Farr’s Law and Social Risk Aversion in the Study of Epidemics

With the recent COVID-19 epidemic, the modeling of the frequency of new cases of infection within a given time period is of interest. Farr’s Law and the related Brownlee-Farr condition on infection counts implies a specific functional form for the related incidence function I ( t ) when the epidemic is under control. This form includes the Gaussian distribution, but also other distributions such as the exponential distribution. It also includes functions that are not probability densities. The Brownlee-Farr condition is shown here to correspond as a mathematical function to the Pratt-Arrow risk avoidance ARA measure and the hazard rate. This closely connects I ( t ) to the concept of social risk avoidance with higher levels of infection posing a direct risk to healthy individuals and society, resulting in risk avoidance behavior. It is suggested that the degree of social control over the epidemic can be measured using the entropy of the observed I ( t ) density.