THE EARLY AND FINAL-STATES OF AN EPIDEMIC IN A LARGE HETEROGENEOUS POPULATION WITH A SMALL INITIAL NUMBER OF INFECTIVES

This paper describes the early and final properties of a general S-I-R epidemic process in which the infectives behave independently, each i nfective has a random number of contacts with the others in the popula tion, and individuals vary in their susceptibility to infection. For t he case of a large initial number of susceptibles and a small (finite) initial number of infectives, we derive the threshold behavior and th e limiting distribution for the final state of the epidemic. Also, we show strong convergence of the epidemic process over any finite time i nterval to a birth and death process, extending the results of Ball (1 983). These complement some results due to Butler (1994), who consider s the case of a large initial number of infectives.