By Nic Lewis
Introduction
I showed in my last article that inhomogeneity within a population in the susceptibility and infectivity of individuals would reduce the herd immunity threshold, in my view probably very substantially, and that evidence from Stockholm County appeared to support that view. In this article I will first provide other evidence pointing to such population inhomogeneity being very considerable. I will then go on to consider how the overshoot of infections beyond the herd immunity threshold could be reduced.
I’ll start with a recap. The basic reproduction ratio of an epidemic, R0, measures how many people, on average, each infected individual infects at the start of the epidemic. If R0 exceeds one, the epidemic will grow, exponentially at first. But, assuming recovered individuals become immune, the pool of susceptible individuals shrinks over time and the current reproduction ratio falls. The proportion of the population that have been infected at the point where the current reproduction ratio falls to one is the ‘herd immunity threshold’ (HIT). Beyond that point the epidemic is under control, and shrinks.
The higher R0 is, the greater the HIT will be. I used an R0 value of 2.4, the baseline value used in the influential Imperial College model (Ferguson20[1]). Standard simple compartmental models of epidemic growth, which assume a homogeneous population, imply that the HIT equals {1 – 1/R0}. For R0=2.4, they imply the HIT is 58%. For R0 value of 3, which is towards the upper end of most estimates, the HIT is 67%. These naïve, unrealistic values probably account for the HIT range of 60–70% for COVID-19 often cited by epidemiologists quoted in the mainstream media.
There is no doubt that inhomogeneity within a population in the susceptibility and infectivity of individuals will reduce the HIT. I cited the Gomes et al.[2] paper as showing this and I adopted, with some modifications, its susceptible – exposed – infectious – recovered (SEIR) compartmental model (Figure 1). I also adopted its gamma probability distribution for population inhomogeneity that arose from varying social connectivity – different rates of mixing with (being in contact with) other people, which affects both susceptibility and infectivity. The gamma distribution can represent the existence of a small number of highly connected “superspreaders” with a very high susceptibility and infectivity, together with a far larger number of people who have a much lower connectivity. I used illustrative coefficients of variation (CV) – a measure of the extent of inhomogeneity – of 1 and 2 in my article for inhomogeneity related to social connectivity. Those levels are consistent with the evidence.[3]
Figure 1. SEIR 4-compartment epidemiological model diagram. Initially all individuals are susceptible. A tiny number are seeded with infection at the start of the epidemic. Exposed individuals are susceptibles who have been infected, but who remain uninfectious until a probabilistic latent period has expired. Once they become infectious they remain so for a probabilistic infectious period and then become ‘recovered’ – which includes some who are still ill and may die, and some who have died while infectious. In the standard model version, the rate of new infections is proportional to the product of the numbers of infectious and susceptible individuals. In the modified model, these numbers are weighted by respectively the infectivity and susceptibility of each of the individuals involved, both of which vary between individuals according to their social connectivity. Individual infectivity and susceptibility also vary separately, with factors specific to each.
Other evidence regarding the effects of population inhomogeneity
Another recent paper, Britton et al.[4], also shows that varying social connectivity will lower the HIT for COVID-19. They use, for illustrative purposes, a much simpler probability distribution, with the population divided into only three segments, with arbitrarily chosen social mixing levels, giving rise to a smaller CV of 0.56, and assume R0=2.5 The result is a reduction of the HIT from 60% to 46%. They point out that it is only the disease-induced HIT that is reduced; the HIT for vaccination is unaffected by population inhomogeneity.
It is becoming evident that, in addition to individuals’ general resistance to infection varying, around half the population may well have pre-existing partial immunity to COVID-19 due to previous encounters with other coronaviruses.[5] [6] [7] Variation in susceptibility related to resistance to COVID-19 infection is therefore an important factor.
A 20th May preprint paper, McGeoch and McGeoch,[8] which divides the population into only two parts, considers variability in susceptibility that is related only to resistance to infection, and not to social connectivity. In my model, such variability was included in the probabilistic factor that reflected non-social connectivity related variability in susceptibility. I used probability distributions with CV values of 0.42 and 0.95[9] to represent that factor, while the CV of their susceptibility distribution is 0.6.[10] They find a significant reduction in the projected HIT and final infected proportion, but a smaller one than in my model. That is to be expected, because their model omits the social connectivity factor, which affects both the susceptibility and infectivity of each individual.
A recent working paper[11] from the US National Bureau of Economic Research reviews models for the spread of COVID-19, both simple and complex, and their policy implications. It has a whole section on heterogeneities that are not included in standard simple compartmental models, limiting their realism. However, it is not very complimentary about more complex models. Regarding the highly influential, complex Ferguson20 model, it says regarding how it treats the effects of policy intervention:
“The changes in contact rates assumed in this model are never justified and, in fact, appear to be entirely arbitrary and in some cases clearly inaccurate”
They are also strongly critical of the simplistic and very limited treatment of uncertainty in Ferguson20.
As I stated in my original article, the Ferguson20 model appears to account for inhomogeneity in susceptibility arising only from a very limited set of factors, with only a modest resulting impact on the growth of the epidemic. Although their model does account for substantial inhomogeneity in infectivity, using the same gamma distribution as I did, in their case inhomogeneity in infectivity appears to be uncorrelated with inhomogeneity in susceptibility, and thus has a negligible effect on the HIT.[12]
Reducing the overshoot beyond the herd immunity threshold
Although inhomogeneity can greatly lower the herd immunity threshold, the ultimate proportion of the population that becomes infected will exceed the HIT, since further infections occur after the HIT is reached. Although such infections are continuously diminishing, if the epidemic is unimpeded they have a major impact on its ultimate size. In the examples I gave, I used a R0 value of 2.4. On that basis, I showed that the final infected proportion is about 1.5 times the HIT if the population is homogeneous, and about twice the (far lower) HIT if the population is inhomogeneous in the way that I modelled. Figure 2 shows the moderate inhomogeneity case that I illustrated, for which the HIT is 24% (against 58% for a homogeneous population) but the final infected proportion is 43% (down from 88%), a lesser reduction. The reason for the large overshoot of the HIT is that there are still many infectious individuals at the time the HIT is reached.
Figure 2. Epidemic progression in an SEIR model with R0=2.4 and a population of 1 million with CV=1 common factor inhomogeneity in susceptibility and infectivity and also unrelated multiplicative inhomogeneity in susceptibility with a CV of 0.42. The latent and infectious periods are 3 and 4 days respectively.
Intervention early on
Government intervention at an early stage appears to have been designed mainly to avoid health systems being overwhelmed, but the subsequent paths of the epidemics show that in most cases it was unnecessarily strong for that purpose. Moreover, as Figure 3 shows in the homogeneous population case, imposing a lockdown early in the epidemic, with the effect of reducing R0 from 2.4 to 0.8, and maintaining it for six months, merely delays the progress of the epidemic, with the final infected proportion barely reducing, from 88% to 86%.
Figure 3 Epidemic progression in an SEIR model with a homogeneous population, where R0=2.4 until a lockdown is imposed (dotted red line) at day 30 after which R0=0.8 until lockdown is ended 180 days later (dotted green line). The latent and infectious periods are as in Figure 2.
The effect of an early imposed, long lockdown is also minor in the heterogeneous population case (Figure 4). The ultimate proportion infected falls by slightly under 5%, from 43% to 41% – still far above the HIT level.
Figure 4 Epidemic progression in an SEIR model with an inhomogeneous population, where R0=2.4 until a lockdown is imposed (dotted red line) at day 30 after which R0=0.8 until lockdown is ended 180 days later (dotted green line). The latent and infectious periods and inhomogeneity are as in Figure 2.
Moreover, intervention can have dangerous longer term effects in relation to infections.[13] Absent vaccination becoming available and providing long-lasting immunity, the virus is likely to resurge in the future if herd immunity is not reached in the original epidemic, and vulnerable people may repeatedly be at risk if not totally isolated.
Intervention at a later stage
However, government intervention at a later stage, as the HIT is approached, could enable the overshoot to be greatly reduced. Suppose the intervention, again reducing R0 from 2.4 to 0.8, is instead delayed until the HIT is being approached.
As Figure 5 shows, applying a short lockdown (30 days) later, hugely enhances the reduction in eventual total infections, compared with an early intervention lasting six times as long. The final infected proportion falls from 43% to 27%, rather than only to 41%. The reason is that dramatically slowing the infection as the HIT is approached greatly reduces the number of active infections as the HIT is crossed, and the lockdown also greatly increases the rate at which infections decline thereafter.
Figure 5 Epidemic progression in an SEIR model with an inhomogeneous population, where R0=2.4 until a lockdown is imposed (dotted red line) at day 53, after which R0=0.8 until lockdown is ended 30 days later (dotted green line). The latent and infectious periods and inhomogeneity are as in Figure 2.
If the population were prepared to obey a lockdown for 60 days at that stage, and its timing were perfect, it would potentially be feasible virtually to eliminate the overshoot of the HIT. Figure 6 shows this case. To three significant figures, the final infected proportion equals the HIT.
Figure 6 Epidemic progression in an SEIR model with an inhomogeneous population, where R0=2.4 until a lockdown is imposed (dotted red line) at day 52, after which R0=0.8 until lockdown is ended 60 days later (dotted green line). The latent and infectious periods and inhomogeneity are as in Figure 2.
Conclusions
The take home lessons are, first, that imposing stricter restrictions early in an epidemic than are necessary to prevent a health system being overwhelmed is likely to have little impact on the proportion of the population that is eventually infected, in the absence of a vaccine becoming available before restrictions are relaxed. And secondly, that a well-timed imposition of strict restrictions for a fairly short period as the herd immunity threshold is approached can hugely reduce the overshoot of the eventually infected proportion above the HIT. States that imposed strict restrictions early on and then relaxed them may find their populations unwilling to see such measures reintroduced. However, the populations of states that introduced milder restrictions and are in reality pursuing a herd immunity strategy may find the imposition of strict restrictions for a short period bracketing the crossing of the HIT to be an attractive option. In either case, the serious illness and fatalities associated reaching the eventual level of infections can be very greatly reduced if elderly and vulnerable people are shielded from infection, as discussed in an earlier article.[14]
Nicholas Lewis 29 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] 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
[3] My lower CV=1 level was also the lower level illustrated by Gomes et al., but I used a more conservative upper level, of CV=2, than their choice of CV=3. That was partly because, unlike Gomes et al., I also had a inhomogeneity of susceptibility factor that was unrelated to social connectivity. However, I cited two COVID-19 studies [3] [3] that gave best estimates for the social connectivity CV of marginally above 3. Gomes et al. also provided some arguments in favour of connectivity-related CV being as high as 3, and argued that such CV probably exceeded 1. They showed that for other infectious diseases CV varies between 1.8 and 3.3, and they said, referring to a SARS-CoV study:
“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.”
[4] Britton, T., Ball, F. and Trapman, P., 2020. The disease-induced herd immunity level for Covid-19 is substantially lower than the classical herd immunity level. arXiv preprint arXiv:2005.03085.
[5] Grifoni, A.et al Targets of T cell responses to SARS-CoV-2 coronavirus in humans with COVID-19 disease and unexposed individuals. Cell doi:10.1016/j.cell.2020.05.015
[6] Braun, J., Loyal, L., Frentsch, M., Wendisch, D., Georg, P., Kurth, F., Hippenstiel, S., Dingeldey, M., Kruse, B., Fauchere, F. and Baysal, E., 2020. Presence of SARS-CoV-2 reactive T cells in COVID-19 patients and healthy donors. medRxiv preprint https://www.medrxiv.org/content/10.1101/2020.04.17.20061440v1.
