Approximation of epidemics by inhomogeneous birth-and-death processes

Abstract

This paper is concerned with the approximation of a class of open population epidemic models by time-inhomogeneous birth-and-death processes. In particular, we consider models in which the population of susceptibles behaves in the absence of infection as a general branching process. It is shown that for a large initial number of susceptibles, the process of infectives behaves approximately as a time-inhomogeneous birth-and-death process. Strong convergence results are obtained over an increasing sequence of time intervals [0, t N ], where N is the initial number of susceptibles and t N →∞ as N→∞.