Reposted from Dr. Judith Curry’s Climate Etc.
Posted on May 10, 2020 by niclewis
By Nic Lewis
Introduction
A study published in March by the COVID-19 Response Team from Imperial College (Ferguson20[1]) appears to have been largely responsible for driving government actions in the UK and, to a fair extent, in the US and some other countries. Until that report came out, the strategy of the UK government, at least, seems to have been to rely on the build up of ‘herd immunity’ to slow the growth of the epidemic and eventually cause it to peter out.
The ‘herd immunity threshold’ (HIT) can be estimated from the basic reproduction rate of the epidemic, R0 – a measure of how many people, on average, each infected individual infects. Standard simple compartmental models of epidemic growth imply that the HIT equals {1 – 1/R0}. Once the HIT is passed, the rate of new infections starts to decline, which should ensure that health systems will not thereafter be overwhelmed and makes it more practicable to take steps to eliminate the disease.
However, the Ferguson20 report estimated that relying on herd immunity would result in 81% of the UK and US populations becoming infected during the epidemic, mainly over a two-month period, based on an R0 estimate of 2.4. These figures imply that the HIT is between 50% and 60%.[2] Their report implied that health systems would be overwhelmed, resulting in far more deaths. It claimed that only draconian government interventions could prevent this occurring. Such interventions were rapidly implemented in the UK, in most states of the US, and in various other countries, via highly disruptive and restrictive enforced ‘lockdowns’.
A notable exception was Sweden, which has continued to pursue a herd immunity-based strategy, relying on relatively modest social distancing policies. The Imperial College team estimated that, after those policies were introduced in mid-March, R0 in Sweden was 2.5, with only a 2.5% probability that it was under 1.5.[3] The rapid spread of COVID-19 in the country in the second half of March suggests that R0 is unlikely to have been significantly under 2.0.[4]
Very sensibly, the Swedish public health authority has surveyed the prevalence of antibodies to the SARS-COV-2 virus in Stockholm County, the earliest in Sweden hit by COVID-19. They thereby estimated that 17% of the population would have been infected by 11 April, rising to 25% by 1 May 2020.[5] Yet recorded new cases had stopped increasing by 11 April (Figure 1), as had net hospital admissions,[6] and both measures have fallen significantly since. That pattern indicates that the HIT had been reached by 11April, at which point only 17% of the population appear to have been infected.
How can it be true that the HIT has been reached in Stockholm County with only about 17% of the population having been infected, while an R0 of 2.0 is normally taken to imply a HIT of 50%?
The importance of population inhomogeneity
A recent paper (Gomes et al.[7]) provides the answer. It shows that variation between individuals in their susceptibility to infection and their propensity to infect others can cause the HIT to be much lower than it is in a homogeneous population. Standard simple compartmental epidemic models take no account of such variability. And the model used in the Ferguson20 study, while much more complex, appears only to take into account inhomogeneity arising from a very limited set of factors – notably geographic separation from other individuals and household size – with only a modest resulting impact on the growth of the epidemic.[8] Using a compartmental model modified to take such variability into account, with co-variability between susceptibility and infectivity arguably handled in a more realistic way than by Gomes et al., I confirm their finding that the HIT is indeed reached at a much lower level than when the population is homogeneous. That would explain why the HIT appears to have been passed in Stockholm by mid April. The same seems likely to be the case in other major cities and regions that have been badly affected by COVID-19.
Figure 1. New COVID-19 cases reported in Stockholm County, Sweden, over the 7 days up to the date shown. Note that in Sweden testing for COVID-19 infection was narrowed on 12 March, to focus on people needing hospital care, so from then on only a tiny proportion of infections were recorded as cases. This would account for the lack of growth in cases during the first week plotted. Since hospitalisation usually occurs several days after symptom onset, this change also increases the lag between infection and recording as a case. Accordingly, from mid- March on the 7-day trailing average new cases figure will reflect new infections that on average occurred approximately two weeks earlier.
The epidemiological model used
Like Gomes et al., I use a simple ‘SEIR’ epidemiological model,[9] in which the population is divided into four compartments: Susceptible (uninfected), Exposed (latent: infected but not yet infectious), Infectious (typically when diseased), and Recovered (and thus immune and harmless). This is shown in Figure 2. In reality, the Recovered compartment includes people who instead die, which has the same effect on the model dynamics. The entire population starts in the Susceptible compartment, save for a tiny proportion that are transferred to the Infectious compartment to seed the epidemic. The seed infectious individuals infect Susceptible individuals, who move to the Exposed compartment. Exposed individuals gradually transfer to the Infectious compartment, on average remaining as Exposed for the chosen latent period. Infectious individuals in turn gradually transfer to the Recovered compartment, on average remaining as Infectious for the selected infectious period.