[7] Le Bert, N. et al., 2020. Different pattern of pre-existing SARS-COV-2 specific T cell immunity in SARS-recovered and uninfected individuals. bioRxiv preprint https://doi.org/10.1101/2020.05.26.115832
[8] Malcolm W McGeoch and Julie McGeoch, 2020. COVID-19 Propagation and Mortality in a Two-Part Population. medRxiv preprint doi:10.1101/2020.05.17.20104356
[9] These CVs resulted from using zero (log)mean lognormal distributions with log standard deviations of 0.4 and 0.8.
[10] However, with their model having only two population segments with different susceptibility rather than a continuous distribution the CV may not be directly comparable with that in my model.
[11] Avery, C. et al., 2020: Policy Implications of Models of the Spread of Coronavirus: Perspectives and Opportunities for Economists. NBER Working Paper No. 27007
[12] 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.
[13] See this interview with Professor Senetra Gupta of Oxford University: https://unherd.com/2020/05/oxford-doubles-down-sunetra-gupta-interview/
[14] A sensible COVID-19 exit strategy for the UK, Nicholas Lewis, 26 April 2020
Originally posted here, where a pdf copy is also available
Thanks for the excellent note. Clear, and interesting. Of course, finding the right point to intervene is a non-trivial exercise. In looking at the JHU website this AM to look for some marker that might trigger your 30-day intervention, I noticed an apparent anomaly. If you look at the number of daily cases in the US, there seems to be a much slower dropoff than for Spain or Italy, for example. Our pattern seemed to fairly closely match Sweden’s. Not sure about the Swedes, but I have to wonder if this might indicate significant undercounting of cases in the US early on. If that’s the case, it implies that it might be very difficult to time the short intervention to avoid overshooting the HIT. The question then becomes what happens if the 30-day intervention is mis-timed. Have you looked at this?
I am a proponent of developing immunity in the general population as quickly as possible (HIT) based on the concept that there will be a second wave in the fall when viruses typically have a resurgence, with the only question being the severity of the second wave .
By developing immunity early & during the summer, the risk if a severe second wave is reduced. I am assuming that covid will be weaker / lower viral loads during the summer and therefore a better time to let the virus spread in order to develop the immunity. ( I concede that I am in the minority in my recommended response to tackling the viruses)
My question to Nick L is whether he has factored the seasonal effect into his projections?
Joe
I haven’t directly factored the seasonal effect into these projections. They should be regarded as illustrations of the fact that while the herd immunity threshold has a clear link to the transmission characteristics of the virus and the population inhomogeneity in susceptibility and infectivity, and is not greatly affected by impermanent restrictions, the excess of the ultimately infected proportion over the HIT has no such link and can be greatly reduced by short duration interventions.
I agree with you that letting the virus spread during the summer to develop immunity is likely to be better than if it spreads in the winter.
What a difference a week makes!
With covid studies appearing at a rate in excess of 1,000 a week, it is hardly surprising that Nic’s effort should be overtaken by events;
https://vvattsupwiththat.blogspot.com/2020/05/mad-covid-disease-cripples-climate-blog.html
Another lame and shameless attempt to drive traffic to his lonely impostor blog. vvery childish
The White House Office of American Innovation should welcome Don as a worthy addition to its Mad Covid Disease Cluster,
That’s really pathetic, rustle.
You are worse than, joshie.
vvery silly
Nic didn’t fabricate his data, rustle. What about your TDS team’s #lancetgate? You may not have heard about it over on your lonely lame ludicrous impostor blog:
http://freerangestats.info/blog/2020/05/30/implausible-health-data-firm
> The take home lessons are, first, that imposing stricter restrictions early in an epidemic than are necessary to prevent a health system being overwhelmed is likely to have little impact on the proportion of the population that is eventually infected, in the absence of a vaccine becoming available before restrictions are relaxed.
This, of course, completely ignores any potential benefit from improved treatment methodologies that could be more widely employed – even if the same number of people are eventually infected – should interventions slow the rate of the spread.
And of course, betting against a vaccine could ultimately cost a huge sum of lives, differentially, as a result of following a strategy that favors a faster rate of spread.
There might be economic advantages to a faster spread approach – but there are huge uncertainties involved. For example, if a vaccine winds up saving large numbers of lives (and infections) the beneficial differential impact economically could be quite large.
Respect uncertainties – and don’t treat them selectively.
Have you factored in the lives lost due to the lockdown due to lack of, or late, diagnoses of cancer, etc? The number of cancer diagnoses is way down the past 2 months. I don’t think cancers are taking a holiday.
Guy –
> Have you factored in the lives lost due to the lockdown due to…
It’s an uncertainty, no doubt. As is the “died with” vs. “died of” issue.
But on the other side of the uncertainties ledger, we have people who died at home or at LTCFs with no testing done, and people who didn’t die in traffic accidents, etc.
Excess deaths points towards one side of the ledger but I think it’s far too early to draw any confident conclusions – although many do so confidently now, with their conclusions usually easily predictable by their ideological orientation.
So that’s why I say don’t treat the uncertainties selectively.
We don’t even know which effects are differentially attributable to “lockdowns” versus just normal reactions to a raging pandemic. And I’m not sure we ever will.
It’s interesting to me that people are so willing to just glide right by so many enormous uncertainties. Not surprising but still surprising at the same time.
Who is gliding?
Everything about this episodes has been infected with uncertainty beginning with the 2.2 million deaths for the US, to transmissibility on hard surfaces. Sometimes it’s best to admit we don’t know what we don’t know.
Kid –
> Everything about this episodes has been infected with uncertainty beginning with the 2.2 million deaths for the US…
What’s interesting about that is that the modelers built in a ton of uncertainty there (if you don’t just cherry pick the high end of the
predictionsprojections). The low end of their uncertainty range should be considered as well.> Who is gliding?
So actually by saying what you said you’re doing exactly what I said by treating the uncertainties selectively. Stop gliding.
Just like Trump when he tells us that his “decisive” action saved a couple million lives
And further, nothing ‘began” with those projections.
https://ftalphaville.ft.com/2020/05/21/1590091709000/It-s-all-very-well%E2%80%93following-the-science%E2%80%94but-is-the-science-any-good%E2%80%93/
Joshua: It’s interesting to me that people are so willing to just glide right by so many enormous uncertainties.
Who has been gliding right by any enormous uncertainties?
Matt –
> Who has been gliding right by any enormous uncertainties?
There are tons of examples, but those that are most salient at the ones that Nic ignored in his multiple posts here. On past posts he has ignored the uncertainties about the differential impact of “lockdowns” relative to other reactions to a pandemic virus (which he has to ignore because they are so large). In the Diamond Princess post he ignored the unrepresentariveness of the uncertainties.
I touched on just a few in this sub-thread as well.
Again you are avoiding the examples of Taiwan, South Korea, Hong Kong. NO lockdowns, extremely low death/population ratios.
You just cannot accept facts that don’t fit your agenda, little Joshie.
iandl –
First of all, in some of those places they did things that snowflakes here complain are government tyranny “lockdowns” (such as closing schools, limiting public gatherings, closing some businesses like gyms and movie theaters, etc.). Secondly, the public responded there in ways that the public would never respond here…
https://judithcurry.com/2020/05/29/when-does-government-intervention-make-sense-for-covid-19/#comment-918308
I don’t think you demonstrated anything in your previous apart from the fact you can take some fragments of (probably bad) data run it through a model and come up with conclusions unrelated to the real world.
In your conclusion of this post:
“The take home lessons are, first, that imposing stricter restrictions early in an epidemic than are necessary to prevent a health system being overwhelmed is likely to have little impact on the proportion of the population that is eventually infected, in the absence of a vaccine becoming available before restrictions are relaxed”.
The main point of restrictions is to keep a health system from being overwhelmed so fewer people die while we are waiting on better treatments and a vaccine. What is strict, too strict, or too lax isn’t a one size fits all determination nor is it something that it is possible to be precise about especially with a new virus. Variables include how much of the populace is already infected at the time of the restrictions, how lethal is the virus, how easily does the virus spread, population density, age distribution, capacity of the medical system, and possibly even the season. Almost none of these things were known or could even be intelligently guessed about at the time the restrictions needed to be put into place.
There was never a time that “restrictions needed to be put in place” at the state or national level. Our fatal mistake was confusing model outputs with reality. The models could not be correct when so many degrees of freedom were involved and the important input values were so poorly understood. A point you made in your post.
Yes, and lockdowns were counterproductive in many (most) places, apart from NYC. But of course the media centers are so provincial they can’t see beyond NYC.
Guy –
> Yes, and lockdowns were counterproductive in many (most) places, apart from NYC
And you know this how? Don’t forget to show your work.
Cancer diagnosis and treatment have declined by about 65%, and unless you believe treatments are worthless, this is a big deal. Many hospitals were required to stop ‘elective’ surgeries like mastectomies, DUE TO THE LOCKDOWNS.
But screw those people, right?
https://tinyurl.com/y6wn8ojg
Guy –
>… unless you believe treatments are worthless, this is a big deal.
Assuming that is directed at me, I never said it isn’t a “big deal.”
What I’ve said is don’t deal with the uncertainties selectively – in particular if doing so confirms your ideological predisposition.
You asked how I knew the lockdowns are counterproductive, and I’ve presented data that support that statement. There are numerous other deleterious impacts of the lockdowns if one bothers to look: schooling, deadly car crashes (people are driving more recklessly), political corruption with the stimulus, crime (some increasing, others decreasing), bankruptcies, etc. These are not virus caused, they are government caused effects.
You haven’t shown they are differential effects of a “lockdown.”. For example, how many parents wouldn’t have sent their kids to school if the local government hadn’t shutterd them? How many teachers wouldn’t havd gone in to teach? Would you have those teachers fired? So they wouldn’t have been paid? Keep the school open with most of the kids staying home? So parents would stay home to take care of their kids that they didn’t want to go to school. And then they would get fired. No unemployment. No stimulus.
You don’t know. Any of this. You dont know what would have happened if there were no “lockdown.”
The assumed IFR was almost certainly too high, and this was pointed out months ago.
It was known months ago that the old and infirm were in most danger from the virus.
The impact of the lockdowns on the economy was known months ago, hence the multi-trillion dollar packages to address that issue.
It was known amongst medical experts that no vaccine exists for any other Coronavirus. Therefore, the assumption that a vaccine would be developed to allow lockdowns to be lifted was, and is, incoherent.
It was, or should have been, known from the beginning that lockdowns could not reasonably remain in place for more than a few weeks.
The impact on our management of other health issues was known, and pointed out months ago.
IMO the decision to lockdown entire states based on model outputs that could only have been correct by chance never made sense.
“ You haven’t shown they are differential effects of a “lockdown.”.
Did you miss the cancer stats? That is 100% due to the lockdown.
If you’re are aren’t aware of the others, you are simply ignorant. The lockdowns sent 100% of the kids home, for example. Only a moron would think that every parent would keep every kid home.
> Did you miss the cancer stats? That is 100% due to the lockdown
What are you talking about? If there’s a raging epidemic at hospitals, and tons of sick people are going to the doctor, people would likewise be avoiding seeking medical care.
So you don’t know how much of the problem is specific to a “lockdown.” For all you know, absent a “lockdown” and with a more widespread raging epidemic, it would be worse and for a longer period of time.
