How Overlapping Community Structure Affects Epidemic Spreading in Complex Networks

Many real-world networks exhibit overlapping community structure in which vertices may belong to more than one community. It has been recently shown that community structure plays an import role in epidemic spreading. However, the effect of different vertices on epidemic behavior was still unclear. In this paper, we classify vertices into overlapping and non-overlapping ones, and investigate in detail how they affect epidemic spreading respectively. We propose a SIR epidemic model named ICP-SIR (Inner-Community Preferred Susceptible-Infective-Recovered) where the inner-community and inter-community spreading rates are different. We consider the case where epidemic process is started by immunizing and infecting multiple overlapping or non-overlapping vertices. The epidemic model is applied on both synthetic and real-world networks. Simulation results indicate that compared to non-overlapping vertices, overlapping vertices play a vital role in spreading the epidemic across communities. The result of our research may provide some reference on epidemic immunization in the future.