APPROXIMATION OF EPIDEMICS BY INHOMOGENEOUS BIRTH-AND-DEATH PROCESSES

This paper is concerned with the approximation of a class of open popu lation epidemic models by time-inhomogeneous birth-and-death processes . In particular, we consider models in which the population of suscept ibles behaves in the absence of infection as a general branching proce ss. It is shown that for a large initial number of susceptibles, the p rocess of infectives behaves approximately as a time-inhomogeneous bir th-and-death process. Strong convergence results are obtained over an increasing sequence of time intervals [0, t(N)], where N is the initia l number of susceptibles and t(N) --> infinity as N --> infinity. (C) 1998 Elsevier Science B.V. All rights reserved.