THE FINAL-STATE OF AN EPIDEMIC IN A LARGE HETEROGENEOUS POPULATION WITH A LARGE INITIAL NUMBER OF INFECTIVES

We describe some asymptotic properties of a general S-I-R epidemic pro cess in a large heterogeneous population. We assume that the infective s behave independently, that each infective has a generally distribute d random number of contacts with the others in the population, and tha t among the initial susceptibles there is an arbitrary initial distrib ution of susceptibility. For the case of a large number of initial inf ectives, we demonstrate the asymptotic normality of the final size dis tribution as well as convergence of the final distribution of suscepti bility as the population size approaches infinity. The relationship be tween the mean of the limiting final size distribution and the initial heretogeneity of susceptibility is explored, for a parametric example .