’s rate of recovery is simply proportional to that segment’s size. Now, that may not reflect reality particularly well, but I can’t see how it violates “Detailed Balance.”

        Nor do I understand the statement that “You can’t consider different connectivity as one of the reasons for varying infectivity and then connect every Susceptible to the mean of the pool of Infected.”

        To make it simple, let’s say infectivity and susceptibility are perfectly correlated and that there are only two population segments: shut-ins and gadabouts. Shut-ins are only one-tenth as likely to get infected as gadabouts are, but they’re ten times as likely to be infected by a gadabout as by another shut-in. Similarly, Gadabouts are ten times as likely to infect someone as shut-ins are, but they’re still only one-tenth as likely to infect a shut-in as they are to infect another gadabout.

        Let’s ignore normalization and say that a gadabout’s infectivity and susceptibility are both unity, while a shut-in’s are both 1/10. With uniform mixing the number of shut-ins who’ll contract the disease over the next day is proportional to 1/10 * S_shutins * 1/10 * I_shutins + 1/10 * S_shutins * 1* I_gadabouts, while the number of gadabouts who will is proportional to 1 * S_gadabouts * 1/10 * I_shutins + 1 * S_gadabouts * 1 * I_gadabouts.

        Another way to express that uniform mixing is that the dSL vector—i.e., the vector of rates at which the different population segments’ susceptibles become latents—is [1/10 * S_shutins * (1/10 * I_shutins + 1 * I_gadabouts), 1 * S_gadabouts * (1/10 * I_shutins + 1 * I_gadabouts)]: it’s (1/10 * I_shutins + 1 * I_gadabouts) * [1/10 * S_shutins, 1 * S_gadabouts]. That vector is therefore the common “infection force” lambda = (1/10 * I_shutins + 1 * I_gadabouts) times the element-by-element product [1/10 * S_shutins, 1 * S_gadabouts] of the vectors Sy = [1/10, 1] and S = [S_shutins, S_gadabouts].

        I haven’t been able to find any problem in that calculation. Could you explain a little more why you believe it’s wrong?

    • There you go, John. The epididdlymologists have a standard assumption. They are doing their best with a very difficult problem, John.

      • John Daschbach

        This is for Joe Born mostly.

        Yes, I agree completely with your math for your model.

    • John Daschbach: Physically the model here is assuming an infinite mixing rate between Susceptible and Infected at all times but then unmixed Infected in the dIR term.

      Not “infinite mixing” but a sufficiently rapid mixing compared to the rates of other processes; analogous to the “pseudo steady state” assumption in the derivation of Michaelis-Menten kinetics.

      The model has been used in lots of cases, and the results are reasonably accurate when the parameters are estimated accurately enough — the usual pragmatic considerations, found also in physics, physical chemistry, and biochemical engineering (e.g. Bailey and Ollis).

      Yes, the models are not based on physics, but on biology and behavior.

      • John Daschbach

        The model has to satisfy physics, which it does not. Detailed balance requires that microscopically rates are time reversible, which they are not in this model.

      • Matthew R Marler

        john Dashbach: Detailed balance requires that microscopically rates are time reversible, which they are not in this model.

        Sorry I missed this when you first put it up.

        You are not modeling mass, you are modeling counts of living people. For them, death is not time reversible.

  120. Alberto Zaragoza Comendador

    Looking at this comment by Joshua:
    “Recorded new cases is a bad measure. They aren’t testing much, and have likely reduced their testing.”
    Testing has generally been increasing. This report goes up to week 19, ending on May 10th. By the way, the report ending on the previous week was discussed in the comments to this article.

    Click to access covid-19-veckorapport-vecka-19-final.pdf

    “As for hospitalization, it could very well be that the reduction comes from the LTCFs, where you’re likely to get the sickest people even as the infection rate among the general public is increasing.”

    See figure 6 in the report I just linked to. The highest share of positives in random PCR tests was in week 14, ending April 5th. Admittedly the data is noisy but if the “infection rate among the general public” were increasing you’d see it.

    Sweden’s daily case data has a lag of one day or so. Excluding the last day available, that is to say May 21st, the 7-day average in Stockholm County cases is 104. This is less than half the peak value for the region. By contrast, outside Stockholm County reported cases are steady around the 400/day mark; the region now has lower cases/day/capita than the rest of Sweden. This does not “prove” Stockholm is now seeing the effects of herd immunity but it’s hard to see what else it could be.

    • Testing may be easier to access in Stockholm than elsewhere, so that more of the population accesses, and positivity rate goes down.
      Also in metropolitan areas, there is more benefit to testing to make decisions about exposure in public places, employment, and the like. In more suburban and rural settings, there is less utility. So in urban settings there is selection bias to well people getting tested than in less densely populated areas.

      In the U.S., New Jersey positivity has gone done from 46% on 5/7 to 28% on 5/21, with no indication of “herd immunity” effect.
      Iowa, South Dakota and Kansas on 5/21 had positivity rates of 14%, 13%, 12% respectively, California 6%, with no implication of “herd immunity”.

      You would need actual serologic or PCR surveys to understand whether case rates reflect infection prevalence or testing distribution.

      If the Swedish data reflects actual unbiased population surveys and not ad hoc testing, I take all this back.

    • Alberto Zaragoza Comendador

      Not sure if others are having this problem but, instead of the link to the report, in my previous comment I only see white gap. If you want to see the report just google:
      Veckorapport om covid-19, vecka 19

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  123. UK went to people’s houses and conducted 14,000 antigen tests. 0.25% currently infected.

    The found no difference in positive rates by age.

