This seems important, and there's a related point that I've only seen mentioned once, in a comment thread on an econ blog.

Discussion of R0 tends to treat it as a constant, or at best a population variable. "Flattening the curve" = laboriously pushing R0 downward at high cost. https://twitter.com/jonkay/status/1253148252733673473

But R0 is also a random variable *within* populations -- the innate immune system varies wildly from person to person, and so does behavior. The link above points out that some behaviors seem to potentiate transmission at orders of magnitude above the theoretical population "R0".

At the other extreme, consider, well, me: I leave the house maybe twice a month under *normal* circumstances.

The SIR model is good as an intuition pump, but it doesn't capture this heterogeneity at all. So what does it mean for the model if R0 is actually Pareto distributed?

Well, (handwaving violently), one implication is that herd immunity shows up a lot sooner, because population susceptibility isn't uniformly distributed. (This isn't quite right, susceptibility and transmission aren't the same thing! But the same factors mostly apply to both.)

In other words, the segment of the population that goes to mass church services, work in hospitals, and ride the subways get disproportionately infected until *they* reach effective herd immunity. Meanwhile, the stay-at-homes and naturally immune are much less exposed.

To abuse 80/20 to the breaking point, just as a toy model: Suppose the most vulnerable 20% need to reach 80% exposure for herd immunity, while the least vulnerable 80% only need 20% exposure. Then you get herd immunity at 32% exposure, while an SIR model might say you need 80%.

Wikipedia's remark here is actually pretty solid. https://en.wikipedia.org/wiki/Basic_reproduction_number#Heterogeneous_populations Suppose as an extreme case that Brooklynites are completely immune to an epidemic that just started in Manhattan. Your estimate of R0 will be based entirely on Manhattanites!

This was a good thread, guys. It's hard out here for an independent scholar/crank, the algorithm's keeping me Down

Summary in one tweet: Pandemics pick the low-hanging fruit first, too, so it's possible for R0 to decline over time independent of other factors, and it's problematic to make long-term forecasts based on current estimates, especially for stuff like herd immunity.