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.
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.
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.
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.
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.
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.
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.
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.