    • This seems to be a test with low sensitivity. Otherwise, the Case fatality rate would be astronomical.

      • It was a PCR test, not an antibody test. Currently infected, not positive for antobodies.

      • Don Monfort

        Antigen test is not PCR, Joshie. Google it.

      • Ms. Google says

        –snip–

        PCR tests are used to directly detect the presence of an antigen, rather than the presence of the body’s immune response, or antibodies. By detecting viral RNA, which will be present in the body before antibodies form or symptoms of the disease are present, the tests can tell whether or not someone has the virus very early on.

        –snip–

        At any rate:

        https://www.google.com/amp/s/amp.theguardian.com/world/2020/may/21/number-of-people-with-coronavirus-in-england-remains-stable-says-ons

        https://www.ons.gov.uk/peoplepopulationandcommunity/healthandsocialcare/conditionsanddiseases/bulletins/coronaviruscovid19infectionsurveypilot/england21may2020

      • I am a physician and I understand what PCR measures.

        My point is this. Your links state that in England they feel they have a plateau of 137000 with active disease during the 2 weeks from May 4 through May 17. Since the activity of the disease by PCR seems to last between 1-4 weeks, the total number of new cases per each two week period would be reasonable estimated as 137000, with a factor of 2 error in either direction.

        The number of deaths on the JHU coronavirus map/dashboard in the United Kingdom rose from 32141 on 5/11/20 to 36996 on 5/25/20, so 4855 deaths during a two week period. [I do not know if Scotland, Northern Ireland, Wales are included or not, so there may be a correction factor.] Deaths usually occur 2 to 4 weeks after infection, so the time frames are skewed, but that will not matter if we are in steady state.

        This gives us a case fatality rate of 3.5% which is an order of magnitude higher than CDC [and my own] estimates of lethality. Such an estimate would imply that New York City with 21259 deaths with 8.2 million population has only had 7% infection rate, although test positivity rates are in low to mid double digits, and would correct further upward because of 63% sensitivity of the test.

        Yet NYC in fact does exhibit data very suggestive of herd immunity.
        Toggle through the case, hospitalization, and death plots on https://www1.nyc.gov/site/doh/covid/covid-19-data.page

        So I believe the testing described in England has either a 10% sensitivity or the sample is quite biased.

      • RTW –

        > This gives us a case fatality rate of 3.5% which is an order of magnitude higher than CDC [and my own] estimates of lethality. Such an estimate would imply that New York City with 21259 deaths with 8.2 million population has only had 7% infection rate, although test positivity rates are in low to mid double digits, and would correct further upward because of 63% sensitivity of the test.

        Seems to me that there’s too much variability in case fatality rates to draw much in the way of conclusions

        And reverse engineering from uncertain cast fatality rates to infer specificity of the test seems even more questionable to me. You’re multiplying uncertainty by uncertainty

      • Don Monfort

        Antigen test, PCR test different animals. Go back to google, joshie.

      • Pages 12-13 should do it:

        protocol-covid-infection-survey-2020-04-20-v1-0-clean-with-ethics-ref.pdf

      • Don Monfort

        Folks taking part in that test are self-swabbing. That is a problem for accuracy. By the way, they are using PT-PCR test. Not an antigen test.

        Most interesting result is that there were 35 positives in 32 households. How many people in each of the 32 households? I will guess 3. Why aren’t there more positives in those households? Did they retest everybody
        in those 32 homes?

      • If sensitivity is 10%, then finding second positive in 3 person household would be 19% of time. in 32 households, about 6 should have more than one. If we postulate 2 person households on average, then 10% or 3 households which is roughly what they got.

      • Don –

        So this, “Antigen test is not PCR, Joshie.”

        Is just wrong. Ms. Google told you so.

        Now if you get a thrill from going into the weeds as to determine whether an RT-PCR is an antigen test, to prove I was wrong when when I said it was an antigen test be my guest. Knock yourself out. And then come back and explain how you got your estimate so wrong.

        LOL.

      • Don Monfort

        Dr. RTW, where would one procure PCR tests that only has a sensitivity of 10%, even under sketchy conditions? Used properly sensitivity of COVID 19 PCR tests can be up to 90%. What am I missing here?

        Seems to me that there is either some significant number of false negatives, or this data indicates that the virus ain’t so contagious. Only 3 of 32 people living with a person who tested positive for the virus is concurrently infected.

      • To my understanding, the lab part of PCR is generally very sensitive, since it involves amplifying the genetic signal until detectable. It may not be so specific due to the amplification with cross-reaction to other coronavirus, etc.

        However, there are now three known factors decreasing sensitivity of PCR testing with SARA-CoV-2. First, there is a temporal course, with varying sensitivity, probably representing the degree of viral RNA production during the disease. This leads to essentially zero detection early in the infection, increasing up to day of first symptoms, and then dropping later in the course.
        See https://www.acpjournals.org/doi/10.7326/M20-1495

        Secondly, there is variable distribution of virus through the respiratory tree and gastrointestinal tract. You could have a rip-roaring pneumonia but for pathologic or anatomic reasons, you might not contaminate part of your nasopharynx with virus at a given time. This lack of sensitivity is likely one of the major contributions to the normal PCR swab test.
        An article on retrieval of virus from different sites in the body with variation of a few percent to 93% in bronchoalveolar lavage. Note specifically that (oro)pharyngeal swabs are only 32% sensitive. https://jamanetwork.com/journals/jama/fullarticle/2762997

        The third factor is technique in sampling which is difficult to determine but is likely a source of great variability in self-administered swabs.

