> then some mass spreading events infecting many more

The point is however that it is impossible that the choir selected their members based on the criteria of "members can be only these who will be easily infected with the at the moment still unknown disease." There the existence of the superspreading event to "80% of some random selection" disproves the hypothesis that "on average much less than 80% of the population can be infected at once". That's obviously not true.

Just because the choir couldn't select its members on the basis of lower immunity, doesn't it mean it didn't select them (or they self-selected on) the basis of some characteristic(s) that happened to correlate with lower immunity, e.g. age, biological gender, ethnicity, socioeconomic status, etc.

The same is true of any other sub-population this is not a true random sample of the global population, like prisons, care homes, even settlements like towns and villages. If you can make any prediction about their members with greater confidence than you could with a random member of the whole population, then they are not random in the sense that matters.

Explaining how and why the characteristics of those sub-populations could correlate with greater natural immunity is certainly a challenge to those advocating for the idea of some level of latent immunity. But, likewise, substantially different outcomes in sub-populations that engaged in similar interventions is a challenge for those advocating that only interventions matter. For example, I've not heard a convincing explanation for Germany's relative success based only on the quality of its healthcare system and interventions. That isn't to deny that they played an important role, just that they may not have been the whole story.

> I've not heard a convincing explanation for Germany's relative success based only on the quality of its healthcare system and interventions. That isn't to deny that they played an important role, just that they may not have been the whole story.

Of course "its healthcare system" is not the whole story alone. "Its healthcare system and interventions" is a good enough precondition, combined with the timing: it was since long obvious that the difference in timing of introducing the interventions immensely changes the number of deaths in the first peak: first order approximation: if the doubling time is 3 days, interventions of 2 weeks earlier compared to some other country could result in 2 ^ 4 = 16 times less deaths per capita. It's very primitive approximation but good enough to make such an argument (even if it's significantly off, it is to show how little time result in big changes). For more detailed elaboration there was recently a paper calculating the difference with more exact models, I believe for the UK. (edit: found one for the US https://www.medrxiv.org/content/10.1101/2020.05.15.20103655v... )

So the story for Germany is: luck, in having the early warning and the capability to act on it: Italy have had its spread earlier and it gave Germany enough of "early warning" which was effectively used. The bigger story is the failure of other countries who also practically had the same "early warning" and remained blind to it, until they recognized that they had do "do something" but with the resulting cost of more deaths.

Europe is a good enough field where a lot of effects could be clearly observed, all countries having in some important aspects significantly more sane health system than the U.S. We also know for sure that the excess deaths due to the all causes together can't be hidden in these countries (see https://euromomo.eu/graphs-and-maps/ ), so we now know exactly how bad which country was hit. Comparing the rich European countries and knowing how they function all the differences among them are indeed very explainable, I don't see any surprises: it's the interventions and learning from the experience of other countries that consistently worked.

U.S. was of course much less ready to learn from anybody. In spite of that, the deaths per million in the U.S. is still 362 while it's 500 in Sweden -- so we all have a good "negative example" from Sweden. Note also that Sweden did close universities and older classes in schools, and suggested everybody who can to work from home, and still got to be that bad -- only because their interventions were by design less strong compared to other European countries.

Reported daily deaths per million in USA, Sweden, Germany and Italy, "by number of days since 0.1 average deaths (per million) first recorded" compared:

https://ig.ft.com/coronavirus-chart/?areas=usa&areas=swe&are...

Note that "it lasted longer in Italy" for almost 20 days -- that was the early warning available to other countries. Some used it. Pity that FT doesn't display simply all the curves based only on the dates. Also, too big entities like the whole USA or China aren't a good comparison, the big less infected areas (due to them being simply less reachable) move the averages down too much -- a better base for comparison would be the entities on the order of 10 millions. E.g. in the USA, NY is definitely a phenomenon that is worth observing separately etc.

No.

If it is true that say 50% have a harder time catching covid then given that there is a superspreading event at a choir to 80% you need to take into account the others choirs at the other end of the tail.

I.e. given 100 choirs there will be a distribution of "not easiely infected" individuals with choirs with few off them.

I am not saying anything of the validty of the claim, just that the choir doesnt disprove it.

> I.e. given 100 choirs there will be a distribution of "not easily infected" individuals with choirs with few off them.

That's a valid point -- one choir alone would not be enough to be the proof, it could still be an accident that such individuals happened to be in one particular choir, but it's not the only such "random sample." Given that we have more "random samples" of different sizes, they can be observed as contributing to the evidence, the logic of the proof is there, and the evidence accumulates, especially as it can be observed that no specific "traits" of the infected could be recognized to bring "the difference" between "less" and "more" easy infections.

One of the arguments supporting the significance in the choir is -- the earlier in the spread of infection we observe such choirs, there's less chance that "100 choirs" from your example were even exposed to the virus, and less chance that that specific choir was exceptional. Similar spreads early in epidemics would also point in non-exceptionality of that one.

That is a fundamental misunderstanding of how probabilities work. There is always bunching, streaking, things that look like patterns but are not, and the like.

