To me, the focus on R_0 or R_e is misguided because, while bringing it below 1 turns an epidemic into a set of isolated outbreaks, the average sizes of these outbreaks depend very much on the degree distribution, not just the average degree in the branching process. (Given the distribution, computing the average outbreak size is a nice exercise in generating functions.) Moreover, we often care about the variance of the outbreak size: if you have 10 small towns, each of whom can handle 10 patients, an average outbreak size of 5 is ok, but not if 1 or 2 of these towns have outbreaks of size 100. (Indeed this is exactly what seems to be happening in rural areas.)

On Apr 18, 2020, at 1:48 PM, Keith F. Lynch <kfl@KeithLynch.net> wrote:

Henry Baker <hbaker1@pipeline.com> wrote:

...

Thus, if one person has an R_e of 0.9 and another person has an R_e of 40.0, there isn't a good way to average the two R_e's to compute a composite R_e.

On second thought, why isn't the arithmetic average appropriate? Wouldn't those two people cause just as many cases as two people with an R_e of 20.45 would?

Of course I'm assuming that what's different is the behavior of the two people, not the virus. The 0.9 person always stays home, and the 40 person works in a crowded grocery store without a mask. Since the virus is only a few months old, I doubt different strains of it yet vary in non-trivial ways. If they did, that would of course quickly select for high values of R_e, so R_e would be going up everywhere. I haven't heard of anything like that being observed.

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