        Returning to the lab end, the Abbott NOW rapid PCR is also known to be less sensitive because of the actual lab procedure, estimated to be 85% vs. 95%+ for the longer in lab tests. Ironically, this means that the White House Abbott NOW testing is only 50% sensitive if you add in the nasopharyngeal specimen issue. So if someone comes to the White House and is infected, the White House testing will only catch it half the time.

      • Don Monfort

        Thank you, Dr. RTW;

        “It may not be so specific due to the amplification with cross-reaction to other coronavirus, etc.”

        Wouldn’t that produce false positives?

        The other factors you mentioned, are I believe sensitivity decreasing. But if a combination of those resulted in a sensitivity of just 10%, PCR would not be very useful, unless serially and properly administered. Which wouldn’t surprise me.

        Anyway, I was just thinking it odd that those English folks living together and having some sort of ‘relations’, were not getting infected at rates comparable to prison inmates, sailors on aircraft carriers, cruise ship passengers etc.

      • Don Monfort

        PS: I forgot nursing homes as virus infection clusters.
        I thought of asking my cousin tonyb, if the English had become less passionate since my ancestors lived there. It occurred to me that I haven’t seen him comment lately. Hope he’s well. Chime in, tonyb.

      • The most accurate data we have is fatalities. Confirmed cases are a fiction determined by testing strategy. Case fatality is calculated by dividing fatalities by actual cases which we do not know.

        PCR testing has sensitivities from 30% to 80% depending on methods, technique, time of collection vs. symptom course. Antibody testing is unclear.

        So I believe extrapolating from fatalities is the most accurate estimation we can make.

        Even in influenza, our estimates of case fatality are just that – estimates. We treat empirically, and rarely do we make a laboratory diagnosis of influenza, usually for public health reasons.

        Finally, recent data from the Korean CDC demonstrates that some positive PCR results represent dead virus, not active disease. https://www.cdc.go.kr/board/board.es?mid=a30402000000&bid=0030

        So our “gold standard” test for active disease has an operational sensitivity of about 63% and a diminished sensitivity as well.

  124. Jasper van Loon

    a Germany study of 9 hopitalized covid-19 cases found that “The serological courses of all patients suggest a timing of seroconversion similar to or slightly earlier than in SARS-CoV infection18. Seroconversion in most cases of SARS occurred during the second week of symptoms.”

    Is it likely that everyone who contracts the coronavirus, including the asymptomatic cases, would start producing antibodies in the second or third week after being contaminated? Or is it more plausible to assume that most people who become contaminated do not need to produce an adaptive immune response (innate immunity, also see Ian W. ‘s comments) to fight of the virus?

    (*) https://www.medrxiv.org/content/10.1101/2020.03.05.20030502v1.full.pdf+html

    • “Is it likely that everyone who contracts the coronavirus, including the asymptomatic cases, would start producing antibodies in the second or third week after being contaminated?”

      I think it is more complicated than that, and depends inter alia on what is meant by “contracts the coronavirus”. If that means “positive by RT-PCR test” then this preprint study suggest that most but not all people do so, although the size of the relevant sub-sample is very small: https://doi.org/10.1101/2020.05.19.20101832

      However, it appears to be possible, at least for younger people, to test negative for SARS-CoV-2 on the standard RT-PCR test, with or without symptoms, and to produce no detectable antibodies against SARS-CoV-2 in the blood, but nevertheless to detect such antibodies in their nasal fluid.

    • Immune response always takes days to weeks to raise a IgM response and the weeks to months to raise IgG. The ability to fight off an infection depends On “innate immunity” consisting of non-specific inflammatory responses, cellular responses, and cross-reactive antibody responses to a new antigen.

      An article about the time course of measured antibody is
      https://www.acpjournals.org/doi/10.7326/M20-1495

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  126. As a physician practicing in skilled nursing facilities in Los Angeles, I find the situation more nuanced than perhaps some other posters.

    Although there is prevalent PCR based infection in many facilities, the fatality rate is quite variable. This variability is not simply a reflection of the quality of care in each facility, because the acute hospital is the safety valve where cases go often. Conservative care is not practiced very widely at all in litiginous L.A.

    What seems to be the case is that inoculum size is important. Close confines for extended periods, perhaps moderated by PPE, seems to determine different clinical courses.

    Given the higher percentage of young New Yorkers with significant disease, one might conjecture that inoculum dose caused by recirculated ventilation might be a factor there, since there is a suggestion that new cases are occurring in those who are distancing and avoiding mass transit.

    So although more are dying in geriatric care facilities and congregate living, these are not just those poised to decline, but are more frail individuals exposed to high inoculum due to the care situation and perhaps airflow patterns. I believe the same situation applies to a lesser degree in urban housing, leading to New York City, choir practice, and religious service hotspots.

    • Thanks for the comment, Dr. RTW. I believe you would find this interesting:

      Dr. Price is a pulmonologist at Cornell Med Center in NYC, 1200 bed hospital that at the time of the video was treating COVID 19 patients, almost exclusively. Dr. Price states that he probably has treated more COVID 19 patients than anyone else in the country. His advice on the transmissibility of the virus and how to avoid catching the nasty thing, seems to me to be well-informed and valuable.

      • Don Monfort

        PS: Poor guy looks like he is worn out. Thanks to all the medical folks on the front line.

  127. This is very good:

    Hopefully it’s related to something like herd immunity. If it’s weather related, hopefully we’ll be prepared for the potential of a 2nd wave in the fall.

