Friday, March 27, 2020

"The Math of Epidemics": statistics, and differential equations; many good videos (2 of them here)

Professor Tom Britton at the University of Stockholm, from Vetenkapenshus (36 min) explains “Mathematics of the Corona Outbreak”.

He models diseases abstractly, and mentions how HIV developed in the 1980s with a smaller totality of susceptible populations but very long incubations which is what resulted in increasing the R-naught.  The R0 came down with changes in behavior and with drugs that suppressed the virus.

The presentation with regard to Covid19 (Sars-Cov2) is relatively abstract and simplified.

Then Trefor Bazett explains “The Math of Epidemics” with an introduction to the SIR Model.   He uses differential equations to model outbreaks (a system of three equations).  This reminds me of an undergraduate course at GW and then a more difficult course in Partial Differential Equations at KU (starting with the Wave Equation, which may matter to quantum theory now) with a text by Blaisdell which was hard to follow as I remember (in 1966).

For predicting the peak of an outbreak (like in New York now), it is the second derivative of the curve that matters, it needs to become negative for the actual slope to flatten. I’m not sure which functions would mimic the curves;  maybe my 1968 thesis “Minimax Rational Function Approximation” (KU in Lawrence, KS)  matters.

The graph on page 12 of my thesis (picture) looks like a poorly controlled pandemic with recurrent waves with sharp peaks, where there had been no social distancing (e.g., Trump). I’ll look into this some more and see if this is a close model to outbreaks.

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