> Only a moron would think that every parent would keep every kid home.
Yes, all the kids went home and their parents could get unemployment and stimulus checks.
Keep them open and parents have to choose between sending their kids to school in an infectious environment, or keeping them home and staying home and get fired with no unemployment and no stimulus checks.
There were huge drops in attendance before the “lockdowns.” it wasn’t a sustainable situation. Would you force teachers to go in and teach in an infectious environment or lose their jobs? What you don’t seem to understand is that there would have been many of the same problems absent a “lockdown.” the schools would have been completely chaotic and would likely have closed anyway.
You still haven’t shown your work.
Give some evidence for the claims you’re making. Or admit you just don’t know.
All will eventually be revealed using our political blame game hindsight. We will be looking to the past with our 20/40 – 20/50 optical quality view of the past – though it is likely all will claim 20/20 hindsight.
“Almost none of these things were known or could even be intelligently guessed about at the time the restrictions needed to be put into place.”
That’s a pretty good statement. Needed to be put into place when we didn’t know. There is too cautious. There were a lot of things ‘needed’ that didn’t make sense. We have schools opening in Western Europe. Was it needed to cancel Summer classes here? Introducing need with uncertainties. That’s nice.
> Moreover, intervention can have dangerous longer term effects in relation to infections.[13] Absent vaccination becoming available and providing long-lasting immunity, the virus is likely to resurge in the future if herd immunity is not reached in the original epidemic, and vulnerable people may repeatedly be at risk if not totally isolated.
The logic here rests on an assumption that is not reflected in the real world. The logic here is that more vulnerable people can successfully be isolated from a more prevalently infected general public, and thus protected during a “herd immunity” approach – because the needed duration of the protection period would be shorter than otherwise.
That has clearly not been the case in Sweden – a country whose infrastructure might, in some ways, make it uniquely suited to employ an approach based on that logic.
The only countries that have successfully protected their vulnerable populations (at least thus far) are those that have employed stringent government supported social distancing and/or comprehensive testing/tracing/isolating policies.
The virus has been prevalent in the significant Somali minority in Sweden. In the rest of the population, not so much.
Who is dying in Sweden? Which vulnerable people have been protected? Then compare to other counties like Taiwan, or New Zealand.
Assume weeks ago, some people were comparing Sweden to Switzerland to say that lockdowns don’t work because the deaths per capita were about the same.
Now, deaths per capita in Sweden is close to double that in Switzerland, and will soon reach that mark.
If all infections in Sweden stopped today, it would take some 200 days for Switzerland to catch up at its current rate of spread.
The rate in Sweden will soon surpass that of France – which has a much higher % of immigrants, and which lies right next to Lombardy and with much higher population density and much lower rate of single-person households.
Bigterguy – do you have a link to swedens covid demographics, including both race and age and any other pertinent factors. Sweden’s results have been both condemned and praised – depending on the persons outlook. Seems that understanding the demographics provides a much better prospective on how to find solutions.
Here in Dallas TX, the greatest fatality rates are in the african american and hispanic zip codes.
Here is one story.
https://abcnews.go.com/International/wireStory/coronavirus-takes-toll-swedens-immigrant-community-70593594
The other factor is that the immune system is aided by vitamin D, which has higher deficiency in darker skin people and in winter or at high latitudes.
Places that have come closer to herd immunity will, of course, suffer less in a second wave and will not need to alter their behavior much.
Oh Joshua;
“Which vulnerable people have been protected? Then compare to other counties like Taiwan, or New Zealand.”
are you saying people in NZ were protected? Friends there point out it was a long hot summer there; everyone out of doors, getting lots of Vit D: these respiratory viruses do not show these wave patterns in summers: Australia was the same: it really worries me you modellers have a very one-dimensional view of things;
you seem to screech for house-arrests Joshua; please get out of doors; get some sunshine; improve your health; go for a long walk; leave your models behind
You screech about Swedish deaths: https://twitter.com/FrankfurtZack/status/1266292852159508480/photo/1 flu has been worse in the past: despite your beloved vaccines available then.
> ” … compare to other counties like Taiwan”
NO lockdown in Taiwan, yet deaths/population ratio extremely low.
ianl –
> .NO lockdown in Taiwan, yet deaths/population ratio extremely low.
I’m glad that you think we should have handled this a lot more like Taiwan. So do I! It’s so hard to get Trump supporters to admit the failures of our federal government, as you are so willing to do.
Do you know that they had plans in Taiwan to implement full lockdowns should there have been a lot of COVID-19 cases? They had simulation exercises to plan exactly how they would do that.
But anyway, I’m glad that you agree with me, that there would have been no need for “lockdowns” here if we had done what they did in places like Taiwan. And if the public in this country had reacted like the public in Taiwan. But that would have required a competent government. And it would have required public that doesn’t see wearing a mask, and getting your temperature checked, and having companies mandated to make masks and sanitizer, and thorough isolation of people who test positive, and stiff penalties for people raise prices on needed goods like hand sanitizer, as infringements of their freedoms to the extent that they go to state houses armed to the teeth to make sure that the government doesn’t expect any accountability from them.
Summer and sunlight were behind New Zealand’s excellent Covid stats?
(0.03% infection rate and 1.5% case fatality rate)
Brazil is in the same hemisphere as New Zealand, experiencing the same summer, but their stats are: 0.56% infection rate, 8% case fatality rate.
You should give those arms a rest – they must be tired with all that waving around.
The most successful were islands that strictly limited people coming in or out- New Zealand, Hawaii.
New York has three times Sweden’s death toll per capita. Sweden has seven times the death toll of Texas.
Hawaii was successful, but has 35% unemployment as a result and has no clear answer to “now what?”
If they open back up will they be New York, Texas or Sweden. If they don’t open back up, what will they be?
“The most successful were islands that strictly limited people coming in or out- New Zealand, Hawaii.”
Em …. NZ put its citizens under house-arrest during a very hot and dry summer; friends there tell us there are numerous anecdotes of corona illnesses from November at least; the State will not allow or discuss these seemingly.
Sad fact: these respiratory viral waves don’t happen in summers; it is as simple as that; they don’t get snow in summer; they don’t get respiratory viral waves in summer;
the myth that is being passed about; that house-arrest works; to justify the madness; instead, alternative viewpoint, Hawaii has wonderful sunshine: Vit D seems crucial to health;
please watch this https://www.youtube.com/watch?v=v3pK0dccQ38
Weather is the big variable in death rate, I think.
Hawaii has boxed itself in policy wise. It’s wholly owned by a political party with a national policy of rejecting reopening and asserting that the dying will begin in Florida and Texas any day now.
Even if the state’s politicians ignore their party and reopen, the national Democrats won’t allow anyone on the mainland to go there. How can you go on MSNBC to rail against the death-dealing governor of Florida daring to open a beach while letting people fly hours over the ocean to do it on a packed Hawaiian beach?
Maybe they’ll get a bunch of folks from Texas.
Terry,
Where do you have any evidence about the seasonality of CV? We are nearing summer in the US and the rates of infection have dropped but they aren’t anywhere near to vanishing. Ecuador has been hit hard. Brazil and Mexico are being hit hard. People in those places must be getting plenty of Vitamin D. All the evidence is that this virus is at best barely affected by warm weather and sunshine.
Jimmy looks at this from the virus preservation perspective. We are not sure if he is playing Devil’s advocate, or just advocate.
It’s Summer in Brazil, too, but they have the 2nd worst death toll so far.
Is this saying that it is possible that Boris, purely by accident, may have, in the long term, got it about right?
“Initially all individuals are susceptible.” Is it an assumption, or a fact, or are you considering only a susceptible part of the population?
It’s the standard assumption in these simplified epidemiological models. But the probabilistic susceptibility distribution that I employ can, depending on the CV levels used, represent a significant proportion of the population having a very low susceptibility to infection by SARS-CoV-2.
Nic Lewis, a valiant but forlorn attempt, in my opinion. Once you showed that the heterogeneity need to be taken into account in any realistic modeling, as you did in the previous essay, then I think you showed that further progress could only be obtained by detailed modeling of the kinds of heterogeneity that are known; and that makes the models intractable. The aspects of the lockdown were respected by different people differently, at different stages of the pandemic, so turning a date of the order into a date of the lockdown, and treating the lockdown as on or off, doesn’t lead to any accurate and dependable models.
The empirical evidence does not provide a lot of guidance. What exactly was the effect of introducing the virus into Italy through its hospitalized elderly population? Into Korea through a well-defined religious sect? What were the effects of the total elimination of traffic between Taiwan and the mainland, Japan and China, and Korea and China (as opposed to the US gradual halt of traffic with China while permitting indirect traffic through Europe)? Did closing the public schools produce measurable effects? In kids only, school staff and parents? How does the New York disaster wrt nursing homes affect your thinking about parameterization? Or the communication links like the NY subway lines and the flights and road lines from NY to the rest of the country? Which differences among Italy, Switzerland, Belgium and Sweden can be shown to have produced the different trajectories of their infection and death rates? What is a modeler to make of the evidence that around half of all deaths were among sick and elderly people, and that a large fraction of them would have died in the upcoming year without contracting COVID-19? It feels cruel even to give those ideas serious consideration, but accurate modeling requires it.
And so on. These and more issues were raised in the comments to your first post.
As always, I appreciate your efforts.
Yes, we need double blind controlled experiments, but that’s nearly impossible since there are so many confounding factors. In the end, the data will be able to be interpreted to fit almost any hypothesis.
Sweden has been held up as an example of common sense prevailing against misguided lockdown over-reaction and irrational economic self-harm.
Well Sweden now is in poor shape. It’s quietly floated to #1 in the international league of Covid deaths per capita.
And very disturbing reports have emerged from Sweden, from Swedish friends and also media articles like this one:
https://www.rt.com/op-ed/490012-swedish-directives-covid-elderly-cruel/
Astonishingly it seems that Sweden are doubling down so hard on their cultivated image as “the one sensible country” that policies bordering on human rights abuse are being enacted. Essentially it seems that intensive medical intervention is being denied to covid19 patients as a deliberate policy and mandate. Intensive care and oxygen are apparently forbidden to be offered to old patients with the virus.
A Swedish friend told me that medical and care home staff who complain about absence of PPE (personal protective equipment) are being sacked for doing so. And the country including its media seem to be coming together to stifle the publicity of any adverse news and sweep under the carpet the whole covid19 outbreak and its growing seriousness in Sweden.
Care home residents have been observed suffocating like goldfish for 24-48 hours before dying, “carers” stand by forbidden to apply oxygen or respirators. Media are forbidden to report. All sacrificed for the sake of the “smart Sweden” story.
It’s not only about numbers. Although Sweden are now world #1 in covid19 deaths per capita. And Sweden’s deaths of covid19 don’t include old people’s homes.
Reblogged this on HiFast News Feed.
Thoughts and prayers:
https://twitter.com/jamesannan/status/1266430221777088515
If there ever was a coup de grace.
I used R0=2.4 because that was the central assumption used by Prof. Ferguson for the Imperial College COVID-19 modelling. James Annan’s own SEIR model based pre-lockdown estimates were around 3 for the UL, France and Italy, higher for Spain and lower (2.5) for Sweden. But they will have been dominated by the early spread in large cities, where R0 can be expected to be higher than in the country as a whole.
Amen.
As I mentioned on an earlier post, the US data simply does not support the idea that lockdowns save lives over what voluntary social distancing had already done. Florida and Georgia were early to open their economies and neither saw a surge in infections, hospitalizations, or deaths.
