Epidemic spreading of evolving community structure

Abstract

Abstract Many complex systems have common community structure characteristics. Studying the community structure can reveal the mechanism of complex systems, so as to better understand and control complex systems. In the present work, we regard a community as an approximate homogeneous network. We use a mean-field approach to obtain an epidemic spreading dynamic model of community structure evolution. The epidemic threshold is given. Randomness is one of the striking characteristics of real-world networks as they evolve. Based on the specific stochastic block model (SBM) to generate synthetic networks with community structure, we use nonnegative matrix theory to analyze the changes in the spread of epidemics during the growth, contraction, division or merger of communities. A reduction in the number of communities, a reduction in the size of communities or a division of communities is conductive to increasing epidemic threshold, and thus mitigating the spread of epidemics. Our conclusion can explain some phenomena. The numerical simulations of real-world and random networks support and enrich our conclusions.