Figure 2. SEIR compartment epidemiological model diagram.
In the case of COVID-19, the diseased (symptomatic) stage is typically reached about 5 days after infection, but an infected individual starts to become infectious about 2 days earlier. I therefore set the average latent period as 3 days.[10]
The infectious period depends mainly on the delay between infectiousness and symptoms appearing and on how quickly an individual reduces contacts with others once they become symptomatic, as well as on how infectious asymptomatic cases are. In an SEIR model, the infective period can be derived by subtracting the latent period from the generation time – the mean interval between the original infection of a person and the infections that they then cause.
The Ferguson20 model assumed a generation time of 6.5 days, slightly lower than a subsequent estimate of 7.5 days.[11] I use 7 days, which is consistent with growth rates near the start of COVID-19 outbreaks.[12] The infectious period is therefore 4 (=7 − 3) days.
I set R0=2.4, the same value Ferguson20 use. On average, while an individual is in the Infectious compartment, the number of Susceptible individuals they infect is R0 × {the proportion of the population that remains in the Susceptible compartment}.
With these settings, the progression of a COVID-19 epidemic projected by a standard SEIR model, in which all individuals have identical characteristics, is as shown in Figure 3. The HIT is reached once 58% of the population has been infected, and ultimately 88% of the population become infected.
Figure 3. Epidemic progression in an SEIR model with R0=2.4 and a homogeneous population. The time to reach the herd immunity threshold, which depends on the strength of the seeding at time zero, is arbitrary.
Modifying the basic SEIR model for variability in individual susceptibility and infectivity
The great bulk of COVID-19 transmission is thought to occur directly from symptomatic and pre-symptomatic infected individuals, with little transmission from asymptomatic cases or from the environment.[13] There is strong evidence that a small proportion of individuals account for most infections – the ‘superspreaders’.
A good measure of the dispersion of transmission – the extent to which infection happens through many spreaders or just a few – is the coefficient of variation (CV).[14] Two different estimates of this figure have been published for COVID-19. A Shenzhen-based study[15] estimated that 8.9% of cases were responsible for 80% of total infections, while a multi-country study[16] estimated that 10% were so responsible. In both cases a gamma probability distribution was assumed, as is standard for this purpose. The corresponding CV best estimates and 95% uncertainty ranges are 3.3 (3.0–5.6) and 3.1 (2.2–5.0). These figures are slightly higher than the 2.5 estimated for the 2003 epidemic of SARS.[17]
CV estimates indicate the probability of transmission of an infection. They reflect population inhomogeneity regarding individuals’ differing tendency to infect others, but it is unclear to what extent they also reflect susceptibility differences between individuals. However, since COVID-19 transmission is very largely person-to-person, much of the inhomogeneity in transmission rates will reflect how socially connected individuals are, and how close and prolonged their interactions with other individuals are. As these factors affect the probability of transmission both from and to an individual, as well as causing variation in an individual’s infectivity they should cause the same variation in their susceptibility to infection.
A common social connectivity related factor implies that an individual’s susceptibility and infectivity are positively correlated, and it is not unreasonable to assume a quite strong correlation. However, it seems unrealistic to assume, as Gomes et al. do in one case, that an individual’s infectivity is directly proportional to their personal susceptibility. (In the other case that they model, they assume that an individual’s infectivity is unrelated to their susceptibility.)
Some of the variability in the likelihood of someone infecting a susceptible individual during an interaction will undoubtedly be unrelated to social connectivity, for example the size of their viral load. Likewise, susceptibility will vary with the strength of an individual’s immune system as well as with their social connectivity. I use unit-median lognormal distributions to reflect such social-connectivity unrelated variability in infectivity and susceptibility. Their standard deviations determine the strength of the factor they represent. I model an individual’s overall infectivity as the product of their common social-connectivity related factor and their unrelated infectivity-specific factor, and calculate their overall susceptibility in a corresponding manner.[18]
I consider the cases of CV=1 and CV=2 for the common social connectivity factor that causes inhomogeneity in both susceptibility and infectivity. For unrelated lognormally-distributed inhomogeneity in susceptibility I take standard deviations of either 0.4 or 0.8, corresponding to a CV of 0.417 or 0.947 respectively. Where their gamma-distributed common factor inhomogeneity is set at 1, the resulting total inhomogeneity in susceptibility is respectively 1.17 or 1.65 when the lower or higher unrelated inhomogeneity standard deviations respectively are used; where set at 2 the resulting total inhomogeneity in susceptibility is respectively 2.17 or 2.98. The magnitude of variability in individuals’ social-connectivity unrelated infectivity-specific inhomogeneity factor does not affect the progression of an epidemic or the HIT, so for simplicity I ignore it here.[19]
Results
Figure 4 shows the progression of a COVID-19 epidemic in the case of CV=1 for the common social connectivity factor inhomogeneity, with unrelated inhomogeneity in susceptibility having a standard deviation of 0.4. The HIT is 60% lower than for a homogeneous population, at 23.6% rather than 58.3% of the population. And 43% rather than 88% of the population ultimately becomes infected. If the standard deviation of unrelated inhomogeneity in susceptibility is increased to 0.8, the HIT becomes 18.9%, and 35% of the population are ultimately infected.
