[mlyle]

A paper doesn't "prove" anything, but it does utilize and cite upon real world mobility data and real world susceptibility and transmissibility data for many diseases, including early estimates of these for SARS-CoV-2, e.g. https://wellcomeopenresearch.org/articles/5-67 is cited and used in the estimate of the coefficient of variation.

There was very little data on overdispersion and differential susceptibility for SARS-CoV-2 at the time that paper was written, but there was some. What existed at the time was in line with the better estimates from SARS-CoV-1, etc, that the paper also used. Further evidence has emerged since, both of variable susceptibility and exposure and of actual mechanisms of variable susceptibility-- some surprising like https://www.medrxiv.org/content/10.1101/2020.04.08.20058073v...

[acqq]

Good, so we agree that nobody has proved for SARS-CoV-2 that less than 70% of can be infected to achieve the so-called "herd immunity" (even when knowing that different people allow some very lax definitions of "herd immunity").

[mlyle]

Yes, and nobody has proven really -anything- about most things, by this metric. All we have is evidence of varying quality.

But, again: it's pretty much settled science that Rt = 1 when 1-(1/R0) is infected is a worst case not very often attained, and the evidence so far with COVID-19 (looking at time series data, evidence of non-uniform susceptibility, clear evidence of non-uniform contact networks, significant evidence of overdispersion, etc) leans strongly that way.

Bigger issue is: if 25% infected yields expected Rt of under 1 (the threshold for herd immunity, and I think this is likely)... you'll still have a fair number of cases, because people will come from other jurisdictions with the disease and it'll trigger chains of spread that only slowly decay / peter out each time. If you're one of the other 75%, you're hardly safe, because you can be exposed to one of these chains. Only vaccination can address this, and it's not even a complete fix.

[acqq]

> if 25% infected yields expected Rt of under 1 (the threshold for herd immunity, and I think this is likely)

That's what I'm missing, what are your sources to think that? I somehow haven't seen that in the links you gave.

[mlyle]

From the very first link:

> The herd immunity threshold (HIT) defines the percentage of the population that needs to be immune to reverse epidemic 15 growth and prevent future waves. Figure 3 shows the expected downward trends in the HIT for SARS-CoV-2 as the coefficients of variation of the gamma distributed susceptibility or exposure are increased between 0 and 4 (to assess robustness to changing the type of distribution see Figure S22 for equivalent plots with lognormal distributions). While herd immunity is expected to require 60-70% of a homogeneous population to be immune given an R0 between 2.5 and 3, 20 these percentages drop to the range 10-20% for CVs between 2 and 4.

Curvefitting from COVID-19 incident waves, past SARS experiences, surveying of contact tracing data, pre-epidemic mobility data in the population, etc, all point to CVs around 3 which corresponds to a herd immunity threshold of 15% or so (hence the paper's 10-20% range). I think this is optimistic and a threshold of more like 30-35% is likely, which with durable aspects of behavior change might really end up being ~25%.

[acqq]

I don't think that that inferred CV from the quote says anything about the "herd immunity" in the sense which most of people would like it to be. If you have an outbreak where people start to suffer, people react, they stop behaving in a way they would do without he outbreak running. The "curve fitting" you quote, the way I see it, therefore doesn't say anything about the inherent resistance of human body or something like that, but about when different communities resort to locking themselves down or taking some other drastic action as the response to the "rising wave", even without any official ban of some activity.

Just reading, in one meat processing plant in Germany, from 3000 workers tested they have 1000 PCR positives (Rheda-Wiedenbrück meat processing plant, 1,029 cases so far (1)). It's already 30% of the tested and almost sure an "infection in one wave" (after some weeks a lot of people are PCR negative again). If it stays at 1000 (they will maybe test more: "On Friday morning, addresses of around 30% of the workers were still missing") it wouldn't mean it would have stayed at 1000 hadn't they closed the whole plant.

1) https://www.dw.com/en/coronavirus-german-slaughterhouse-outb...

[mlyle]

The whole point of the paper is that coefficient of variation affects the herd immunity threshold. And it obviously does, if you read the paper. The problem is, we don't know for sure what the CV is-- we can only guess based on history and observations.

> Just reading, in one meat processing plant in Germany, from 3000 workers tested they have 1000 PCR positives

This makes me think you don't understand any of the argument. A) CV includes things like contact network structure. OK, meat plants are an unfavorable contact network structure: this proves the point! If we have an observed R0 of 2.5 or 3.0, it includes (disproportionately) people who spend time in places with unfavorable conditions and contact others with unfavorable network structure. If there's a CV, what that means is that in some subgroups of contact structure and individual susceptibility (e.g. meat plants) we have an R0 much higher than 3, and in the bulk of the population we have an R0 much lower than 3.

B) Even ignoring this, there's nothing to say you won't overshoot a herd immunity threshold. The herd immunity threshold is just the threshold where each infection results in less than 1 new infection, on average: it isn't a place where infection magically stops, but instead where the number infected can be expected to naturally decrease. Obviously it's advantageous to have the infected count as low as possible when this happens, because it's only a slow decay from that point.