Collective epidemic models.

Abstract

A number of models have been proposed to describe the spread of infectious diseases of the S-I-R type. Most of them account for variable infectivity levels, and very few incorporate variable susceptibility levels. In the present work, a new epidemic model, called a collective model, is constructed that combines both variabilities in a general way. It is then established how to determine the exact distribution of the final state and the severity of the epidemic when the infection process stops.