New York which is still shut down has 14 times the total fatalities of Florida. Florida has slightly more residents than New York and a higher percentage of vulnerable senior citizens. Currently, daily death rate in New York is about 3 times that in Florida and current new daily infections in New York are about twice those in Florida. New York in objective terms was vastly the worst state in the US.
Another interesting fact is that Swedish new hospitalizations are declining much more rapidly than new infections. I’m starting to think that there is some other factor at work here that is not in the simple models being explored here by Nic and by Annan.
One factor that would help explain this is that Sweden unfortunately let infection spread to care homes, the elderly inhabitants of which are many times more likely to be hospitalised if infected. That may now largely be in the past. And it might perhaps also reflect a widening of testing, which I believe had since mid-March been largely focused on hospitalised patients. But there might be other factors involved.
Yes Nic, That’s one of my hypotheses also. If it is true that in the early going a high percentage of seriously ill people had their deaths accelerated and relatively few less vulnerable people died, we should see a strong dip in overall mortality once the peak is past. Europe actually has much better mortality statistics than the US. One chart I’ve seen indicates that non-covid deaths in the UK are already below normal.
> Sweden unfortunately let infection spread to care homes
So all one has to do is not to let infection spread to care homes.
If only any competent ever thought of that.
Go Team Denizens!
Florida and Georgia get sunshine; NY is way north, and has bad air pollution: sunshine and Vit D seem crucial; I know everyone would rather be head down and bum up, studying complex mathematical models in a dark room;
please watch this https://www.youtube.com/watch?v=EP81YMvs4yI and then this https://www.youtube.com/watch?v=v3pK0dccQ38
Terry,
I replied above about your Vit D theory but you also need to factor that the statistics in both Georgia and Florida have likely been significantly manipulated. I live in Georgia and we are spiking and experts are saying it is not just an artifact of testing.
Spike in Georgia COVID-19 cases partly from virus spread, expert says
https://www.ajc.com/news/breaking-news/spike-georgia-covid-cases-partly-from-virus-spread-expert-says/ScJKBSS7S4UMhVG60iALxL/
What evidence do you have that the stats from Georgia and Florida have been manipulated, jimmy? Who is cheating the virus? Orange Man Bad?
New York, the nation’s fourth largest state by population, has more than 3 times as many fatalities as the top three states combined. Florida, Texas, California.
Combined.
That disparity cannot be explained by lockdown policy or national political response.
Most of New York’s fatalities were in New York City and it’s immediate suburbs.
It is fair to ask if it was ever possible to lock down a densely populated city or, at the very least, how to do it much more effectively.
California, Texas and Florida have big cities but they are much more automobile focused and suburban than NYC.
And we’re going to read a lot more about how the best policy may have been to lock New Yorkers in their city- quarantine it.
“The coronavirus outbreak in New York City became the primary source of infections around the United States, researchers have found.”
https://www.nytimes.com/2020/05/07/us/new-york-city-coronavirus-outbreak.html
I think I worry that you modellers; whilst earnest and well-intentioned; seem to have no background in past events; or other stuff .. you are great people, make no mistake …….
eg https://twitter.com/FrankfurtZack/status/1266292852159508480/photo/1 so deaths from flu have happened in the past; viruses come and viruses go;
read about how they behave here; https://www.nature.com/articles/d41586-019-01880-6
“Sorek and his colleagues had found phages actively discussing their choices. They realized that as a phage infects a cell, it releases a tiny protein — a peptide just six amino acids long — that serves as a message to its brethren: “I’ve taken a victim”. As the phages infect more cells, the message gets louder, signalling that uninfected hosts are becoming scarce. Phages then put a halt to lysis — the process of replicating and breaking out of their hosts — instead staying hidden in a sluggish state called lysogeny1.”
and so many believe it is house-arrest that slows the virus!! Human hubris surely.
Need to consider the unintended consequences of lockdown.
https://www.bmj.com/content/369/bmj.m1931
“Staggering number” of extra deaths in community is not explained by covid-19.
Under reporting especially during a pandemic is less likely than at other times.
Huge drop in presentations to emergency departments from fear of contacting the virus. Heart attacks, strokes, appendicitis, fractures … plus suicides.
Many people don’t seem to get SARS-CoV-2.
Maybe cross reactivity with circulating common cold corona viruses.
https://www.cell.com/cell/fulltext/S0092-8674(20)30610-3
Lockdown has enormous costs as will be revealed over the years ahead.
I see some love for Vitamin D on this thread.
https://www.healthline.com/nutrition/vitamin-d-dosage
At first I thought I’d get 4000 IU but got conservative and went with 2000 IU.
Summer and all seems to be the off season for this junk. Why?
The simpliest answer. Let’s try that one.
“It is becoming evident that, in addition to individuals’ general resistance to infection varying, around half the population may well have pre-existing partial immunity to COVID-19 due to previous encounters with other coronaviruses.[5]”
No. WRONG.
1. that is not what they concluded
2. they studied 20 whole patients.
get a grip
“While it was important to identify antigen-specific T cell responses in COVID-19 cases, it is also
of great interest to understand whether crossreactive immunity exists between coronaviruses to any
degree. A key step in developing that understanding is to examine antigen-specific CD4+
and CD8+
T
cells in COVID-19 cases and in unexposed healthy controls, utilizing the exact same antigens and
series of experimental techniques. CD4+
T cell responses were detected in 40-60% of unexposed
individuals. This may be reflective of some degree of crossreactive, preexisting immunity to SARSCoV-2 in some, but not all, individuals. Whether this immunity is relevant in influencing clinical
outcomes is unknown—and cannot be known without T cell measurements before and after SARSCoV-2 infection of individuals—but it is tempting to speculate that the crossreactive CD4+
T cells may
be of value in protective immunity, based on SARS mouse models (Zhao et al., 2016). Clear
identification of the crossreactive peptides, and their sequence homology relation to other
coronaviruses, requires deconvolution of the positive peptide pools, which is not feasible with the cell
numbers presently available, and time frame of the present study.
But Steven, it was time well spent on a nice little pilot study that lays some important ground work. Of course, not as interesting as watching K-pop videos.
You’ve just cherry picked ONE of the three studies that I cited in support of my quite nuanced “may well have pre-existing partial immunity” statement. And more evidence directly or indirectly supporting it is coming in. I refer to Palm et al (https://doi.org/10.1101/2020.05.18.20105189, 22 May 2020), Shomuradova et al (https://doi.org/10.1101/2020.05.20.20107813, 25 May 2020), Lee et al (https://doi.org/10.1101/2020.05.20.107292, 20 May 2020).
The Cell paper Leon L posted above is a good one coming out in the June issue on this same topic.
“Importantly, we detected SARS-CoV-2-reactive CD4+ T cells in ∼40%–60% of unexposed individuals, suggesting cross-reactive T cell recognition between circulating “common cold” coronaviruses and SARS-CoV-2.”
Some of the authors work here:
https://en.wikipedia.org/wiki/La_Jolla_Institute_for_Immunology
The first author listed on the Cell paper looks qualified to me.
Nice cherrypick of the study write up, go to the last page and you will see that they actually tested the T-cells in these blood samples for reactivity against the current coronavirus. And so what if it is only 20 people, do you really think that somehow they just happened to find the only people in the country who are going to have those T-cells. It has been apparent since the start of the epidemic that the reason large numbers of people, in fact the vast majority, either don’t get infected or have asymptomatic or mild infections is almost certainly that there is likely some pre-existing immune defense from prior coronavirus infections or exposure, which are very, very common. If you have a better explanation for those clear characteristics of the epidemic, let’s hear it.
Some people just seem to have a bias to unnecessarily lock us all down forever, damn the economic and health consequences.
“For a while, it appeared that the developing world was being spared the worst of the pandemic. As of April 30, with 84 percent of the world’s population, low-income and middle-income countries were home to just 14 percent of the world’s known covid-19 deaths, according to a Brookings Institution report. This can be explained in part by a lack of testing and a failure to attribute deaths to covid-19.
But there may be other factors. Nursing homes, which have accounted for a large share of deaths in wealthy countries, are uncommon in the developing world, so the elderly are not clustered together. Heat may have some effect in reducing the spread of the virus. Some medical experts privately speculate that the populations in these countries have stronger immune systems because they have been exposed to many more diseases over their lifetimes
There is another possibility. The developing world was spared the disease in the early months because it was less connected, by travel and trade, to the initial hot spots (China and Europe). In the past few weeks, however, the coronavirus has moved slowly but steadily across South Asia and Latin America. Brazil now has about 1,000 recorded deaths a day — and cases are rising exponentially. Africa has not had a large spike in confirmed cases — so far — but anecdotal evidence suggests the disease is spreading there as well. The Wall Street Journal reports that in the northern Nigerian city of Kano, gravediggers are running out of space and have resorted to burying corpses between existing graves or putting multiple bodies in a single grave”.
https://www.washingtonpost.com/opinions/global-opinions/the-pandemics-second-stage-is-here–and-its-getting-ugly/2020/05/28/7f9d1d38-a10f-11ea-b5c9-570a91917d8d_story.html
So much for the immunity of the “sun belt”.
Nigeria, a country of 200 million, doesn’t seem to have been hit particularly hard, as of yet. They have 261 deaths and Kano, a city of 3.2 million, has 42 deaths. The country has experienced single digit deaths most of the days since early April. Nigeria has one of the highest infant mortality rates in the world. They also have 2.3 million deaths per year. I assume the grave diggers are always busy.
Nigeria has a median age of 18 which is significantly lower than Italy’s age of 47 and less than half of America’s 38. There are 200 countries older than Nigeria. Perhaps one of the reasons for Africa’s low death rate, as of now, is the relatively low median age of so many countries. Uganda and Niger are at the bottom at around 15 median age. Many other African countries are in the bottom 20. But the number of cases is extremely low for those countries as well, so the reasons for the low death rates are most likely more complex than just this factor.
The total deaths for Africa a couple of days ago was still under 4,000. In order to reach the 3.3 million deaths identified as an upper bound by a U.N., report, the rates have to dramatically rise from the last 2 months.
When you mentioned South Asia, which countries were you thinking of, since Vietnam, Cambodia and Laos have 0 deaths and the death rate in Thailand is still low.
You revel in the destruction caused by this virus, jimmy. We wish you would do it somewhere else.
An example of responsible government intervention would be for example the case of typhoid Mary –
Mary Mallon, or Typhoid Mary, was the “an infamous asymptomatic typhoid carrier,” refuse to abstain from cooking for others, requiring that she be forcibly quarantined for the good of the public, despite the fact there is an argument that she had personally done nothing wrong except for her refusal to eschew occupation The occupation of her choice. I don’t see that as a valid argument because, that’s essentially like allowing a business to sell a product without informing the public of some inherent danger that the public wouldn’t otherwise be aware of when using the product.
Mongolia shows that covid can be controlled by lockdown
https://kottke.org/20/05/the-country-with-the-best-covid-19-response-mongolia
This is a wierd example to pull out of your hat. It’s a totally different country than any Western country and has a very low population density. Travel is probably much less common. So it really shows little of value except that a stopped clock is right twice a day.
Ignoring the obvious population density differences. Would US culture accept such a lockdown? And to what end? A lockdown that isolates a population needs a vaccine as a get out of jail card. There are no vaccines for any other Coronavirus. Doesn’t mean there won’t be one for this one, but I wouldn’t count on it.