Figure 4. Epidemic progression in an SEIR model with R0=2.4 and a population with CV=1 common factor inhomogeneity in susceptibility and infectivity and also unrelated multiplicative inhomogeneity in susceptibility with a standard deviation of 0.4.
Figure 5 shows the progression of a COVID-19 epidemic in the case of CV=2 for the common social connectivity factor inhomogeneity, with unrelated inhomogeneity in susceptibility having a standard deviation of 0.8. The HIT is only 6.9% of the population, and only 14% of the population ultimately becoming infected. If the standard deviation of unrelated inhomogeneity in susceptibility is reduced to 0.4, those figures become respectively 8.6% and 17%.
Figure 5. Epidemic progression in an SEIR model with R0=2.4 and a population with CV=2 common factor inhomogeneity in susceptibility and infectivity and also unrelated multiplicative inhomogeneity in susceptibility with a standard deviation of 0.8.
Conclusions
Incorporating, in a reasonable manner, inhomogeneity in susceptibility and infectivity in a standard SEIR epidemiological model, rather than assuming a homogeneous population, causes a very major reduction in the herd immunity threshold, and also in the ultimate infection level if the epidemic thereafter follows an unconstrained path. Therefore, the number of fatalities involved in achieving herd immunity is much lower than it would otherwise be.
In my view, the true herd immunity threshold probably lies somewhere between the 7% and 24% implied by the cases illustrated in Figures 4 and 5. If it were around 17%, which evidence from Stockholm County suggests the resulting fatalities from infections prior to the HIT being reached should be a very low proportion of the population. The Stockholm infection fatality rate appears to be approximately 0.4%,[20] considerably lower than per the Verity et al.[21] estimates used in Ferguson20, with a fatality rate of under 0.1% from infections until the HIT was reached. The fatality rate to reach the HIT in less densely populated areas should be lower, because R0 is positively related to population density.[22] Accordingly, total fatalities should be well under 0.1% of the population by the time herd immunity is achieved. Although there would be subsequent further fatalities, as the epidemic shrinks it should be increasingly practicable to hasten its end by using testing and contact tracing to prevent infections spreading, and thus substantially reduce the number of further fatalities below those projected by the SEIR model in a totally unmitigated scenario.
Nicholas Lewis 10 May 2020
[1] Neil M Ferguson et al., Impact of non-pharmaceutical interventions (NPIs) to reduce COVID-19 mortality and healthcare demand. Imperial College COVID-19 Response Team Report 9, 16 March 2020, https://spiral.imperial.ac.uk:8443/handle/10044/1/77482
[2] A final infection rate of 81% implies, in the context of a simple compartmental model with a fixed, homogeneous population, that the ‘effective R0‘ is between 2.0 and 2.1, and that the HIT is slightly over 50%. Ferguson20 use a more complex model, so it is not surprising that the implied effective R0 differs slightly from the basic 2.4 value that Ferguson20 state they assume.
[3] Flaxman, S. et al., Estimating the number of infections and the impact of non-pharmaceutical interventions on COVID-19 in 11 European countries. Imperial College COVID-19 Response Team Report 13, 30 March 2020, https://www.imperial.ac.uk/mrc-global-infectious-disease-analysis/covid-19/report-13-europe-npi-impact/
[4] Based on the Ferguson20 estimate of a mean generation time of 6.5 days, which appears to be in line with existing evidence, an R0 of 2.0 would result in a daily growth rate of 2.0^(1/6.5)= 11%. That is slightly lower than the peak growth rate in cases in late March in Stockholm County, and in early April in the two regions with the next highest number of cases, in both of which the epidemic took off slightly later than in Stockholm, and in line with the growth rate in Swedish COVID-19 deaths in early April
[5] https://www.folkhalsomyndigheten.se/contentassets/2da059f90b90458d8454a04955d1697f/skattning-peakdag-antal-infekterade-covid-19-utbrottet-stockholms-lan-februari-april-2020.pdf
[6] John Burn-Murdoch, Financial Times Research, 2 May 2020. http://web.archive.org/web/20200507075628/https:/twitter.com/jburnmurdoch/status/1256712090028576768
[7] Gomes, M. G. M., et al. Individual variation in susceptibility or exposure to SARS-CoV-2 lowers the herd immunity threshold. medRxiv 2 May 2020. https://www.medrxiv.org/content/10.1101/2020.04.27.20081893v1
[8] The 81% proportion of the population that Ferguson20 estimated would eventually become infected is only slightly lower than the 88% level implied by their R0 estimate of 2.4 in the case of a homogeneous population.
