A stochastic SIR epidemic on scale-free network with community structure

The scale-free degree distribution and community structure are two significant properties shared by numerous complex networks. In this paper, we investigate the impact of these properties on a stochastic SIR epidemic which incorporates the stochastic nature of epidemic spreading. A two-type branching process is employed to approximate the early stage of epidemic spreading. The basic reproduction number R0 is obtained. And the influences of scale-free property and community structure on R0 are analyzed by numerical simulations.