Impacts of cluster on network topology structure and epidemic spreading

Abstract

Considering the infection heterogeneity of different types of edges (lines and edges in the triangle in a network), we formulate and analyze an novel SIS model with cluster based mean-field approach for a network. We mainly focus on how network clustering inuences network structure and the disease spreading over the network. In networks with double poisson distributions, power law-poisson distribution, poisson-power law distributions and double power law distributions, we find that cluster is positive(the clustering coefficient is increasing on the expected number of triangles) when the average degree of lines is fixed and the moment of triangles is less than some threshold. Once the moment of triangles exceeds that threshold, cluster will become negative(the clustering coefficient is decreasing on the expected number of triangles). For the disease, clustering always increases the basic reproduction number of the disease in networks with whether positive cluster or negative cluster. It is different from existing results that cluster always promotes the disease spread in the homogeneous or heterogeneous network.