[9] https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology#The_SEIR_model
[10] Gomes et al. instead set the latent period slightly longer, to 4 days and treated it as a partly infectious period, unlike in the standard SEIR model.
[11] Li Q, Guan X, Wu P, et al.: Early Transmission Dynamics in Wuhan, China, of Novel Coronavirus-Infected Pneumonia. N Engl J Med. 2020; 382(13):1199–1207.https://www.nejm.org/doi/10.1056/NEJMoa2001316
[12] Once a SEIR model has passed its start up phase, and while a negligible proportion susceptible individuals have been infected, the epidemic daily growth factor is R0^(1/generation time), or 1.10–1.13 for R0=2.0–2.4 if the generation time is 7 days.
[13] L. Ferretti et al., Science 10.1126/science.abb6936 (2020).
[14] The coefficient of variation is the ratio of the standard deviation to the mean of its probability distribution. It is usual to assume a gamma distribution for infectivity, the shape parameter of which equals 1/CV2.
[15] Bi, Qifang, et al. “Epidemiology and transmission of COVID-19 in 391 cases and 1286 of their close contacts in Shenzhen, China: a retrospective cohort study.” The Lancet Infectious Diseases 27 April 2020. https://doi.org/10.1016/S1473-3099(20)30287-5
[16] Endo, Akira, et al. “Estimating the overdispersion in COVID-19 transmission using outbreak sizes outside China.” Wellcome Open Research 5.67 (2020): 67. https://wellcomeopenresearch.org/articles/5-67
[17] Lloyd-Smith, J O et al. “Superspreading and the effect of individual variation on disease emergence.” Nature 438.7066 (2005): 355-359. https://www.nature.com/articles/nature04153
[18] For computational efficiency, I divide the population into 10,000 equal sized segments with their common social connectivity factor increasing according to its assumed probability distribution, and allocate each population segment values for unrelated variability in susceptibility and infectivity randomly, according to their respective probability distributions.
[19] A highly susceptible but averagely infectious person is more likely to be removed from the susceptible pool early in an epidemic, reducing the average susceptibility of the pool. However, no such selective removal occurs for a highly infectious person of averagely susceptibility. Therefore, as Gomes et al. point out, variability in susceptibility lowers the HIT, but variability in infectivity does not do so except to the extent that it is correlated with variability in susceptibility.
[20] On 8 May 2020 reported total COVID-19 deaths in Stockholm County were 1,660, which is 0.40% of the estimated 413,000 of its population who had been infected by 11 April 2020. COVID-19 deaths reported for Stockholm County after 8 May that relate to infections by 11 April 2020 are likely to be approximately balanced by deaths reported by 8 May 2020 that related to post 11 April 2020 infections.
[21] Verity R, Okell LC, Dorigatti I, et al. Estimates of the severity of COVID-19 disease. medRxiv 13 March 2020; https://www.medrxiv.org/content/10.1101/2020.03.09.20033357v1.
[22] Similarly, the HIT may be significantly higher in areas that are very densely populated, have much less inhomogenous populations and/or are repeatedly reseeded from other areas. That would account for the high prevalence of COVID-19 infection that has been found in, for instance, some prisons and residential institutions or in city districts.
Originally posted here, where a pdf copy is also available
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From British eggheads today: they claimed – based on serology and antigen testing – that only 4% of the UK population contracted the virus. That would be a staggering difference compared with Sweden if Nic’ estimation are – even very roughly – correct.
Is there a link to this information?
That was from today PM evening briefing with profs. Whitty and Vallance; from 33 min onward:
https://twitter.com/i/broadcasts/1lPKqVXOOmwGb
Thanks.
So 4% in the whole country, 10% in London. Would have liked to know the specifics of the test but you can’t have everything.
The UK situation was that the NHS was not coping with business as usual, due to UK Gov policy of dismantling the NHS.
What else could be done
“Have you got any evidence of this “dismantling”?
The NHS treats around 40% more A& E patients than it did 10 years ago and carries out about 45% more elective procedures.
