Limit theorems for a random graph epidemic model

We consider a simple stochastic discrete-time epidemic model in a large clo sed homogeneous population that is not necessarily homogeneously mixing. Ra ther, each individual has a fixed circle of acquaintances and the epidemic spreads along this social network. In case the number of initially infectiv e individuals stays small, a branching process approximation for the number of infectives is in force. Moreover, we provide a deterministic approximat ion of the bivariate process of susceptible and infective individuals, vali d when the number of initially infective individuals is large. These result s are used in order to derive the basic reproduction number and the asympto tic final epidemic size of the process. The model is described in the frame work of random graphs.