    • Interesting. Thanks.
      The normal flu vaccine process in the US is based in no small part on what happened in Australia over our summer, which is winter of course down under.
      We will all be watching to see how the second wave happens in the place where “fall” is starting and not many people caught the virus in the first wave.
      Australia is loosening lockdowns by the way.

      Here’s the NYT on Australia and the flu, published way back in September of last year when it was still acceptable for Dem-leaning news outlets to admit the 2017 flu season killed 80,000 Americans.

      • Sorry, your politics are showing.

        Annual influenza has an estimated case fatality rate of .1% to .3%. In a nation of 333 million, the estimated fatality rate of 80000 to 100000 represents 25-30% infection rate because of vaccination and cross-reactivity to prior flu exposure [herd immunity].

        The best estimate of lethality for COVID-19 is that it is no more lethal than common flu. However, because of lack of vaccination, a long presymptomatic period when the disease is transmissible, and a significant fraction of cases which are clinically asymptomatic, the attack rate is far higher than influenza. So total deaths are a factor of 4 or more higher than influenza, and outbreaks are temporally compressed causing disruption of healthcare and essential social services.

        Furthermore, because it appears more and more likely that the severity of disease seems proportional to inoculum dose, possibly through recirculated ventilation in congregate living situations, the severity of outbreaks is exaggerated in densely populated urban areas, as well as group gatherings – choir practice, religious services, concerts, fairs – in more rural areas. These are the factors which render this pandemic more problematic than the common flu.

    • It does not imply herd immunity. The original testing was woefully inadequate so that Positivity rates were much higher than in the general population. As we expand testing, the rates will drop dramatically.

      If the actual number of positives drops slightly, it is more likely to represent the public health distancing measures, and I would expect that these will rise again as such measures are loosened currently. Death rates should rise in 2-4 weeks.

      • RTW –

        > Death rates should rise in 2-4 weeks.

        What I’ve been struck with is that fatalities are dropping three weeks after some of the highest case identification rates.

        So is the case fatality rate dropping, perhaps due to better treatment? Maybe as you refer to above, the cases aren’t as severe because the are less comprised of cases in high density areas like NYC (less intense exposure to the virus).

      • Actually Josh, the data from Sweden seems to be showing something similar. New cases have been essentially constant for weeks, but new hospitalizations are way down and deaths are decreasing somewhat.

        As I’ve mentioned many many times, IFR estimates almost always decline over time sometimes dramatically.

      • With respect to the death rate in Sweden, here is the number of deaths reported through the JHU database on each date:
        4/5/20 401
        4/9/20 793
        4/16/20 1333
        4/23/20 2021
        4/30/20 2586
        5/6/20 2941
        5/13/20 3461
        5/20/20 3831
        5/27/20 4220.

        The degree of slowing of deaths seems relatively minimal, and I suspect the data represents an initial exponential growth associated with the most densely populated areas of Stockholm, with moderation by voluntary distancing and spread to less populated areas but certainly not decelerating like NYC where I believe true herd immunity effects are seen in the data which I have previously cited in terms of the curves for cases, hospitalization, and deaths https://www1.nyc.gov/site/doh/covid/covid-19-data.page

        During this time Sweden’s per capita fatalities per million increased from 40 to 422. Denmark, Norway, and Finland are currently at 94, 47, and 52. Within another two weeks Sweden will have passed Italy, France, and Spain despite starting about a month later than those countries. Compared to its Scandinavian neighbors, Sweden will have an excess of 4000 deaths, even with a population density of 23/km2 vs. 135, 16, and 16.

        Whether these deaths were worth the purported economic and social benefits is in the eye of the beholder. The excess will become permanent if we have a vaccine soon. It will diminish until we do get a vaccine, but may increase or decrease depending on whether immunity is complete or partial, and transient or persistent.

      • The data from Diamond Princess is incomplete. I have not been able to see a citation about how many passengers and crew actually were tested. It appears that some asymptomatic individuals were never tested. Even though nominally only 17% were documented as infected, it is likely that more were infected, asymptomatic, and never tested. In any event, I believe there are now 13 deaths in 712 PCR positive cases. These would be almost 2% CFR which is certainly on the high end. If the CDC current estimate of .4% is correct, the expected number infected would be close to 3500 out of 3700 passengers and crew, which would be a very high attack rate, but more consistent with what we know of the disease.

        For a better documented study of cruise ship COVID-19 transmission see
        https://thorax.bmj.com/content/early/2020/05/27/thoraxjnl-2020-215091
        where attack rate was 60%, 80% were of PCR positives were asymptomatic, and the authors report the false negative rate for PCR is likely significant, and CFR was .8%.

      • Joshua Brooks

        The Diamond Princess is a non-representative sample in nearly all resources. The population is an outlier in many aspects which predict health outcomes, and the treatment conditions are completely idiosyncratic.

      • RTW –

        Thus may be consistent with your thoughts:

        > A new study has revealed that more than 80 percent of passengers and crew members on a cruise ship that contracted COVID-19 were asymptomatic.

        […]

        > The first fever was on the eighth day of the trip and isolation protocols started immediately, with all passengers confined to their cabins and everyone was issued surgical masks. Personal protective equipment was also worn by anyone who came in contact with passengers.

        https://www.foxnews.com/science/81-percent-of-covid-19-patients-on-cruise-were-asymptomatic-study-says-raising-concerns-on-lifting-lockdown

      • RTW –

        > Within another two weeks Sweden will have passed Italy, France, and Spain despite starting about a month later than those countries.