As an aside it is worth noticing postmortem results in Hamburg Germany.
Professor Klaus Püschel, head of Hamburg forensic medicine, remarks:
“All of those we have examined so far have had cancer, a chronic lung disease, were heavy smokers or heavily obese, suffered from diabetes or had a cardiovascular disease.”
“This virus affects our lives in a completely exaggerated way. This bears no relation to the danger posed by the virus. And the astronomical economic damage now arising is not commensurate with the danger posed by the virus. I am convinced that corona mortality will not even make itself felt as a peak in annual mortality . . .” (my emphasis)
https://www.mopo.de/hamburg/rechtsmediziner–ohne-vorerkrankung-ist-in-hamburg-an-covid-19-noch-keiner-gestorben–36508928
Why are journalists not carefully analysing and looking at the implications of this?
Why did our politicians not factoring this in in their draconian lockdowns and protracted opening up plans?
They probably didn’t factor these things in because that’s not what they were told at the time of the lockdown. In the UK the government were advised that the outcome could be half a million deaths, and a collapsing health service. That outcome has influenced their policies ever since. Just a couple of days ago the warning was that there could be a hundred thousand deaths (extra? – the media didn’t say / think to ask), if the lockdown is ended too soon.
Lockdown measures should vary because of population density.
New York State demonstrates what happens when lockdown is not soon enough.
And it was more important that New York city lockdown was before New York state due the city’s higher density.
Though it’s not about some arbitrary city boundary line and for example it’s more about mass transit routes
and other factors.
The densities of New York State demonstrates what went wrong globally with this virus and New State has
the highest death per million as compared anywhere in the world, and currently it’s 1,381 deaths per million.
Or in terms of the world, one reason to lockdown is about the rest of the world, rather than region which is locked down. New York city delay in lockdown caused area near it, to also have high deaths per million, New Jersey has 1,048 deaths per million.
One could say the main purpose of the lockdown is because you don’t want to lockdown too late- like New York city did. The nature of this virus would have lockdown NYC without anything done by government, and government did manage to lockdown before this situation occurred.
It seems NYC and Wuhan were similar in terms of being to too late to lockdown- Wuhan infected the entire world, and to such an extant that herd immunity and other lockdown measures resulted NYC only causing high death per million to the region near it. No doubt NYC was victim of the hell inflicted by WHO and China, but NYC delay caused a smaller but stronger hell.
And would say NYC was late by at most, 1 week. If it hadn’t lockdown, with an addition 1 week of delay, it would have “naturally” had a lock down- and would been even worse.
Of course, UK also did a NYC and seemed to even delay longer than NYC.
It seems the difference largely has to do with how elderly were isolated.
In terms of death per million, it’s largely/exclusively about isolation the elderly.
Though death per million of elderly, has nothing to do protecting the rest of the world. They aren’t the cause of the endangerment, the cause of the hell of this pandemic. Or you need a lockdown {rather just isolating the elderly] because the large amount serious illness and small chance of death to rest of population.
The lockdown is for the +20 to 65. The isolation of elderly is from what the +20 to 65, cause at the time of near peak spread which has a high viral load environment.
One say complete isolation of +65 during the Passover. Though very early isolation of elderly and once you get herd immunity, it’s safer for elderly, but it seems now nowhere in the world has it reached point of “safer for elderly”. But would say it’s safer almost everywhere world for below 65. And other than moderate measures in terms social distancing, was it ever problem for people less than 20 year old.
But there was unknowns regarding the younger population and could be still significant unknowns. As example children with deficiencies in vitamin D. And I don’t think there any significant problem with prison population {other than elderly population within prisons]
The problem with NYC, Boston, London, Paris, Chicago is mass transportation modalities (underground subway and bus systems) are the perfect environment to spread a respiratory pathogen like SARS-CoV-2 in the air and via touching likely contaminated hand-holds, seats, ticket machine buttons, and turnstiles.
Out in LA and San Francisco fewer take those public modalities and many drive their own car, as seen in the linear parking-lot freeways of SoCal in normal economics times past.
Plus the elevators.
We need better elevators and mass transit.
I see no reason it should cost much to improve them so they aren’t breeding grounds for pathogens.
Buses should be easy, elevators and airplane also fairly cheap. The subway trains with their tunnel systems might be expensive.
Please reconcile those conclusions with NY/NJ, where 36K are dead out of a population of 30M. The very lowest “death” rate is already past 0.1% of the population. Each day more die, that number grows.
Anytime a fixed number (the death rate) changes with the wind – I have to question the entire premise.
I was already questioning it with this statement: ” little transmission from asymptomatic cases.”
CDC contradicts this directly.