We obviously have a huge variation in spread. Indeed, the choir is evidence of superspreaders who produce many cases, and we have an average R0 of 2-3. Singing loudly in enclosed spaces with many people is an example of a contact network structure that causes greatly increased susceptibility and contagion. Indeed, it proves the whole point!

But, the belief that herd immunity = 1 - (1 / R) is based on the assumption that those infected have equal susceptibility and equal probability of spread. This is a fair assumption when it comes to a vaccination program which will administer doses not correlated to susceptibility and contact network structure. It is not a fair assumption when it comes to actual spread of disease in the wild, which will preferentially spread in the more susceptible networks.

Reality is certainly better than this; the question is how much better. There's been some quality analysis of time-series data that implies the threshold may be 20-30%.

I believe that New York City's quick decline in death rates compared to jurisdictions with similar or stricter controls but lower seropositivity may imply that ~20% exposure is enough to significantly attenuate spread.

> There's been some quality analysis of time-series data that implies the threshold may be 20-30%.

Please provide the sources. I however don't expect it can be that good, and I'm quite sure it will be proven that it's impossible to expect for the epidemics to stop once 20 or 30% of the population is infected, if that is your claim. If your claim is that once that "threshold" is reached the speed of the spread changes, well that speed changed already much earlier: most people just don't have any motive to sacrifice for the "economy" or the rich or whatever. You don't need the laws for the people to figure out that much.

This is a good introductory treatment of the topic:

https://www.medrxiv.org/content/10.1101/2020.04.27.20081893v...

> well that speed changed already much earlier

Your comment is a bit self-contradictory and muddled. That is, we're talking about the herd immunity threshold under baseline behavior; what percentage of the population needs to have been infected to result in infections decaying with original behaviors.

The point I was making is that it seems like case counts are decaying much quicker in regions with high seropositivity than other regions with similar regulations and similar empirical measures of mobility. This would imply that under current conditions even the modest immunity reached seems to make a bigger difference than naive assumptions about immunity and resulting Rt imply.

We already know that contact networks are not uniform (source: duh); further, individual susceptibility apparently varies significantly (from genetic studies). These factors significantly change the percentage that must be organically infected to reach herd immunity.

It's worth noting that this difference has both optimistic and pessimistic implications. Optimistic: regions that have high seropositivity are more likely to have the worst behind them. Pessimistic: the amount of vaccination to have equal effect probably far out-strips current seropositivity rates, because it can't effectively be targeted based upon susceptibility and network structure.

I tried but I don’t see that the paper proved anything about the current pandemics?

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...

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").

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.

> 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.

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%.

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...

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.

Have you noticed that the curves are following Gompertz-Model?

https://www.facebook.com/photo.php?fbid=10157283645163015

https://www.youtube.com/watch?v=8aHrx68IT7o

There is no constant CV>1 - it all depends on the situation.

I simply can't imagine that anybody who even basically understands the related topics could believe the facebook post you posted (I'm referring to the graph). If I'm wrong and they do exist I'm very, very sad, and even scared imagining having to deal with such people.

Also update from yesterday: in Germany's plant today's score is "more than 1500"

https://www.dailymail.co.uk/news/article-8450221/1-500-worke...

Feel free to take a look at the official data yourself.

https://www.ecdc.europa.eu/en/publications-data/download-tod...

You need nothing but Excel/LibreOffice and a few simple formulas to get this picture.

Germany has a heavy 7 day rhythm, because they're doing their reporting in a very strange way. Using 7 day averages helps a lot to get rid of the reporting-noise.

You need: Daily death (averages over 7 days) Total death (Sum) (averages over 7 days)

daily/total

Just use SUM() and /

I don't doubt that one can produce the picture. The problem is that these drawn lines over the real data don't mean anything.

https://en.wikipedia.org/wiki/Rorschach_test

R² > 0,995

If you subtract the trend of the first outbreak from the main trend it's R²>0,995 from the beginning down the point where old people started to wear masks and go to church. Here things get worse - as expected.

New trend is still collapsing exponentially - numbers now are so low that the curve has reporting issues (national deathcount on Sunday was -1).

The Saturday and Sunday are the "weird" death data in most of the countries, and not because people die less on these days, but because not all those that report the deaths do that on these days: even in hospitals in the middle of epidemics some people in administration simply don't work on weekends.

So what I see for Germany is the number of detected cases increased the last week, therefore I expect in 2-4 weeks the increase of deaths in Germany, that's how much the delay is between more cases and more deaths.

I don't see anything else that is a realistic "signal" about anything.

Currently in Germany it maybe works the other way around.

Last month around me it worked like this: Big spikes in case were caused by a test-campaign around somebody who died (or was ill). So a trend in case might in fact be an old trend of death - and the burst in case might in fact be asymptomatic or mild cases not leading to any death.

When you try to fit the spikes of death and case things are strange. In Germany maybe case and death have completely detached from each other.

Currently there are a lot of corrections going on. Bavaria had a deathcount of -3 on Saturday. Maybe they are piling up to report a big spike soon, or they stopped someone from reporting nonsense? We will see...