Mongolia sets an example showing the conclusions of this analysis are fallacious.
https://medium.com/@indica/covid-underdogs-mongolia-3b0c162427c2
Antarctica is probably a better example, rabbette.
One thing they had going for them, at -20F in January they weren’t patrolling the streets looking to shut down pool parties. Do they even come out of their houses until summer?
Amusing: “Mongolia’s growth is almost completely export-driven, so they were taking a huge economic hit here, especially with zero cases. However, they were not like the dinosaurs in the west, looking at an asteroid saying “but the economy!””
So Mongolia is perfectly set up to get hammered whenever they relax the lockdown and an infected traveler appears.
Or they could remain locked down forever.
It ain’t over till it’s over.
And it ain’t over.
Squirrel. The World is not Mongolia. I expect better.
Closed borders. Got it.
Lockdown early then monitor and control visitors
https://colinmathers.files.wordpress.com/2020/05/controlled.jpg
https://www.zerohedge.com/s3/files/inline-images/lockdown%20jpm.jpg
Do you understand who you sound like?
Who goes to Mongolia?
Pingback: When does govt intervention make sense for COVID-19? – All My Daily News
Macromolecular Studies in Łódź, the Polish Academy of Sciences (PL: CBMiM PAN) composed of M. Turek MA, dr. E. Różycka-Sokołowska, prof. M. Makowska-Janusik, dr. M. Koprowski and dr. K. Owsianik under the direction of prof. P. Bałczewski developed a two-component drug that can be used not only in the treatment of COVID-19 disease caused by SARS-CoV-2 infection, but also as the prevention of its development and a way of strengthening the immune response directed against SARS-CoV-2. The invention was filed with the Polish Patent Office (- patent application of 29.04.2020, P.433749).
The main component of the developed drug is the active substance used so far to treat hypertension, affecting the ACE2 (angiotensin-converting enzyme 2), which is also a receptor of SARS-CoV-2, with the help of which the virus penetrates into the cell. By blocking this receptor, the active substance can prevent the development of acute respiratory failure syndrome, which is the main cause of death of patients infected with SARS-CoV-2. What is more, it also increases the Ang-(1–7) production. Currently, worldwide in less than 2 months, 38 active clinical trials have already been recorded on the effects of this active substance and other drugs in this group on SARS-CoV-2. An additional beneficial effect of the developed formulation is provided by the second component (a nutraceutical), which is a key compound that allows the strengthening of the immune response, mainly in viral infections, and also prevents ventilator-induced lung injury, which is especially vital in treating COVID-19. Importantly, the main component of the developed drug is characterised by poor solubility, which results in its low bioavailability. The developed co-amorphisation methodology, which allows for a dual-track drug system, has led to a stable pharmaceutical form, characterised by up to 24 times higher solubility of the starting component and proportionally greater bioavailability.
The carried out research was funded from the National Science Centre Preludium project (M. Turek) No UMO-2019/33/N/ST5/01602 and the statutory research subsidy of the Division of Organic Chemistry of the Centre of Molecular and Macromolecular Studies in Łódź, the Polish Academy of Sciences (PL: CBMiM PAN) No. 500-02.
http://www.en.ujd.edu.pl/news/view/drug-formulation-for-treating-covid-19-patients-developed-by-researchers-of-jdu-and-centre-of-molecular-macromolecular-studies
Yet. In most places in the world there have been no COVID-19 virus. And in most places that had some virus, it is now extinct. So why should they open up and invite the “old lady of the pest” in? Stockholm may reach the herd immunity, but Lappland? I think most people of non-infected areas want to stay protected, and will welcome some restrictions. Just ask the people of Mongolia or Iceland.
Everyone is free to isolate themselves without government permission if they want to stay safe. My family is doing this because we have 2 immunocompromised members. But those who are not concerned with the virus or are willing to take personal risks should be free to do so. They won’t be harming us and will help reach herd immunity sooner in the general population. That would actually be helping people like my family.
The virus is like a great forest fire. Many areas are greatly affected. The only way to meet it where it is out of control is to let it burn until there becomes no fuel left. Some measures can be taken to prohibit too big destructions. But other places it is possible to limit it. And most places it can be extinguished. And then there will be lots of places with smoldering fires. so watch and prepare. And the costs of a fire can be huge.
> ” … elderly and vulnerable people are shielded from infection”
A common enough assertion. Whenever I have asked the following question, there has never been a direct answer. I expect Nic Lewis on this topic to be just as diffident (somewhat cowardly, actually), although I certainly respect most of his analyses, both on COVID-19 and various climatic topics.
Q: does “shielding elderly people” mean enforced isolation/incarceration for an indefinite period for those over 70, healthy or not, with groceries dumped outside the front door every fortnight, no visits from children, grandchildren or friends ? Does this scapegoating take into account the damage done by such discriminatory penalties for simply existing to that age ?
I do not expect a direct, coherent reply since doing so exposes the true valuation of older people. In short, “you will be locked up in isolation indefinitely for our own good.”
“shielding elderly people” Good question ianl.
I would think that some social distancing would be enough for elderly living in their own apartments. The claim to be locked inside the houses must be a great misunderstanding, as minimum of infections happen outdoor. So they can meet their family.
The great problem is elderly in health institutions. When the virus had spread for months, as in Italy, Spain, and perhaps Sweden, it was to late. Many health workers were infected without knowing it. The “fire” of infection became to difficult to control. Then there is no help in the mantra “shielding elderly people”. A vicious circle of infection, From health care workers to patients, and from patients to health care workers.
“…“shielding elderly people” mean enforced isolation/incarceration for an indefinite period for those over 70, healthy or not, with groceries dumped outside the front door every fortnight, no visits from children, grandchildren or friends?”
Maybe it means old people make their own decisions. If under power of attorney, those decisions are made by who has that.
I can shield my Dad by not visiting him. People can do that.
People said someone on the Right was too much like a dictator. Now they are acting like dictators. Saying someone on the Right is not enough of a dictator.
When did shielding start meaning lock them up? Stop the silly hysteria. Those most vulnerable are the folks confined to nursing home and hospices. They don’t enjoy a lot of freedom, as is. The idea of shielding is to keep infected people out of those places. There would be no reason or desire to force old folks living on their own to stay in their residences. Make efforts to help them avoid infection. Spend a hundred billion dollars or whatever making sure they have food and medical care, if they choose to isolate themselves.
does “shielding elderly people” mean enforced isolation/incarceration for an indefinite period for those over 70″
No it doesn’t, so far as I’m concerned. I would advovate for a voluntary isolation basis for elderly and vulnerable people. The government would advise them to do so, perhaps accompanied by a warning that they would not be at the front of any queue for state-provided hospital care if they decided not to do so and became ill with COVID-19, and the state health system were unable to meet all demand at that time.
No doubt many authoritarian minded people would not be happy with letting aged and vulnerable people make their own decisions, but I don’t see that they have any right to interfere with other people’s lives in these circumstances.
Not that I regard everyone over 70 as elderly or vulnerable in any case.
> No it doesn’t, so far as I’m concerned. I would advovate for a voluntary isolation basis for elderly and vulnerable people.
Do you really have no idea how unrealistic that is for many “vulnerable” (and elderly) people? People who live in multi-generational households? Grandparents who care for their grandchildren (in the US, there are around 2.5 million grandparents who are primary caregivers alone, let along those who live with their children and grandchildren). People who are essential workers? People who need to go out and shop?
> No doubt many authoritarian minded people would not be happy with letting aged and vulnerable people make their own decisions,
That’s a strawman. We don’t remotely have the infrastructure necessary to enable your picture to be realistic. It doesn’t necessarily require an “authoritarian” mindset to think that your scenario doesn’t stack up to reality.
Nic said
“The government would advise them to do so, perhaps accompanied by a warning that they would not be at the front of any queue for state-provided hospital care if they decided not to do so and became ill with COVID-19, and the state health system were unable to meet all demand at that time.”
Logically the vulnerable include the obese, those also abusing their health through poor lifestyle choices, those not social distancing or taking other sensible measures and the BAME population.
Are they also to be refused hospital treatment as we would be talking about a large proportion of the population?
tonyb
Nic Lewis: The government would advise them to do so, perhaps accompanied by a warning that they would not be at the front of any queue for state-provided hospital care if they decided not to do so and became ill with COVID-19, and the state health system were unable to meet all demand at that time.
I sympathize, but I doubt such an approach would be enforceable outside a police state. Quarantining the sick who have actual positive diagnoses is about as far as people are willing to consent to, and even then you have to show with evidence that it works in order for the consent to continue. Obese people, long time smokers, alcoholics and drug abusers are already over-represented in critical care facilities; these “life style choices” impose burdens on everyone, healthy, sick, health-care professionals, but they are rarely denied care because of that.
> No it doesn’t, so far as I’m concerned. I would advovate for a voluntary isolation basis for elderly and vulnerable people. The government would advise them to do so, perhaps accompanied by a warning that they would not be at the front of any queue for state-provided hospital care if they decided not to do so and became ill with COVID-19, and the state health system were unable to meet all demand at that time.
Magical thinking.
Totally uninforceable.
How are you going to decide who has and who hasn’t remained isolated? Just ask them?
Suppose someone is an essential worker or is the primary caregiver for a grandchild? Will you just punish them nonetheless?
I am going to go out on a limb J. Old people have a primary motivation. To be useful. The portrayal at times is as a vulnerable burden.
My Sister became a Grandmother about 2 months ago. Hasn’t held the baby yet. The baby’s Mother is a neonatal nurse at a tier one hospital.
These are tough decisions. Government should not make them.
https://www.theguardian.com/books/2020/may/30/this-man-knows-hes-dying-as-surely-as-i-do-a-doctors-dispatches-from-intensive-care
There is only one way to kill this virus. That is an infected person must live with it for 14 days until it kills itself . The ASYMPTOMATIC MUST BE REMOVED FROM CIRCULATION.
Back around the 21st I asked for the essential workers to make an exerted effort to hit the testing system with everything we had. I am asking to do it again. We are treading water at about 20,000. That means the 14-day limit is removing 20,000 a day by curing them, we are removing 20,000 a day by asking them to self-isolate, and the infected are infecting 40,000 a day. The object of this is to see if the very large number of tests can get the percentage of positive to total close to 1% or lower.
22,452 is 6.5% of total tests. yesterday it was 4.2%. A gain of 54.7%
This means we lost control and by tomorrow at this time the virus infected walking the streets of the USA will have doubled in 48 hours.
WE NEED TO ACT NOW. TEST, TEST, TEST.
There is only one way to kill this virus. That is an infected person must live with it for 14 days until it kills itself.
The virus doesn’t ‘kill itself’ – human immune response kills the virus.
And in the aggregate, exposure is the only way to induce human immune response. Unfortunately, of course, age and the chronic diseases of civilization diminish immune response.
We cannot change chronological aging ( something we aspire to ).
We can change the diseases of civilization.
To do that, we need knowledge and choice.
Fortunately, the same civilization that brings the chronic diseases also brings knowledge and choice.
The ASYMPTOMATIC MUST BE REMOVED FROM CIRCULATION.
No, much better that the vulnerable voluntarily remove themselves from circulation and civilization continues.
Robert Clark: The ASYMPTOMATIC MUST BE REMOVED FROM CIRCULATION.
It makes more sense, and is a greater respecter of individual liberties, for the vulnerable to remove themselves from circulation.
Early on, CDC guidance recommended testing only the symptomatic. Now, in the US, testing capacity seems to exceed the willingness of the people to be tested.
tomorrow at this time the virus infected walking the streets of the USA will have doubled in 48 hours.