(*e.g., more will die where fewer hospitals exist)
How many of those people actually died from CCP-19?
…” little transmission from asymptomatic cases.”
That is what it actually is written in the reference about it:
“The model estimated R0 = 2.0 in the early stages of the epidemic in China. The contributions to R0 included 46% from presymptomatic individuals (before showing symptoms), 38% from symptomatic individuals, 10% from asymptomatic individuals (who never show symptoms), and 6% from environmentally mediated transmission via contamination. Results on the last two routes are speculative.”
So just a guess, no proof.
Well a coronavirus has never reached more than about 20% infection of a human population, so why should this one be any different. Partly because the virus really doesn’t care which mammal it infects as long as it exists. Rhino can reach 60% and flu very rarely above 40%.
Nice model, but it really wasn’t needed.
+10
Well the number of new cases has dropped dramatically in NYC, is this due to lock down or herd immunity being reached ? Other states with similar lockdowns are not seeing cases drop as much as NYC so I tend to believe herd immunity playing a role in NYC.
One interesting thing is if you are 80 do you prefer to get the disease now, or risk getting it next year when you may not be as healthy. A year can make big difference at that age.
“Well the number of new cases has dropped dramatically in NYC, is this due to lock down or herd immunity being reached ? Other states with similar lockdowns are not seeing cases drop as much as NYC so I tend to believe herd immunity playing a role in NYC.”
there is zero evidence for herd immunity occurring anywhere.
the observational evidence required to establish herd immunity as a cause is not easy to collect.
To prove herd immunity you cannot simply look at the number of cases.
Example. People decide to wear masks and wash their hands religiously.
spread will slow and stop.
has zero to do with herd immunity.
basically Nic is playing with a model and hoping it is true.
“New study from Germany finds that every COVID-19 death was someone who had cancer, lung disease, was a heavy smoker or morbidly obese”
“Head of Forensic Pathology in Hamburg on covid19 autopsy findings: “not a single person w/out previous illness has died of the virus in Hamburg. All had cancer, chronic lung dis, were heavy smokers or heavily obese, or had diabetes or cardiovasc dis” 1/3 https://t.co/u4Pi9ntRT0 pic.twitter.com/PaSdh2UnF5″
“New York City: 99% of fatalities of all age groups had underlying conditions
Italy: 98%
Britain: 95%https://t.co/uAhg…//t.co/sxqTq51mvkhttps://t.co/TUNgUyFcJf”
Edit or delete this
Switzerland rolls back coronavirus lockdown earlier than expected. Schools to reopen since children rarely get virus or transmit it. Even better, Swiss tell those over 65 they can resume their lives. https://t.co/y9QrXP1Jmc via @TheLocalSwitzer
“In my view, the true herd immunity threshold probably lies somewhere between…”
But is it true herd immunity? As I understand the analysis, it says that the observed R₀ is inflated by subgroups where the virus spreads more easily, and when they develop immunity, effective R₀ is lower. But the herd is not immune. Well, of course, it never is, completely. But the problem is that this immunity derived from inhomogeneity is dependent on maintaining the inhomogeneity. Suppose, for example, that the spreading groups are occupational, and employment changes. Then the spreading starts again.
It appears that this number of 20% of a given population being infected by the covid-19 is a recurrent one and constitutes very likely the maximum of contamination that a population will experience. We found exactly the same numbers on the Diamond Princess, the Theodore Roosevelt and many serology studies across the world. There should not be any place left for doubt.
This tells us that mass confinement was a useless strategy.
However the increase in the rate of developing antibodies means that the much sought-after group immunity – where there are so many people immune to the virus that it has little or no opportunity of spreading – is still a long way off.
Experts generally reckon that it would take a minimum of 70% of people with antibodies before group immunity is present. At a rate of 3% every three weeks, that target would only be attained in late July 2021.
https://www.brusselstimes.com/all-news/belgium-all-news/110383/only-6-of-population-have-antibodies-group-immunity-still-far-off/
Do we need herd immunity when the only people at risk are the old and already ill.
It is really just another illness the old and ill will have to deal with.
If you know personally somebody who got a stroke in his 20’s without any listed co-morbidity but with SARS-CoV-2 you might change your opinion.
Happens that that is the case for the colleague of my colleague’s husband. Whole program: facial paralysis, loss of speech etc. Fortunately in way better shape now, speech back and in rehabilitation.
Wonder what the microembolisms do to the heart and brain of children when you can already see them on their feet.
A NOVEL virus with no previous human experience. The only sensible way to deal with it is to crush it by depriving it of hosts. It can be crushed in a month – Taiwan and other countries have proven that.