      • Dangit…

        Yes, I’ve noticed Sweden inexorably climbing up the charts, as it moved past the Netherlands and Switzerland and other countries on that metric. Unfortunately, it sure seems that soon it will move past France, which didn’t seem possible not long ago. It doesn’t seem to me it will move past Spain and Italy…but yah, I would have said that about France as well.

  128. Continued drop in deaths, at a rate that doesn’t parallel identified cases 3 weeks ago. Again, I have to wonder if the treatment has gotten more effective?

    • Treatment is no different in specific terms. Main difference would be increased familiarity about the disease course which can better inform the timing of therapeutic decisions. Main drawback will be fatigue of health care providers.

      Less fatal disease could be occurring if distancing is resulting in decreased inoculum in each case, so severity of disease is slightly less.

    • Identified cases may represent increased testing of mildly symptomatic or asymptomatic cases with resulting better prognosis of “total cases” diluting baseline severe cases which are hospitalized and easily identified.

      • Joshua Brooks

        > Identified cases may represent increased testing of mildly symptomatic or asymptomatic cases

        That seems entirely likely to me. But still, many places are limiting testing to primarily those who are symptomatic, so I studied it may only be a partial explanation.

        It also seems likely to me that there was progress in treatment, both in terms of timing and procedure – such as with better timing in the use of ventilators, and possible use of alternative procedures in some situations (as we have seen described by some doctors in NYC).

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  132. This sounds consistent with the Diamond Princess “petri dish”, where despite the laughably poor quarantine conditions, only about 20% contracted the virus, and half of those were asymptomatic.

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  139. John Daschbach

    Joe Born posted the S^\dot equations for a simple two channel model with mixing. I agree that this is the correct math. Briefly he considers two channels the ‘shutins’ and the ‘gadabouts’ He chose to use 1/10 for the susceptibility and infectiosness of the ‘shutins’. I filled out his equation. (using m instead 1/10)

    He has (without the beta and m = 1/10):

    dSs = m Ss m Is + m Ss Ig
    dSg = Sg Ig + m Sg Is

    The full set, in R:

    t.parms <- c(b,g,d,m)
    names(t.parms) <- c('b','d','g','m')
    f.state <- c(1.0-i.init, 1.0-i.init,0,0,i.init,i.init,0,0)
    names(f.state) <- c('Ss','Sg', 'Ls','Lg','Is', 'Ig','Rs','Rg')
    sir.loc <- function(t, state, parms) {
    with(as.list(c(state, parms)),{
    dSs <- -b*Ss*Is*m*m – b*Ss*Ig*m
    dSg <- -b*Sg*Ig – b*Sg*Is*m
    dLs <- -dSs – d*Ls
    dLg <- -dSg – d*Lg
    dIs <- d*Ls – g*Is
    dIg <- d*Lg – g*Ig
    dRs <- g*Is
    dRg <- g*Ig
    list(c(dSs, dSg, dLs, dLg, dIs, dIg, dRs, dRg))
    })}

    This satisfies that every state variable has a corresponding derivative and detailed balance holds.

    It doesn't appear Joe coded this or ran it.

    If you run this at m=1 (uniform susceptibility) (for the I0 and beta chosen) and determine the time at which the first derivative of total infectivity goes to zero and the total fraction infected at the steady state endpoint for (m, t(days), fraction infected) you get:

    1.00 100 0.9

    Now what happens as we reduce m, that is we make the susceptibility and infectiosness of the 'shutins' lower by the same amount:

    0.80 132 0.8
    0.60 183 0.6
    0.50 219 0.5
    0.40 264 0.4
    0.30 316 0.3
    0.20 373 0.3
    0.10 420 0.2

    and higher:

    1.60 55 1.0
    1.40 65 1.0
    1.20 79 0.9

    Now the code Nic wrote for the two channel model of Joe has for the dS terms:

    dSs <- -b*Ss*((Is+Ig)/2)*m*m – b*Ss*((Is+Ig)/2)*m
    dSg <- -b*Sg*((Ig+Is)/2) – b*Sg*((Is+Ig)/2)*m

    1.00 99 0.9
    0.80 134 0.8
    0.60 207 0.6
    0.50 287 0.5
    0.40 478 0.3
    0.30 1842 0.1
    0.28 6406 0.01

    1.60 57 1.0
    1.40 67 1.0
    1.20 80 0.9

    This changed code becomes too stiff to run for m < 0.28 (the code with the explicit mixing can obviously be run at m=0 which then becomes the standard SEIR model)

    The tailing in the lower m values for the Nic model vs. the Joe model is dramatic so they are easily seen as different models.

    In both cases the mixing is non-physical, it is not possible. You can't infinitely mix all I channels in the dS equations and not in the dI channels. But if you are going to infinitely mix then the physically correct equations are Joe's.

    • Mr. Daschbach:

      Since I don’t understand what your result lists represent, I can’t really respond. Now, I can say that I agree with your characterization of my scenario, but I don’t agree that (modulo the normalization that I omitted for the sake of simplicity) Mr. Lewis’s code differs from what mine would be.

      Let’s follow the logic of your code:

      dSs <- -b*Ss*Is*m*m – b*Ss*Ig*m
      dSg <- -b*Sg*Ig – b*Sg*Is*m

      Those operations could equivalently be performed as:

      dSs <- -b*Ss * m * (Is * m + Ig)
      dSg <- -b*Sg * (Is * m + Ig)

      That is, there’s a common factor lambda = (Is * m + Ig)

      If we rewrite those operations in terms of the following vectors

      S = [Ss, Sg]
      I = [Is, Ig]
      Iy = [m, 1]
      Sy = [m, 1]

      we get

      lambda = sum(I * Iy)
      dS = lambda * Sy * S

      Except for his division by N and the fact that his Iy and Sy vectors are normalized, that’s what Mr. Lewis’s code says for the rho = 0 case.