How can you support that? My calculations based on the data presented at worldometers has the daily new case rate and daily death rate in the US at a little under 1.5% for the last two weeks, maybe down a little from just over to just below. That’s approximately a 70 day doubling time — not great but also not every other day. What makes you think that the count of untested asymptomatic is doubling every other day? At that rate, the number of asymptomatic infectives in the US will be over 500B by the end of June.
Chicken Little
A couple of observations.
1. Flu is highly seasonal because the virus is aerosolized, the primary route of infection is inhalation at distance in dry indoor winter air where virions remain breathable for hours. In summer humdity, not so much
Colds, including corona common colds, are only weakly seasonal. That is because the primary route of infection is close personal proximity—contact. The Wuhan virus is a beta corona, just like 2 of the four common cold coronas. This has two consequences. First, it explains partial immunity. Second, it means it is unlikely there will be a big second wave in the fall.
2. If Wuhan is aerosolized, then anything less than an N95 mask is useless. If it is not, then social distancing (EU 1 meter suffices), frequent hand washing, and not touching face is effective; masks are again useless. Stop the mad masking.
> If Wuhan is aerosolized, then anything less than an N95 mask is useless. If it is not, then social distancing (EU 1 meter suffices), frequent hand washing, and not touching face is effective; masks are again useless. Stop the mad masking.
Aerosolized is a fairly vague term. There is no precise cut-off point. And you are creating an unrealistic binary structure. There could be a combination of vectors of infection. And masks (non-N95) could be partially effective even if the particles that are infectious are those that are aersollized and extremely small. But we don’t even know if the infection pathway is so limited.
People who are studying this have reached different conclusions. Some in strong disagreement with your categorical conclusions.
Meantime, we have some real world, indirect evidence. Countries where mask-wearing is prevalent have dealt more effectively with the spread of the virus. It isn’t perfect evidence. Some countries were mask-wearing isn’t highly prevalent have also dealt with the spread well. And the countries where mask-wearing is prevalent have taken measures to prevent the spread – such as careful testing, tracing and isolating.,
But the bottom line is that your categorical pronouncements are highly irresponsible until more evidence is collected.
But I thought Joshua that you have repeated scores of times that comparisons of different countries are fraught with issues. I would be very careful trying to generalize from Asian countries that in some cases are islands. Generally Asian cultures are more accepting of strong government controls and mandates.
The evidence on masks is very inconclusive. Mask wearing is not based on strong science except perhaps for the more intrusive cover the face variety used in paint hangers. These are well tested and certified.
What about the humidity in Guayaquil?
“The country is widely regarded as the pandemic’s epicenter in Latin America and the Caribbean – especially its overwhelmed port city of Guayaquil, which was recently the awful scene of corpses lying unburied on sidewalks”.
https://www.wlrn.org/post/ecuador-health-minister-horrifying-coronavirus-plague-better-contained-now#stream/0
“Last month, the port city of nearly three million gained global notoriety when videos surfaced showing dead bodies left in the city’s streets after morgues and funeral homes were overwhelmed. Many families made the choice to put loved ones outdoors for fear of infection and because the smells were unbearable”.
https://www.cnn.com/2020/05/07/americas/ecuador-coronavirus-missing-intl/index.html
“The average annual percentage of humidity is: 77.0%.”
https://weather-and-climate.com/average-monthly-Humidity-perc,guayaquil,Ecuador
I am with joshie on this one:
“But the bottom line is that your categorical pronouncements are highly irresponsible until more evidence is collected.”
Don’t listen to Rud. Listen to the WHO and CDC who are not making categorical pronouncements. Well they do, but then they change their little expert minds and pronounce the opposite of previous pronouncements.
Nah. On second though, we should just take Rud’s word for it. He worked with Fauci, doncha know.
https://www.medrxiv.org/content/10.1101/2020.04.17.20069567v4
https://theconversation.com/masks-help-stop-the-spread-of-coronavirus-the-science-is-simple-and-im-one-of-100-experts-urging-governors-to-require-public-mask-wearing-138507
https://www.preprints.org/manuscript/202004.0203/v2
Just to be clear – I’m saying that we should wait for more evidence before making categorical pronouncements.
We don’t yet know whether only aerosolized droplets are infectious. And aerosolized droplets exist along a continuum; we don’t yet know whether the really small ones contain enough virus to be infectious, or if so under what kinds of conditions.
Respect uncertainty.
Tell that to the confused apparatchiks, joshie. I am pretty sure that Rud is not making policy pronouncements. My guess is he is better informed than you are. And about a thousand times more intelligent. We don’t need to go into credibility. OK, I will. You have none.
But Rud know more than the people actually researching this…because Fauci.
https://science.sciencemag.org/content/early/2020/05/27/science.abc6197
This guy actually researches the issue. Has a Gesunheit machine in his lab (happens to be a good friend of someone in my family). Peope like Fauci go to him to get information.
But you know, Rud worked with Fauci.
Oops. Forgot the link. I know you wouldn’t want to miss it so you can come back and explain how Don is wrong.
https://www.wsj.com/articles/is-it-time-to-wear-a-face-mask-11585855788
But Rud has a brother-in-law with a brand new sneeze machine. OK, Karen. You are just going to have to report Rud for making categorical pronouncements. Good luck with that. I would suggest that you don’t use 911 this time, with all that’s going on, but up to you.
https://twitter.com/aginnt/status/1267125598540840961
“Flu is highly seasonal because the virus is aerosolized,”
“oft-repeated claims are frequently mistaken for facts”:
please read this ristvan: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2134066/pdf/jhyg00034-0042.pdf
there seems more to flu than your belief .. IT IS .. BECAUSE …
Terry,
I am not sure that Rud has this right, but I am fairly sure that your paper’s hypothesis is not valid. Latency in certain viruses is well known, and some latent viruses are reactivated by sunlight. However, no-one has discovered any mechanism whereby a latent flu virus can be reactivated by an absence of sunlight. The work you cite was done before a multitude of studies highlighting the role of Vitamin D in viral immunity, a more likely explanation for seasonality.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6121423/
So. Back to yesterday, 29 May. What was R to 2 sig figs? Was it 0.99? Or was it 0.94.?
If it was 0.99, it allows the gov. to say truthfully that it is ‘below one’ and fulfils their criterion. But unless it is below 0.95 it does not allow Sir Patrick to say truthfully at the afternoon gov.uk briefing that it is in the range 0.7 to 0.9.
Both Sir Patrick and Dr Whitty emphasised that it was only just below 1. So did Professor Edmunds. Is the Cabinet Office weaponising rounding errors?
Nic,
Very nice post. It think it is very important that the possibility of full or partial resistance to infection, due to earlier infection with related viruses, be carefully considered, since there is now fairly strong evidence. It is good you point out the multiple recent studies, which are all consistent with the obvious immunity against smallpox gained from a vaccinia infection. In places like New York City, with covid19 seropositive rates somewhere over 20%, the pandemic appears to be running out of susceptible individuals…. once again suggesting a fraction of the population has some resistance to infection; the measure (and estimated) rate of infection to date is far too low to establish herd immunity.
Abstract
COVID-19 has become a global pandemic, resulting in nearly three hundred thousand deaths distributed heterogeneously across countries. Estimating the infection fatality rate (IFR) has been elusive due to the presence of asymptomatic or mildly symptomatic infections and lack of testing capacity. We analyze global data to derive the IFR of COVID-19. Estimates of COVID-19 IFR in each country or locality differ due to variable sampling regimes, demographics, and healthcare resources. We present a novel statistical approach based on sampling effort and the reported case fatality rate of each country. The asymptote of this function gives the global IFR. Applying this asymptotic estimator to cumulative COVID-19 data from 139 countries reveals a global IFR of 1.04% (CI: 0.77%,1.38%). Deviation of countries’ reported CFR from the estimator does not correlate with demography or per capita GDP, suggesting variation is due to differing testing regimes or reporting guidelines by country. Estimates of IFR through seroprevalence studies and point estimates from case studies or sub-sampled populations are limited by sample coverage and cannot inform a global IFR, as mortality is known to vary dramatically by age and treatment availability. Our estimated IFR aligns with many previous estimates and is the first attempt at a global estimate of COVID-19 IFR
https://www.medrxiv.org/content/10.1101/2020.05.11.20098780v1
Josh, You have posted this before. It’s a statistical modeling study based on case fatality rates around the world. Since these numbers vary from under 1% to perhaps 15% I think such studies are dramatically inferior to studies based on serological testing. Even for those studies there is a large range of results probably depending on the demographics of those infected. The larger the percentage of vulnerable people infected, the higher the apparent IFR will be.
Pingback: Look Over There! – Me Thinks
There is a basic logic fail that is highly prevalent.
We can’t compare countries that are extremely unlike, in order to evaluate the effect of “lockdowns,” for a fairly simple explanation: the unlike conditions are part of the reason why some countries have chosen “lockdowns” as compared to those that haven’t.
Even comparing more like countries – say Denmark to Sweden, is highly problematic because even they are unlike in meaningful ways. But even if we ignore that reality, comparing the condition of “lockdowns” in like countries such as Denmark and Sweden tells us nothing about places like the US because again, what we find out from comparing those countries wouldn’t apply to the US.
And then there is the illogic of thinking that you can clearly or unambiguously disaggregate the effects of “lockdowns” from the vast effects of the raging pandemic in and of itself. The data show that such a disaggregation is extremely difficult: For example, mobility reduced dramatically before any “lockdowns” were implemented.
When I was 5 years old my Grandmother put me on her knee and softly whispered into my ear “Remember, sweetheart, no 2 lockdowns are ever the same.”
Josh, It’s a little like medicine itself. Most issues are surrounded with massive uncertainty and many treatments have pretty small benefits. Doctors are trained to do the best they can for each patient taking into account the patients desires. You can’t force a patient to comply with doctor’s orders so you rely on voluntary compliance and hope the treatment is not too unpleasant.
The problem with lockdown is that it was done in a climate of panic and fear consciously generated by the media who are just totally corrupt and worthless. Science had little to do with it because the science was very uninformative at the time.
DATE ISOLATED increase % # TESTS
5/19/2020 23,764 5,133 27.5 477,701
5/20/2020 18,882 -4,882 -20.5 357,771
5/21/2020 24,816 5,234 31.4 1,501,704
5/22/2020 27,559 2,743 11 429,222
5/23/2020 25,349 -2,210 -8 472,287
5/24/2020 19,173 -6,176 -24.3 368,126
5/25/2020 19,608 435 2.2 419,573
5/26/2020 20,088 480 2.4 377,548
5/27/2020 20,648 560 2.7 357,949
5/28/2020 19,421 -1,227 -5.9 460,934
5/29/2020 22,452 3,031 15.5 345,392
5/30/2029 27,263 4,811 21.4 491,402
27,263 is 5.5% of total tests. that is 15.3% less than yesterday.
You have done over a million in a day before. Talk to your fellow workers.
TEST TEST TEST
Nic,
Ferguson’s model is far more complex than a simple SIR or SEIR model. He models social interaction between population centres geographically, and with age profiles for different countries , schooling, transport, air travel etc. The epidemic is initially seeded with a fixed number of cases and then infections are simulated with a random number generation based on R0. This stochastic model also allows him to model lockdown social distancing type measures.
I have it up and running on my iMac for the UK although it runs out of memory for the US! It is not true you need a supercomputer.