Sweden’s expert is horrified by the number of deaths but it is his strategy that is responsible for their death. A blind person can see that a slow burn through the population will result in tens of thousands of deaths and take years. Why choose that path when there is a much quicker, less costly approach. Particularly when the long term health impacts are unknowable. We already know the virus has much broader impact than just respiratory stress.
The median age of test-positive deceased is 80 in Italy, 83 in Germany and 84 in Switzerland.
This elegant analysis is in common with much mathematical modelling of of epidemics is that it physical and does not encapsulate the biology of infections. I don’t mean as a criticism of the author but to make the point that the conventional modelling can only very crudely reflect reality.
He makes the point that relatively small changes in assumed susceptibility, which is a biological trait, can lead to markedly different predictions. I think most medics are well aware of variability of susceptibility to infections, even novel infections which may be due to genetic variability in NK lymphocytes or by recognition of CV19 proteins that are recognised as structural homologies by T cells and stimulate existing clones of B cells. This has been very difficult to quantify in the past and becomes simply part of the estimate of R although it has huge significance for understanding epidemics.
This is particularly the case in CV19, which which appears to have different clinical characteristics to other respiratory viral infections and epidemiological models based on one disease may not the applicable to others. For example, the pneumonia associated with CV19 seems to be very unusual ( a high V/Q abnormality leading to hypoxaemia without respiratory distress) and this may be one of the reasons ventilator capacity has been overestimated.
Use of the SEIR model is based on the assumption that infection confers immunity. How many people out there are immune to the common cold?
Infection MAY confer immunity, or the whole essay may be Garbage In Garbage Out. Mr Lewis could at least grant that he has made an assumption.
I am going with garbage in garbage out. Mathematics is not a life form. More and more mathematics seems to have failed the life sciences.
Unsurprisingly, Maoris were 7 times more likely to suffer Spanish Flu than the European New Zealanders, as Fijians were to suffer measles etc, so this would affect Ro? However societies with just two racial groups are rare now, and it is not totally apparent that different ethnicities will provide protection or susceptibility, what is certain is that perhaps in Iceland where one ethnicity dominates one should expect variations in degrees of infectivity?
Why are only Florida and Texas making special efforts to reduce fatalities by protecting the elderly? Both States could still do better at their nursing homes, but they are focusing some resources where the problem is.
Few of the over 70 elderly (95% of fatalities) are still working, so are far easier to sequester. Common sense screams out for focused protection of those over 70 to have any chance of reducing fatalities during the period of widespread viral exposure.
NY did the opposite of a focused protection of the elderly when they relocated patients with the viral infection into Nursing Homes…resulting in thousands of deaths. The resulting journalistic silence at this outrageous incompetence is telling. Imagine the outcry if Trump had made an idiotic Exec order that resulted in thousands of deaths.
Common sense epidemic management is broken.
Journalism is really broken.
Calculating Ro appears to be a very complex business
(see https://www.ncbi.nlm.nih.gov/pmc/articles/PMC1804098/)
In order to calculate crude estimate (I called it Rp) of what is going in your country you can do a simple exercise using MS Excel.
column A – date
column B – number of daily infections
column C – in C5 cell type following: =(AVERAGE(B3:B9)/AVERAGE(B2:B8))^2
now copy C5 cell result and paste it from C6 all the way to nearly the end of your data, leaving the last three cells clear. For detail see the inset in the graph I did for the UK
http://www.vukcevic.co.uk/Rp.htm
whereby the blue line is a hand-drawn approximation.
Rp it is simply square ratio of the 7 day average for any day of interest and the 7 day average for the previous day.
I don’t know much (or anything) about virology, but I do know math. The author states:
The ‘herd immunity threshold’ (HIT) can be estimated from the basic reproduction rate of the epidemic, Ro – a measure of how many people, on average, each infected individual infects. Standard simple compartmental models of epidemic growth imply that the HIT equals {1 – 1/Ro}.
If true, and if HIT = 17% in Sweden (as stated), then algebra indicates that Ro = 1.2.
It seems to me, and again I am not a virologist, that Ro is conditional upon circumstance. An infected person who is coughing on a crowded subway train is going to infect a lot more people than one who is alone in the middle of a desert. Similarly, an infected lab tech at a Chinese wet market is going to infect more people than a bat in a cave in the wilderness.
Rather than being a fixed property of the virus, Ro is more of an emergent property dependent on the physical social environment. I just guessing here, not being an expert.
Thus we might speak of “effective Ro” given the conditions. In which case, an effective Ro of 1.2 in Sweden is just as likely as Philandering Fergie’s 2.4, a number that apparently appears out of nowhere as far as I can tell. But what do I know? Please don’t hesitate to correct me if I am wrong (as I probably am).
