I wanted to discuss the degree to which population immunity may be contributing to curbing #COVID19 in Florida, Arizona and Texas, where recent surges have resulted in substantial epidemics. 1/16
After increasing dramatically in June and July, daily case counts in Florida, Arizona and Texas have begun to subside. Data from @COVID19Tracking. 2/16 
This corresponds to a peak Rt of between 1.2 and 1.4 in late-May / early-June and steady reductions since this point. Declining case counts correspond to Rt < 1. Rt estimates from rt.live. 3/16
The recent uptick in Rt in Texas comes from increasing test positivity and the algorithm used by rt.live to convert test positivity to infections. I'm not exactly sure what's going on here, but I wouldn't ascribe too much weight to this particular estimate. 4/16
I (and others) have argued that the main thing curbing these epidemics have been societal responses, but I believe there is also a role for population immunity in controlling these epidemics. 5/16
If we take the simplest model of population immunity, we expect Rt will equal R0 ⨉ fraction of the population susceptible. This is where the usual "herd immunity threshold" comes in. If we assume R0 of 2.5 then we need 60% of the population immune to bring R0 down to 1. 6/16
However, societal behavior has dramatically reduced Rt through social distancing, mask wearing, etc... The surge in Florida had Rt of only ~1.4 at its peak. Because of this reduction in transmission through social means, we don't need as much immunity to impact spread. 7/16
Here, we expect Rt will equal R0 ⨉ fraction of the population susceptible ⨉ relative social connectivity. If R0 is 2.5 and social connectivity is 56% of normal then realized Rt will be 1.4. In this case, the herd immune threshold would be 29%. 8/16
We can plot out the general relationship between Rt (as red vs blue) vs population immunity (on the x-axis) vs social connectivity (on the y-axis). With R0 of 2.5, to keep Rt<1, we need either lots of immunity, very strong social distancing or something in between for each. 9/16
At this point, we think that a substantial fraction of the population of Florida has had COVID-19. If we use a 8:1 ratio of confirmed cases to underlying infections, we'd estimate 510k x 8 = ~4M infections in Florida or roughly 20% of the population. 10/16
Similarly, covid19-projections.com/us-fl currently estimates 21% of Florida has had COVID-19 at this point. 11/16
Assuming a large majority of infections leave enough immunity to be protected (which I believe to be the case, though correlates of protection are still being worked out), population immunity of 20% will have real impact if societal behavior has already reduced Rt to ~1.2. 12/16
I've been thinking of this as: to get to R0 of 1.0 with no immunity we need avoid 60% of transmission events. However, if 20% of the population is immune, then we need to avoid 50% of transmission events. 13/16
Or, with 20% population immunity, we can behave as though Rt is 1.25 and still get an epidemic that no longer propagates. 14/16
Thus, I believe the substantial epidemics in Arizona, Florida and Texas will leave enough immunity to assist in keeping COVID-19 controlled. However, this level of immunity is not compatible with a full return to societal behavior as existed before the pandemic. 15/16
That said, the costs for this immunity have been substantial and are continuing to accrue. We need a vaccine to achieve population immunity in a fashion that doesn't kill people. 16/16
Follow up #1: My use of 20% total infected in Florida is not the point I was trying to make. I think it could easily be 10% of Florida infected at present. The point being even 10% population immunity starts to make a difference when behavioral Rt is ~1.2.
