## Monday, March 16, 2020

### ESTIMATE YOUR CORONA VIRUS RISK

The key to your risk reduction will be to minimize the number, N, of possibly contagious people you have contact with during this epidemic and choose those less likely to be contagious.

The simplest model: your probability, P, of catching the virus is the multiplication of the fraction, f, of those in your locale who are infective times the number, N,  you have contact with

P = f N

While you can do little about f, you can choose to keep N very small.

This model is not correct for P near or larger than 1, but such an answer indicates you almost certainly will get the virus.

A more sophisticated model gives a more accurate estimate (although f will often be just a guess): it multiplies N successive probabilities that you escape contagion despite contact N times:

Escape = 1-infected = 1 – P’ = (1-f)(1-f)…(1-f) = (1-f)^N,

This is the product of N escapes, (1-f) to the Nth power.
When f N is much smaller than 1, they give almost the same answer:

e.g.,

P = f N = (0.1) (3) = 0.30, a 30% chance of catching the virus.

1 – P’ = (0.9)(0.9)(0.9) = (0.9)^3 = 0.73

P’ = 1-0.73 = 0.27, a 27% chance of catching the virus, virtually the same as the simplest model.

Both models indicate you should avoid contact with others (keep N small), especially those likely to have the virus (keep f small).

Sharing a closed environment with many people clearly raises your risk.

About f: it will change over time, as the virus comes to your locality, infects some, and they will be put out of your reach, hopefully. Swine flu in 2010, H1N1, infected some 62M Americans, about f=0.20 of the population. With thought, you can choose low-f contacts versus high-f ones.