One interesting discovery is that he needs to normalise the model to the number of deaths actually recoded at a particular date to get sensible results.
“One interesting discovery is that he needs to normalise the model to the number of deaths actually recoded at a particular date to get sensible results.”
.
Maybe that helps to explain his model’s projections, which have consistently been utter rubbish.
Clive Best: He models social interaction between population centres geographically, and with age profiles for different countries , schooling, transport, air travel etc. The epidemic is initially seeded with a fixed number of cases and then infections are simulated with a random number generation based on R0.
You make it sound too complicated to get good results.
Thanks, Clive. My congratulations on getting Ferguson’s model running – a very worthwhile achievement.
I appreciate that Ferguson’s model is far more complex than a compartmental model. I think the transmission model it uses is basically as set out in the Supplementary Information of Ferguson’s 2005 paper “Strategies for containing an emerging influenza pandemic in Southeast Asia”, maybe since modified.
So far as I can tell, in Ferguson’s model there is no explicit individual variability in susceptibility. There is some indirect variability in susceptibility through the effects of geography, age, membership of different groups (school, workplace, household, community), etc. However, that seems to have only a modest impact on the final infected proportion, so the effective variability in susceptibility must be fairly small. There is variation in individual infectiousness, but since in his model that is uncorrelated with variability in susceptibility, it does not affect aggregate transmission.
I agree that his model is better suited than a SEIR model to simulating the effect of social distancing type measures on the spread of the epidemic, if individuals’ changes in behaviour can be accurately represented. But I suspect that a well calibrated SEIR model with population inhomogeneity in susceptibility matching that in Ferguson’s model and where interventions are represented by the same reduction in transmission/ effect on Ro, as happens in his model will produce fairly similar results to his model.
In any event, in this post I was mainly trying to make a point of principle, which has very little dependence on model realism. Some people have implicitly assumed that the large size of the overshoot of the herd immunity threshold in an unimpeded epidemic, resulting in a much higher eventual infected proportion, was an inevitable drawback of pursuing a herd immunity strategy. My aim was to show this is not so, and that the overshoot can in principle be hugely reduced by a well-timed short duration social-distancing intervention.
It’s very interesting that Ferguson needs to normalise the model to the actual number of deaths. On my reading of his papers, enough information is fed into the model for it to estimate the actual number of deaths from the assumptions made, without any normalisation. Do you agree? And can you tell whether and to what extent his model over or under estimates deaths prior to the normalisation?
Nic,
Each run of Ferguson’s model, at least as defined on GITHUB, needs two parameter files. The first is for the “no intervention” and here you can specify an “Initial immunity profile by age”. In all of COVID runs these are always set to zero. i.e. he assumes there is no variability in initial susceptibility. However it would be possible to apply such an initial immunity value.
I have read several suggestions (e.g. Michael Levitt), that once you reach 20% infection rates the epidemic tends to die out naturally. That would imply something like 50% of the population already have some resistance to infection, perhaps from exposure to cold like coronaviruses. Let’s hope he is right !
There are plenty of other parameters to be set and of course no documentation as to what they mean. One though specifies the number of deaths on day ‘n’ and for the UK this is set to 10,000 on April 10th. This forces the model to agree to the data on that date. Another parameter defines the intervention day March 23.
The ‘lockdown” interventions themselves are contained in a second parameter file, again with no documentation. However you can guess most of their meanings. Place closures, household quarantine, social distancing etc. These are applied after March 23 but the resultant deaths are forced to agree on April 10th. I tried changing the lockdown date to a week earlier and a week later and this has a large effect on final accumulated deaths. It is probably best to also modify the normalisation date.
If anyone else wants to get it running I could help. You need to have Python, R, and C++ compiler installed first. It also uses cmake.
Clive
Clive,
I’d like to take you up on your kind offer of help in getting the Ferguson model working. I’ll email you directly about this, if that’s OK.
Clive Best: There are plenty of other parameters to be set and of course no documentation as to what they mean. One though specifies the number of deaths on day ‘n’ and for the UK this is set to 10,000 on April 10th. This forces the model to agree to the data on that date. Another parameter defines the intervention day March 23.
Can you modify the parameters meaningfully to get accurate computations of the trajectories of cases and deaths observed so far in diverse countries such as Sweden and Switzerland, United Kingdom and Belgium, or states such as Texas, Florida, Georgia and New York? This would seem like a good time to find out how much or how well the model has to be tweaked to ever be accurate.
Do you have any evidence that the model parts and associated parameters are accurate representations of any of the social and biological processes involved?
I probably sound petty or naive, but I did pharmacokinetic modeling in preclinical and early clinical drug development; and modeling of the circadian rhythms of some bodily processes such as melatonin secretion and metabolism, cortisol secretion and metabolism, and some others. You can have a simple, unrealistic model that is nevertheless accurate enough for its main purpose (e.g. setting drug dosing schedules), in a setting where an accurate and realistic model can’t be obtaine in finite time. Hence my comments elsewhere about making a simple model too complex by trying to model too many processes.
R0 is not a fundamental value. Instead the fundamental values are:
1) the “contact rate” – or how many people an average person meets each day.
2) the number of days on average an infected person remains contagious unless they get sick
Lockdown can artificially changes 1)
but not 2) !
well, prove me wrong, because did ‘your’ categorical pronouncements’ are just ‘fact based:’.
.Did you live thru H1N1 in summer 2009 with Fauci? I did.
Totally unscientific approach.
Prove that they don’t work. You can’t.
As I said, there are a variety of views among the people on the ground who are researching this directly. Doing physical experiments. It’s easy to find that. A modicum of research will turn that up.
Your catigorical pronouncements are absurd.
–snio–
Most models of epidemic spread, including many designed specifically for COVID-19, implicitly
assume that social networks are undirected, i.e., that the infection is equally likely to spread in either
direction whenever a contact occurs. In particular, this assumption implies that the individuals most
likely to spread the disease are also the most likely to receive it from others. Here, we review results
from the theory of random directed graphs which show that many important quantities, including
the reproductive number and the epidemic size, depend sensitively on the joint distribution of in- and
out-degrees (“risk” and “spread”), including their heterogeneity and the correlation between them.
By considering joint distributions of various kinds we elucidate why some types of heterogeneity
cause a deviation from the standard Kermack-McKendrick analysis of SIR models, i.e., so called
mass-action models where contacts are homogeneous and random, and some do not. We also show
that some structured SIR models informed by complex contact patterns among types of individuals
(age or activity) are simply mixtures of Poisson processes and tend not to deviate significantly
from the simplest mass-action model. Finally, we point out some possible policy implications of
this directed structure, both for contact tracing strategy and for interventions designed to prevent
super spreading events. In particular, directed networks have a forward and backward version of
the classic “friendship paradox” — forward links tend to lead to individuals with high risk, while
backward links lead to individuals with high spread — such that a combination of both forward and
backward contact tracing is necessary to find superspreading events and prevent future cascades of
infection.
https://t.co/GpD3DGeZyo?amp=1
Thanks for the link. I’ll take a look.
My modified SEIR model does incorporate unrelated variability in susceptibility and infectivity, which it looks like this paper is about, as well as related variability.
Thanks for the link. I’ve now read this paper, which makes many good points. I think it supports all my approach, and shows that structured models informed by complex contact patterns among types of individuals (age, activity), of which the Ferguson/Imperial model is an example, simply represent mixtures of the simplest compartmental (SIR) model and produce results that do not deviate much from those of a single SIR model. It concludes:
“Such models … can not truly embrace the full heterogeneity of risk and spread produced by biology, demographics and human behaviour”.
“
You might also want to read this:
https://wellcomeopenresearch.org/articles/5-89
Nic:
Not sure if you have seen this SIR modeling from mathematicians at Rochester Institute of Technology.
https://phys.org/news/2020-05-scientists-method-epidemiologists-covid-.html
Keith,
No, I hadn’t. Thanks for the link.
Nic:
Have you by chance reviewed this work from Bristol?
https://phys.org/news/2020-05-solution-century-old-math-problem-transmission.html
Keith, no, I hadn’t seen that either, thanks. But I can’t spot a link to the paper concerned?
As far as the UK is concerned the biggest ‘certainty’ prior to the arrival of SARs-CoV-2 was that many regional A&Es had not only failed to cope with the combined effects of seasonal influenza and normal levels of patient presentation over several years, but had also struggled outside influenza seasons. Much of the ‘news’ about these shortcomings may have been lost to general media noise since much of it may have happened to people who are habitually largely ignored in areas of serial deprivation of normal health care standards (e.g. the latterly named ‘postcode lottery’), the very thing the NHS was set up to mitigate against.
When it is possible for politicians and their advisors to easily lose track of life’s certainties, then how on earth can you deal with ‘uncertainties’ in any model when you are adding to that list daily? I’d suggest that if more interest had been taken in the normal ‘flu years as to transmission tracking systems, potentially unhealthy contact areas of high risk, etc., then the whole concept of widespread lockdown would not have been entertained as anything other than a panic response to a long term issue.
I believe we are seeing too much short term thinking about foreseeable problems that regularly stare us in the face. Conversely we pretend we have a handle on the imagined future dangers of fossil fuel burning via investment in alternatives that have no long term future. Muddled thinking everywhere but why is it happening and how do we stop it?
Uk weather lass.
Entirely agree.
The govts wild over reaction to covid -and the likely greater death toll than if they had done nothing- through clearing the hospitals, decanting the elderly into care homes and letting covid rip through both, also needs to be added to the huge numbers that will die through existing treatment being cancelled or new problems not being diagnosed.
As you say, we have a big problem every bad influenza year and the logic of the current situation is that in order to save lives we need to imprison people in their homes for the flu season, allow any virus to run rampant inside it and close down the economy once again.
One interesting point relating to ‘climate change’; is the desire to switch everyone from gas heating to heat pumps. The latter require tightly sealed houses to work anything like efficiently
Imagine an often obese population locked inside some of the smallest houses in Europe and with very little access to external fresh air. That will work well
tonyb
I like your take on this. It’s a problem we’ve had for a long time. Or a similar problem. It’s got away from us. Those of us that are supposed to be stable.
We can resume our lives.
Nic:
The following link gets you to a pdf file for Bristol math paper
https://journals.aps.org/prx/pdf/10.1103/PhysRevX.10.021045
Nic states that he has included connectivity in S and I by using an intensive modification to S and I. But connectivity is an extensive modification, and so the math has to be based upon this. A set of coupled ODEs with an extensive modification requires that there is mass balance. In a 2 state system this means that if we have a term \gamma * I_1 then the corresponding term is (1-\gamma) * I_2. The model Nic uses is not physically possible and the resulting math he uses is fundamentally wrong. Garbage in, garbage out.
What John says is wrong. For anyone who wants to understand why, I suggest reading the extensive discussion between John Daschbach and Joe Born following this comment: https://judithcurry.com/2020/05/10/why-herd-immunity-to-covid-19-is-reached-much-earlier-than-thought/#comment-917770 and continued here: https://judithcurry.com/2020/05/10/why-herd-immunity-to-covid-19-is-reached-much-earlier-than-thought/#comment-918184
John Daschbach: A set of coupled ODEs with an extensive modification requires that there is mass balance.
When you are modeling chemical reactions, but not when you are modeling dying. Check out Mathematical Biology by J. D. Murray, the sections on predator-prey modeling: The Lotka-Volterra model is most famous, but you don’t have to get too fancy — you already know that populations can die out completely, i.e., go extinct.
