There are parts of NYC with 68% positive antibodies a month ago- so I wouldn't be surprised if a lot more people in NY have been infected than is reported. But not sure I'm following your math from R0 5.6->80%?
That's from one clinic, for people seeking an antibody test.
Anyway, the first link I mention is the broader dataset from all the clinics like this, so it helps smooth out anomalies. But, the big caveat in all of this is that these suffer from selection bias - it's not a randomized sampling of people in each borough. It's still useful data, but it's far from being able to tell one the incidence rate to a reasonable degree of precision. Still, many reasonable inferences one can make.
CDC Data from mid June had NYC at only 20% prevalence. Considering their low new daily cases since then, it's hard to believe they are anywhere near 68%.
So, I think the proposed math is something like: 1/3rd of infected don't show antibodies so that 20% means 30% were infected. Another study showed pre-existing T cell reactivity (maybe immunity?) in 40% of people, so if you combine those you're at 70%.
I find it hard to believe, with the R0 numbers we were seeing initially, that 40% had a significant level of immunity. If the numbers were that high, then R0 among those without memory T-cell immunity would have been significantly higher, which suggests that the level of exposure/immunity necessary for herd immunity to set in would be significantly higher as well.
What you're saying makes sense. Looking at some tables of it, it seems like if we imagine it in a naive population having a 50% higher reproduction number, it seems like it only bumps the herd immunity number by about 10% because it is such a high proportion already, if I'm understanding the charts right. It isn't clear if the numbers come together, but it does make me wonder if it could be close.
68% tested positive at a clinic in one neighborhood. Getting tested, without proper controls, is highly subject to self-selection bias. People were sick, couldn't get a test at the time, want to know if it was COVID, go in for an antibody test later. The people who were healthy, unless selected for a prevalence study, would much less likely to be tested in the first place.
Even in your first link, the highest percent positive is the Bronx reporting 33%. Not sure where you're getting 51% from, but it very much seems like you're trying to cherry pick data to support your argument.
Well, R0 is by definition different for different populations - density, demographics, etc. R0 and the herd immunity threshold have a clear mathematical relationship; it's just a restating of the definition. So if you argue the threshold is lower for a subpopulation, you're also arguing that R0 is lower for that same subpopulation.
It also depends on the interconnectedness of the population. Person A may not be very connected, only being particularly likely to infect their own household, and maybe one or two other people outside. Person B might be highly connected and in a position to infect dozens of people. If you had a population of 80% "Person A" and 20% "Person B", this might average out to an R0 of around 6 -- but the actual reproductive rate would drop rapidly as "Person B"s gain immunity.
That makes intuitive sense to me, that over the lifetime of an unrestrained virus propagation, the R0 value would start out higher and slowly decrease until the herd immunity threshold is reached. Not sure if that is commonly observed in the epi community but it wouldn't surprise me.