      Also, I can't make sense of your assertions such as “You can't infinitely mix all I channels in the dS equations and not in the dI channels.” Why not? Or, more properly, what does that even mean?

      The “dI channels” merely specify how quickly shut-ins and gadabouts turn from latent to infectious and from infectious to recovered. How would the rate at which, say, shut-ins proceed from latent to infectious or infectious to recovered depend on how well they’re interspersed among the gadabouts? That is, the dI calculation differs from the dS calculation, in which the rate at which susceptible shut-ins get infected does indeed depend on how many gadabouts they’re interspersed with.

      So I don’t see what you’re getting at.

      • John Daschbach

        Joe, I don’t see why you don’t understand my code and the use of list(). What I wrote is the standard approach in R. Nic’s R code is very messy, but he does the same thing. x<- matrix(state, ncol=4)

        # force of infection lambda, weighting by infectivity if correlated with susceptibility
        if(identical(Iy,1)) {
        lambda= parms[1] * sum(rho*x[,2] + x[,3]) / N
        } else {
        lambda= parms[1] * sum(Iy * (rho*x[,2] + x[,3])) / N
        }

        dSL= lambda * Sy * x[,1]
        dLI= parms[2] * x[,2]
        dIR= parms[3] * x[,3]

        dx= array(0, dim=dim(x))
        dx[,1]= -dSL # change in susceptible
        dx[,2]= dSL – dLI # change in latent
        dx[,3]= dLI – dIR # change in infectious
        dx[,4]= dIR # change in recovered
        list(as.vector(dx))
        }

      • Sorry, I now see that the “t(days)” in your previous comment wasn’t intended to be the R-script transpose of some undefined R matrix “days” but instead an explanatory comment. So I now see what your result lists, e.g.,

        “0.80 132 0.8
        0.60 183 0.6
        0.50 219 0.5,”

        were intended to mean. (I had no problem with using R’s “list” data structure.)

        Again, though, you adapted Mr. Lewis’s code incorrectly, so it isn’t surprising that the results you got from adapting his approach differed from what you got from your adaptation of mine.

        Anyway, that’s all rather beside the point, because the question before the house is not your code but rather why you assert that “You can’t infinitely mix all I channels in the dS equations and not in the dI channels” when, in contrast with the “dS equations,” the “dI channels” involve no infecting; they calculate only the net of the rates of transition from latency to infectiousness and from infectiousness to recovery, so for the dI calculations the concept of mixing is irrelevant.

        I’m afraid that if you can’t answer that question creditably I see no point in pursuing the discussion further.

      • John Daschbach

        Joe, are you not familiar with coupled differential equations? Your math above suggests not. Each state variable must have a corresponding differential equation. If you have state variables Sg and Ss then you have equations Sg^\dot and Ss&\dot. In my earlier post I described your system as required for valid coupled ODEs, and I showed how the Nic modification, is not equal to your set of equations. Each state variable on the RHS has to have a corresponding differential on the LHS. Even if this is true As I showed your correctly written code runs perfectly, all the way to m=0. This is as we expect because there is nothing inherently stiff in the math. I mean you can run that set of equations using a crude euler method instead of lsoda. But once you put the mean on the RHS the system becomes very stiff and then non-solvable for smaller m values. Anyone with experience with coupled ODEs observing this would recognize that there was a mistake in their mathematics and/or derivation describing the system. The obvious mistake is the physically unrealistic mean force of infection. You can include this, as I did in the Nic modification to your equations, but you have to have all the explicit mixing terms, and when you write them out, as I did, you see terms which are not physically possible. For instance the term b m Is Sg. How does the Is population fully mix with the Sg population? It doesn’t. The factor m, physically, is a difference in intensive characteristics, not extensive, in the coupled ODEs. Physically this term is stating that there is complete mixing between Is and Sg but Is Infectivity is scaled by m. It is not that only a fraction m of Is interacting with Sg because then you have to mass balance Is in the b Is Ss m m term with a (1-m). You have to do the same with Ig if you are arguing that it is connectivity (an extensive property) that is responsible for differences in infectivity. The equations Nic has used correspond to an impossible physical situation for this system, infinite mixing of I with different intensive characteristics (susceptibility, infectiousness). This is very different from a system with differences in connectivity of extensive properties (I) where the equivalent of mass balance holds. That is, if m is a connectivity factor for Infection the you will have a term m Ig Ss and the corresponding term (1-m)Ig Sg. Coupled ODEs are common in Physical Chemistry, I have derived and numerically solved many systems. Here is an older paper of mine with a large set of coupled ODEs as part of the analysis.

        https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.92.198306

      • Mr. Daschbach:

        Sorry, but I’m going to disengage here; I don’t think any further effort on my part would result in any further enlightenment on yours. But I’ll leave the following comment for the benefit of any lurkers.

        Beyond the fact that Mr. Daschbach seems unable or unwilling to explain his view that mixing must be taken into account in calculating the state-velocity components dLI and dIR, the problem is not one of coupled differential equations, as he seems to imply, but rather of vector algebra.

        Specifically, Mr. Daschbach characterizes two of Mr. Lewis’s code lines as follows:
        dSs <- -b*Ss*((Is+Ig)/2)*m*m – b*Ss*((Is+Ig)/2)*m
        dSg <- -b*Sg*((Ig+Is)/2) – b*Sg*((Is+Ig)/2)*m
        Note that, although those lines differ, the terms Is and Ig are weighted equally (“Is+Ig”) within each line.