Italian doc says virus is getting puny and no second wave. However, yuuge second wave of TDS coming in November:
https://www.reuters.com/article/us-health-coronavirus-italy-virus-idUSKBN2370OQ
New coronavirus losing potency, top Italian doctor says
“In reality, the virus clinically no longer exists in Italy,” said Alberto Zangrillo, the head of the San Raffaele Hospital in Milan in the northern region of Lombardy, which has borne the brunt of Italy’s coronavirus contagion.
“The swabs that were performed over the last 10 days showed a viral load in quantitative terms that was absolutely infinitesimal compared to the ones carried out a month or two months ago,” he told RAI television.
A successful virus does not kill its hosts. Then it will die. Least energy path. It gets greater transmission when people aren’t so afraid of it. What ever related virus there is that we can’t beat, does this.
I am feeling better about my IRA balances. Everything will be Okay.
–snip–
This technical report describes a dynamic causal model of the spread of coronavirus through a population. The model is based upon ensemble or population dynamics that generate outcomes, like new cases and deaths over time. The purpose of this model is to quantify the uncertainty that attends predictions of relevant outcomes. By assuming suitable conditional dependencies, one can model the effects of interventions (e.g., social distancing) and differences among populations (e.g., herd immunity) to predict what might happen in different circumstances. Technically, this model leverages state-of-the-art variational (Bayesian) model inversion and comparison procedures, originally developed to characterise the responses of neuronal ensembles to perturbations. Here, this modelling is applied to epidemiological populations—to illustrate the kind of inferences that are supported and how the model per se can be optimised given timeseries data. Although the purpose of this paper is to describe a modelling protocol, the results illustrate some interesting perspectives on the current pandemic; for example, the nonlinear effects of herd immunity that speak to a self-organised mitigation process.
https://wellcomeopenresearch.org/articles/5-89
Thank you.
“…the nonlinear effects of herd immunity that speak to a self-organised mitigation process.
Because we will do only what we are directed to do by the government and we are just the result. Not rational beings.
I did not tell my clients to protect themselves. They did that on their own. The tax preparation cycle at my office is delayed and that curve was flattened. I realize this is not a clean situation. The government allowed them to delay filing. But the filing deadline is arbritrary and not the result of science. Or maybe it is. Science that hasn’t changed the filing deadline in the past 30 years.
Many people wouldn’t have been able to social distance without government support.
This is what a lot of the openers miss -because they were not in that kind of situation.
And for many others, it’s a lot like “Keep the government’s hands off my Medicare.”
Or… “Don’t bail out those demoRAT states (that keep my state afloat by having a positive balance with the federal government while my state has a negative balance. ) “
So government does A. Then it sees results B. But there’s everything that would’ve happened with A and without A just the same.
It’s the idea of self organization. Which government is terrible at. When they see a Free Market, they’ll tell what it’s doing wrong.
But which is the Master?
Joshua: https://wellcomeopenresearch.org/articles/5-89
thank you for the link. I had not previously learned of GNU/Octave
An idiotic meme that goes viral can decimate the credulous as surely as smallpox, witness Don’s blanket rejection of everything sober and disinterested medical scientists have to say :
NATURE NEWS 29 MAY 2020
Safety fears over drug hyped to treat the coronavirus spark global confusion
A study that suggested using hydroxychloroquine — a malaria drug — to treat people with COVID-19 could be dangerous has slowed clinical trials, but the study itself has also been questioned.
https://www.nature.com/articles/d41586-020-01599-9?utm_source=Nature+Briefing&utm_campaign=32981e1f33-briefing-dy-20200601&utm_medium=email&utm_term=0_c9dfd39373-32981e1f33-44545345
Lancet just issued “Expression of concern” over the fake Lancetgate paper on HCQ. Poor rustle, made a fool again:
https://twitter.com/TheLancet/status/1267901995848957953/photo/1
https://twitter.com/CT_Bergstrom/status/1267659926811230209
https://twitter.com/CT_Bergstrom/status/1267590022842036224
https://www.reuters.com/article/us-health-coronavirus-who-transmission/who-and-other-experts-say-no-evidence-of-covid-19-losing-potency-idUSKBN23832J
https://twitter.com/CT_Bergstrom/status/1242314692514598912
https://twitter.com/CT_Bergstrom/status/1267567420379549696
“What is Michael Levitt is talking about here? If a fraction of the population is already immune due to cross-reactivity, you still expect exponential growth, just at a lower rate.”
Yes. However, the Gompertz function that Michael Levitt fits does show exponential growth initially, before gradually tailing off. So the question should be: what is Carl Bergstrom talking about here?
Try asking him
Look for a nice big coronavirus spike in the USA and maybe London after the current street covid19 parties happening in every city.
NYT headline June 18:
Coronavirus spike in inner cities; minorities hardest hit due to racism.
I have read all the comments. Joshua (whoever he is?) makes a lot of sense to me.
There is a trend developing of big corporate interests and the left’s interests intersecting and finding common cause.
As Michael Moore and Jeff Gibbs brilliantly exposed in “Planet of the Humans”, the renewable scam has proved lucrative for big business.
Now the campaign against the drug Hydroxychloroquine that has been widely taken for a century but now suddenly turns out to be dangerous, (HCQ) again unites the left with big pharma. The left are overwhelmed by inchoate rage against a drug which bad-orange-man recommended, for none but tribal reasons. Big pharma are similarly innately hostile to any off patent drug because … it’s off patent.
So once again the left and big business are in bed together over a politicised issue, the good but suddenly bad, the safe but suddenly unsafe antimalarial drug HCQ.
And both together again find themselves with egg on their faces as the whole Surgisphere fiasco is exposed as fabrication – a fact obvious from the start.
https://www.bbc.com/news/health-52929916
Possible early signs of benefits from rolling back lockdowns:
https://www.cnbc.com/2020/06/05/jobs-report-may-2020.html
How do you explain a high second wave in a country that was very late to react in the first wave? Having a lot of cases does not seem to offer much protection against a high second wave. https://www.bbc.com/news/world-middle-east-52903443
https://www.amazon.com/gp/product/B089P216NP/ref=dbs_a_def_rwt_bibl_vppi_i16
See if you can spot the inaccuracies related to fatality rate:
https://www.foxnews.com/opinion/unreported-truths-covid-19-lockdowns-alex-berenson
Hasidim kids outsmart the capo tuti Cuomo-underboss DeBlasio syndicate’s lockdown dictate:
https://twitter.com/JakeTurx/status/1268970681351405575
I would like to ask one simple question:
‘Why was the world not put into permanent lockdown after Spanish Flu, which killed 50 million (hence putting SARS-CoV2 to absolute shame at this time)?’
This is actually the most fundamental question out there. Medicines back then were far, far more primitive, but did we have wave upon wave of decimation in the decades ahead? No we did not. There were three waves at or soon after 1917 but the rest of the 20th century was free of similar pandemics, although Hitler did spark off quite a bit of killing, and the US did likewise in Vietnam, Indonesia, Iraq (twice), Syria, Libya, a few places besides.
So apparently now we are all so weakly and fear-ridden that we must permanently be constrained in our actions.
The vast majority of us are NOT at risk and it is high time that OCD narcissistic control-freaks were put in their place as to how society should function for the rest of the 21st century.
Thinking that we must all wear masks forevermore is a sign of only one of three things: psychopathy; mentally subnormal cretiinism; or wilful imposition of ‘open prison’ life for the vast majority of humanity.
You are missing “The Corona Bonanza” for LDCs like Pakistan.The Opportunity is being missed out.
Bonanza 1
There will a temporary shock to the government fiscal revenues as Imports will crash,CIF rates of imports will also crash,domestic production has stopped (as tax on MRP less deductions is paid at the time of production and not sale),domestic MRP rates will also crash.That is Y the state has not passed the benefits of lower crude and palm rates to the people.dindooohindoo
The Bonus is in non-salary expenditures of the state,which are on ARC (Annual Rate Contracts) or other RC.With crash in commodities and surplus capacities – Pakistan can easily make and re-negotiate its procurements.Large nations like Hindoosthan,will face disaster,as they will face supply risks,per se.W.r.t the purchases by the Pakistani state,the state can declare Force Majeure,especially on International contracts.
There is no immorality in this,as the suuply and value chain of the suupliers to the state – will,in any case,declare Force Majeure – which will ensure that the suupliers will default on the government contracts.The supliers will make supplies at ARCs,only to the extent of the existing stocks,as at March 15th,2020.They cannot be allowed to supply,from new purchases at the old ARC rates.
Global suppliers will be glad to dump their stocks – with depots in Pakistan – for sale to the Pakistani State.
This could easily reduce the costs by 30-50%,on a one time and recurring basis.Once this Cost is saved,in phases,the benefit of oil price crash on fuels and edible oils and also power tarriffs and fertilisers,can be passed on to the public.That will be pure jannat.
Bonanza 2
The Only Solution to the supply chain risk in USA/EU (w.r.t their supply chains in PTRC) lies in massive robotics and AI – which will make humans obsolete in manufactuirng and also,in part,in IT.The question is,what to do with the humans.That is Y the virus is sought – Simple !
For Pakistan – the crash in Raw Materials and cost of capital, availability of capital and crash in logistics costs will make manufacturing and exports viable.That makes existing unviable manufacturing units viable and jobs and decline in NPAs.No fresh capacities should be launched,solely based on the current cost structure.Crash in costs plus the low labour costs in Pakistan and stable PKR – is the Alt-AI and Robotics
The Pakistani people should thank its prior leaders,that they made manufacturing unviable in Pakistan,and made it a trading nation. Had the state set up manufacturing units – they would be unviable,banks would be busted and there would have been mass skilled unemployment. Just look at Hindoosthan. dindooohindoo
This is the time for setting up manufacturing units – SME and others.
The military,food,telecom,technology and health secuirty of the USA and EU is in the hands of the PRC.These nations will be FORCED to move at least 10-20% of their supply chain,to other nations.They have no choice.
Bonanza 3
The SBP and the treasury of the private sector,should suck in the Corona rate cuts and packages in EU/Nippon/North East Asia and the USA – and restructure the entire FX loan portfolio,w.r.t tenor,spreads,risk premiums,swaps and hedges. One simple way,is by trade finance,which is based on underlying trade and other activties with those nations.
Bonanza 4
After doing 3 and 4 above,the state should invite bids to build and repair infrastructure on BOOT basis.The Cost of infra should reduce by at least 30%,supplemented with long term soft loans and grants.
With viable manufacturing and exports,lower cost of debt – an already cheaper infra cost – will make infra financing and operations,all the more viable
Bonanza 5
To lock in the gains to the people and industry,the SBP and the State should lock in to NYMEX crude and futures,at current rates (on CBOT or with large funds etc.) – for as long as possible,with reasonable contangos or maximum backwardation.A large nation cannot do this – as it will move the premiums,in the derivatives market.
The State should thereafter, lock in the oil and gas rates – and then affix power and fertilisr tarriffs, for the same tenor – with a priority for industrial zones – after meeting the consumer needs.Edible oil contracts can also be struck with large funds,in the USA/EU.
This is also the time for the state to declare Force Majeuer on the ulra high cost RPP/IPPs.With reduced power demand,the entire power demand of Pakistan, can be met from fuel and coal plants,at less than half of the previous marginal cost. For several people, this power supply can be free of cost,as the Marginal cost of power on current fuel costs,should be around 1-2 Rupees (which is not worth collecting from marginal users).
It is time to celebrate !
Perpetual LDCs run like Pakistan, will continue to be perpetual.