## Note to Self: Heterogeneity in the S, I, R Model...

So instead of doing my day job this afternoon, I began wondering about how much the Susceptible, Infected, Recovered (or Not)'s suppression of individual heterogeneity affects its conclusions.

Suppose that people have different amounts of gregariousness/infectiveness. If everyone were like the most gregarious and vulnerable people the R_0 for the epidemic would be 5. If everyone were like the least gregarious and vulnerable people the R_0 for the epidemic would be 0. And suppose we have the population varying linearly between those extremes.

How much different would the course of the epidemic be than for a society where everyone was identical, and R_0 was 2.5?

The answer is: substantially.

If I have not made a mistake in my model-building or my python code—always an "if"—then the difference is substantial: 26% of the population escapes the epidemic for R_0 distributed between 0 and 5 with an average of 2.5. Only 10% escapes the epidemic if everyone's R_0 is 2.5.

The intuition is clear: By the time half of the population has been infected, an overwhelming number of those with high R_0's have been infected. Thus those who are still susceptible have personal R_0's much lower than the average. In the early stages, however—before any noticeable component of the population has been infected—the course of the epidemic tracks the average R_0 very closely. It is when it begins to fall off the exponential that the differences become apparent: not only are some of those who would be infected by exponential growth now immune (or dead), but those left who could be infected have lower R_0's than the average.

**weblog support**: https://github.com/braddelong/weblog-support/blob/master/coronavirus-r0-heterogeneity.ipynb

nbViewer: https://nbviewer.jupyter.org/github/braddelong/weblog-support/blob/master/coronavirus-r0-heterogeneity.ipynb

datahub: http://datahub.berkeley.edu/user-redirect/interact?account=braddelong&repo=weblog-support&branch=master&path=coronavirus-r0-heterogeneity.ipynb

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#coronavirus #notetoself #publichealth #2020-05-03
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