Abstract:

We used the theory of dynamic random graph as the tool to investigate the convergence of a stochastic discretetime epidemic model in a large population by means of the method of branching process approximation. The significance of the paper lies in the improved \%SIR\% model. Each individual has a certain number of acquaintances with a fixed distribution. As the number of initially infective individuals stays small, a branching process approximation for
 the number of infective individuals is in force. Using the results of the branching process, we will have the main results, that is, the number of new infective individuals will present some almost surely limit properties with the size of the population extending.

Key words: random graph, epidemic model, branching process, almost surely convergence