        But in Mr. Lewis’s script the calculation of those quantities’ combination is coded as “sum(Iy * x[, 3]),” which instead would correspond to (m*Is + Ig)/2. That is, it would not, as Mr. Daschbach seems to suppose, correspond to (Is+Ig)/2)*m + (Is+Ig)/2.

        Again, though, that issue is rather subsidiary. The larger question remains why he asserts that the dLI and dIR components’ calculation must involve some mixing. Since in my view he has not creditably addressed that question I see no reason to pursue his objection further.

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  145. Very interesting article, thank you for the perspective. I would like to add that if the infected and dead metadata are transformed a better estimation of actual total infected number (including the unknowns) can be made by using a population group with the fewer unknowns to calibrate other population groups.This has been done for the UK and Germany, whereby Germany with a more comprehensive testing policy has fewer unknowns. Assuming that 2.4% of Germans are infected, which is the average of German (positive infections)/(population) and (positive infections)/(total tests) then the following rough estimates can be made for the final total infections at the end of the contagion: England 15.4%, UK 15.5%, London 15.6% and Scotland 10.5%. Of course the first three numbers are the same within the accuracy of the estimate, but they are comparatively low, which seems to be in line with the the Swedish data you have presented. Also Scotland has a relatively lower level, which would be expected from a low population density group. Perhaps such a comparison could also be undertaken using Swedish data.

  146. Matthew James

    The graph at “Figure 1” is wildly at odds with the published data. Please issue a Correction.
    For example, 22 & 23 Apr each had over 280 new infections in Stockholm County; 5 May was 148, 6 May was 190, 7 May was 234.
    https://en.wikipedia.org/wiki/COVID-19_pandemic_in_Sweden
    I will check the accuracy of the rest of this essay once that is fixed.

  147. Is there somewhere where you explain your second model that incorporates a CV value? Or is it simply SEIR with a modified beta based on that? If so can you publish the full set of parameters for the various models in the paper. Thanks.

  148. Karl Friston: up to 80% not even susceptible to Covid-19
    The influential professor’s statistical observations could radically change how we lift lockdown
    https://unherd.com/2020/06/karl-friston-up-to-80-not-even-susceptible-to-covid-19/

    Covid-19 expert Karl Friston: ‘Germany may have more immunological “dark matter”’
    https://www.theguardian.com/world/2020/may/31/covid-19-expert-karl-friston-germany-may-have-more-immunological-dark-matter

    • Dark matter? Nice analogy.
      “Dark matter is a form of matter thought to account for approximately 85% of the matter in the universe… Its presence is implied in a variety of astrophysical observations, including gravitational effects that cannot be explained by accepted theories of gravity unless more matter is present than can be seen.” (from wikipedia).

      Well, how about more matter IS present than can be seen or some other explanation. Alternative theories abound (see the wiki article).

      The same goes for the newly discovered virus – it’s not necessarily new. The extent of hysteria and panic were of course very new.

    • If there is significant immunity based on prior exposure and cross-reactivity to other coronaviruses, etc., you would have to explain why people in Wuhan, NYC, New Jersey did not have such prior exposure.

      I believe cross-reactivity exists, and that there may be a minimal partial immunity, but clearly inocula of sufficient size will overcome such immunity. You could only prove this issue by exposing human subjects to SARS-CoV-2 inoculum, which we can not do at this time.

      • Actually, there is a cohort of people with known high level exposure to SARS-CoV-2: Spouses/significant others who had been sleeping ~8hr/night and/or sharing bodily fluids with infected individuals during the 2 days prior to symptom onset.

  149. Matthew R Marler

    brentns1, thank you for the links. Here is the Cell article that they cite:

    https://www.cell.com/action/showPdf?pii=S0092-8674%2820%2930610-3


    In Brief:

    An analysis of immune cell responses to
    SARS-CoV-2 from recovered patients
    identifies the regions of the virus that is
    targeted and also reveals cross-reactivity
    with other common circulating
    coronaviruses

    Highlights
    d Measuring immunity to SARS-CoV-2 is key for
    understanding COVID-19 and vaccine development

    d Epitope pools detect CD4+ and CD8+ T cells in 100% and
    70% of convalescent COVID patients

    d T cell responses are focused not only on spike but also on M,
    N, and other ORFs

    d T cell reactivity to SARS-CoV-2 epitopes is also detected in
    non-exposed individuals

  150. Stephen Anthony

    It seems the Gomes paper has gone mainstream, Mat Ridley has picked up on it in the telegraph. I wonder if Nic had a hand in that, You (Nic) certainly have done good in publicising it here. Well done Nic,

    https://www.telegraph.co.uk/news/2020/06/06/has-british-scientific-establishment-made-biggest-error-history/

    “If you tell the models there is thus a correlation between susceptibility and infectiousness you get much lower forecasts of cases and deaths. Add that we now know that cross-immunity from common colds probably allows 40-60pc of the population to resist Covid-19, and the result is – as the work of Gabriela Gomes at the Liverpool School of Tropical Medicine indicates — that herd immunity is probably reached when as little as 15pc of the population is infected, rather than the 50-60pc implied by Imperial’s model. Hence the epidemic is petering out in London despite crowded streets.”

  151. To investigate variation in susceptibility, has anybody researched the other end of the spectrum? Are there any studies on people who had extremely high levels of exposure to SARS-CoV-2. How many of them developed infection and/or antibodies after 6 weeks? Are there any common characteristics among the ones who did not? A readily identifiable cohort for such a study would be the spouses/significant others who shared a bed during the infectious period of known COVID-19 cases during April.

