## Sunday, March 15, 2020

### CORONA VIRUS LIMITING CASES

If the virus is in a location, and there is no human migration in an out of there, it will infect most or all and then die out in a few weeks. Thus, limit human movement.

If it is going to spread throughout the country, it is best that it spread slowly, so that the various locations can adapt to a slowly developing hazard. Again, limit human movement.

A simple model predicts a time dependence of -2At + B, with a final duration of t = B//2A.

From my prior blog:

A century ago John Brownlee showed that Farr's law gives an exponential function:

I(t) = exp[-At^2 + Bt + C] = exp(C) exp[-At^2 + Bt]

this is a constant term times an exponential term of growth (Bt) and one of decrease (-At^2).

From the beginning, t near zero, to the end, t >> 1  or -At^2+Bt << -1, I(t) looks somewhat like the bell-shaped curve of the Normal, Gaussian, statistical distribution, exp(-a(t-b)^2).

Setting  -At^2+Bt << -1 lets one predict the effective end of the epidemic, given A and B from fitting the curve function  to the data.

This link shows the Wuhan corona virus incidence data, pretty much a bell-shaped curve with the exception of one day, and it shows a duration of about 40 days:

https://www.ecdc.europa.eu/en/geographical-distribution-2019-ncov-cases

This blog post is based on an excellent article by Santillana et al.  from the journal, Infectious Disease Modeling, in 2018. It describes and analyzes the growth of the number of newly infected over time, I(t), in an epidemic, relying on a relationship, Farr's Law, found by an epidemiologist, Dr. William Farr, about a century and a half ago. I will explain part of the research. Here is he link:
https://www.sciencedirect.com/science/article/pii/S2468042718300101