Epidemics and random graphs

Abstract

The idea of this note is to point out that the simple random graph G(η,ρ) (Bollobás (1985)) can be used as an internal description for the Reed-Frost.cha~n-binomial epidemic model (Bailey (1975)). This relationship is mutually beneficml: It allows us to deduce new results on each model from old results on the other, and also points to possible extensions of work on each. It also makes clear that the Reed-Frost model, in its contact structure if not its development in time, is, pace Jacquez (1987), one of the simplest and most elegant of epidemic models (see also Lefevre and Picard, 1989).