    • The Argentine cruise vessel revealed 59% attack rate with 81% asymptomatic cases https://thorax.bmj.com/content/early/2020/05/27/thoraxjnl-2020-215091

      • Interesting! While the cruise ship was a closely contained environment, measures were taken to isolate cases and lockdown guests, so some people might not have been exposed. On the other hand, a person sharing a bed with a victim for about 8hr/night during the most contagious phase would practically guarantee exposure.

      • It would be very interesting if the cruise vessel study included data on positive/negative correlation among people sharing cabins.

    • Additional data from USS Roosevelt, with 62% attack rate and 20% asymptomatic: https://www.cdc.gov/mmwr/volumes/69/wr/mm6923e4.htm?s_cid=mm6923e4_w

      Weakness is “convenience” sample which could be biased, but demonstrates correlation with sharing sleeping berth with other COVID-19 infected individual. Also demonstrates correlation of increased risk with lack of public health measures.

    • Although there may be some sort of variation in susceptibility, the main difference in severity of disease and symptomatic transmission would seem to be based on inoculum size.

      The situations with most dramatic outbreaks – skilled nursing facilities for both residents and health care workers, choir practice and church services, and NYC – all would appear to involve exposure to persistent exposure to aerosols or potentially aerosols in the setting of poorly ventilated or recirculated ventilation areas, e.g. high-rise apartments. If one believes there may some mild immunity imparted by T-cells and antibody crossreactivity even in SARS-CoV-2 naive individuals, there may be a lower threshold for inoculum size to overcome this naive immunity, which would explain the apparent 60% attack rate even with high risk environments. However, over these thresholds, we have effective infection with seroconversion.

      There is also information that suggests that more severe disease produces higher viral loads in secretory specimens which would lead to more transmission and more severe disease caused by exposure to sicker patients. https://www.bmj.com/content/bmj/369/bmj.m1443.full.pdf

      These would seem to be the factors most prominent in variations seen in apparent attack rate and severity of disease. The major factor in susceptibility would seem to be the vulnerability in lethality associated with underlying medical conditions.

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  153. Neil Thompson

    A question from a non-specialist: do people who test positive for SARS-CoV-2, but who are completely asymptomatic, go on to produce antibodies that would be detected in serological surveys?

  154. This article was written on the 10th of May. It is now the 10th of June and the “Swedish experiment” keeps on rolling. Daily new infections are at an all-time high (according to WHO), daily deaths have plateaued but are still high and 4x the UK per capita, GDP down by 6% (so no economic miracle either), the over 80s largely excluded from ICU (<5% of admissions). But at least the bars are still open!

  155. People say that the COVID death rate is 0.40% ! This was circulated in several news channels also !

    Me Thinks the death rate is beyond 10%,on aggregate count,and for some nations it is way beyond.

    As per – https://www.worldometers.info/coronavirus/#countries = there are 7.5 million cases and 420000 dead.Simple numerics place it at proximating 6%.

    Wrong me says ! dindooohindoo

    India,Brazil,Russia have seen a sharp rise in cases,in the last 30 days.40% of their cases came in the last 30 days,and for India,it will worsen exponentially.If you see the kill data of the RIB in the BRICS – it has increased sharply,in the last 30 days (which proves my thesis)

    People dying today,were in the quasi morgue (hospitals) 30-60 days ago.Let us take it,at 30 days.

    So we rewind to 30 days ago,and exclude the jump in RIB of BRICS,in the last 30 days. So we have say 4.5 million cases and the kill quant is 420,000

    Rate proximates 10% ! But that is also wrong,as the infected are NOT solely on RTPCR mode.Many nations cannot afford it and are doing antibody tests.An antibody positive may be RTPCR negative,and the vice versa is less likely. If you exclude these specimens from the infected tally,the % rises further.

    Also have to exclude the recovered cases – as those with immunity will recover in 30 days – AS THE VIRUS was DESIGNED THAT WAY.Unlike HIV and Cancer – where patients are NOT likely to recover- on a generic mode.But those who recover from COVID -WILL (in part) come back again,and then die.That will double count the infected cases.Hence,we exclude the recovered cases (which are 4 million,as per site stated above).

    These Johnnies who recouped,may have been infected,say 15 days ago – and if you rewind to 15 days ago,and deduct the spike in the RIBs of the BRICS – you will have an infected base of,say 6 million.If you remove the recovered (4 million),and then ratio it,to the dead of 420000 – then you have a kill ratio of 21% !

    Cannot compare the dead to the entire population – as of this instant – as it would include billions of aged,morbid and asymptomatics – who will get infected very soon.

    If we take a 1 year horizon – then post the 1 year – you could take the global population – as that by that time,the virus would have had enough time,to spread,evolve and mutate (across the latitudes and seasons).At that stage,a ratio w.r.t the population,would be a meaningful statistic – to benchmark intra and inter se,with other diseases.By that time the death rate will mature and the complete breakdown of the health infrastructure will be apparent (to explain the future geometric rise)

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  158. Pingback: Sweden’s Outbreak Will Peter Out After 1000 More Test-Positive Deaths for a Total Infection Fatality Rate of 0.06% – Anti-Empire

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  161. I 100% agree that heterogeneous distributions in population characteristics for connectivity and susceptibility will greatly lower the herd immunity threshold commonly sited for the simple homogeneous assumptions commonly used when reference 70% infection rates. See my analysis from May that breaks it down with some case studies:

    https://covidplanningtools.com/are-we-closer-to-herd-immunity-than-the-experts-say/

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