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So I'm trying to find a way to calculate expected social cost (from COVID-19 deaths) if I take a trip. (I've made a much more detailed post here.) I've gotten parts of a calculation that seem reasonable (e.g. how probable it is I'll get C19, how much lifespan an average C19 infection costs, etc.), but the primary remaining thing I don't know how to handle is the expected number of infections resulting from one root infection, assuming it takes place in the current USA environment. Most models I've seen for disease spread seem to assume simple exponential growth (though perhaps I'm mistaken), but that just doesn't seem to fit the data. Consider the active case graph here - there's only a few particular places on that graph that actually look exponential, to me. Most of it seems linear, in fact.

In the case of exponential growth, it would be easy to predict the total number of cases resulting from a single infection: R0^(number of generations you're considering). However, with C19's estimated R0 of ~2, (or really any R0 > 1) you get an unreasonable number of cases in a fairly short amount of time. And, like I said, the exponential model doesn't appear to fit the actual data. This question asks about logistic regressions, and could more accurately reflect the spread of COVID-19, but I'm not sure how much research supports this argument or not. Even if it were more accurate, I don't know how to use that information to predict the spread from a single infection.

So, given the current number of infections, how do you predict the eventual total number of infections, in the case where you add one extra right now, vs the case where you don't? (If it helps, perhaps we can assume that a vaccine is distributed in 6 months and the disease is effectively halted.)

(Also, if anybody has feedback on my aforementioned post, I'd like to hear it.)

Erhannis
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    You mean "logistic growth", not "logistic regression". Anyway, for the sake of your work, you can assume logistic growth...it's a pretty common assumption. – Itamar Mushkin Aug 09 '20 at 05:30
  • Growth rate depends heavily on prevalence. Also, on social behavior. One speaks of the number of new cases each infected person is responsible for. When it's < 1, the growth rate tends to go down. Hence discussions about wearing masks and avoiding unnecessary contacts and travel. – BruceET Aug 09 '20 at 05:49
  • As of last week, the epidemiologists I was listening to at the JSM emphasized that nobody's even trying to predict the eventual total: it's just too uncertain and not a terribly useful number anyway. – whuber Aug 11 '20 at 20:31

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