Rather than being wrong you are right. That has been proven by all the countries that had it raging internally and reversed that process by getting the reproductive rate below 1. Spain is a very good example for CV19:
https://www.worldometers.info/coronavirus/country/spain/
You see Spain had a very rapid rise and a less rapid fall. Most draconian measures of all countries. China’s most draconian measures were applied in Wuhan.
Australia had a three prong approach – border control to prevent importing infection; quarantining as many of the population as possible in their own home and then manual contact tracing of those showing positive to CV19:
https://www.worldometers.info/coronavirus/country/australia/
The rapid rise followed by a rapid fall because the virus really did not get into the community. With the high initial R0 in crowded communities, hours mattered in getting people separated. The most effective of the three measures was border controls because the virus did not get going in the community apart from isolated outbreaks.
Taiwan by far the most effective. Got in early with border controls and just crushed the virus in a matter of days with good testing and electronic as well as manual contact tracing:
https://www.worldometers.info/coronavirus/country/taiwan/
Their pandemic was done and dusted in a single month!
It has been repeatedly stated by some political leaders that “No one is immune from this virus”. it is apparent from the fact that when Covid-19 invades some people it causes no, or very mild symptomatic effects, indicating some degree of immunity. The only thing I have seen reported that seems significant have been the posts by Monckton and one other post on WUWT about the possible impact of Vitamin D Insufficiency. I’ve read an analysis done by LSU where 86.4 percent of their ICU patients were Vitamin D insufficient or deficient. 100 percent of the patients under the age of 75 were insufficient or deficient. While I think this one small analysis is not enough to indicate that spending more time in the sun or supplementing with Vitamin will and possibly does render some immunity to some of the herd, it should be studied in relation to the relative health status and comorbidities of known patients. Any correlations can be applied to the models being used to predict herd immunity. But better yet if by simply spending a little more time in the sun or taking an inexpensive supplement most of us can live with this virus let’s find out.
“it is apparent from the fact that when Covid-19 invades some people it causes no, or very mild symptomatic effects, indicating some degree of immunity.”
That has most likely nothing to do with immunity because asymptomatic cases seem to have the same viral load as the worst symptomatic.
Therefore, it is probably something else that modulates severity of the symptoms. If we would figure that out we would have a target for a therapy that helps as long as there is no vaccine.
Herd immunity is just a euphemism for herd culling.
Right now in my state, there are counties with zero cases which are having their plans for reopening being rejected as not “conservative” enough — that is to say trying to reopen too quickly. The quacks have come to dominate public health temporarily, or they are reasoning using their limbic system, or fear, or superstition, or….
The acceleration of new cases declined precipitously in this state during the period March 15-21. The orders to close some public amenities, and begin social distancing came out on the 18th, so there was no way that this order caused the epidemic to become essentially steady state as the peak of transmission must have been before March 15-21 and the orders didn’t become effective until well after. I think the very susceptible population, for whatever reason, was smaller than people imagined. Epidemics burn themselves out and always have — some go away to never return, some maintain a small presence, some drift and reappear periodically as a scourge.
Nonetheless, not to let observation guide them in any way, our “public” broadcasters continue to beat the drum about a coming peak of infections in two weeks time. There is so much to learn about this disease and how we should respond more intelligently if it does reappear, but the propagandists among us are planning to sabotage it.
It’s not clear that Sweden is past peak as the article seems to suggest, but if it is it might be because the population of Sweden (my stereotype based on acquaintances and other observations) is overall culturally civic minded and generally highly educated and likely to “do the sensible and responsible thing” even if they are not forced to do so. It’s also a relatively sparsely populated country. I guess we in the US will find out what happens when restrictions are lifted in a denser population where people are often, well, not like that. I hope it all turns out well, but we definitely should watch the numbers as time progresses.
Sweden has the 7th highest recorded death rate at 322/million] , US has 10th highest at 247/million.
Of “proper” countries Belgium leads the pack at 751/million.
Norway, neighbouring Sweden, sits at 39th with 41/million.
Sweden claims a much lower infection rate than the US but has a lot lower rate of testing.
Time will tell whether different approaches lead to different long term health and economic results.
Will Sweden recover economically faster than Norway?
A stochastic simulation with two groups of “people”. One lot that has frequent interactions with the public and one group with few interactions – plus details regarding the probabilities – would quickly show that the infection dies out when only around 20% of the population has antibodies.
Changes of policy such as encouraging young people to get harmlessly infected in school and protecting the elderly would be the best approach. There is little new about this version of influenza. Its epidemiological behaviour is well-understood.
It is amazing that they use models like that of the arrogant idiot Ferguson.