Impact of contact heterogeneity on initial growth behavior of an epidemic: Complex network-based approach

Abstract

The initial growth behavior of the scalar susceptible-infected-recovered (SIR) epidemic model is fully determined by the basic reproduction number. However, increasing individuals’ contact heterogeneity may invalidate the classical results and cause complex dynamics. Thus, we first consider the SIR model in annealed networks with bimodal degree distribution and derive some sufficient or necessary conditions that determine the monotonicity of densities of infected individuals in each degree class around the initial time t=0. Then, we consider the SIR model in annealed networks with arbitrary degree distribution and analyze the initial growth behavior of it. Interestingly, if we assume that initial densities of infected individuals in each degree class are proportional to the right eigenvector of a specified non-negative and irreducible matrix, then the initial growth behavior of infected individuals in each degree class is completely determined by the basic reproduction number. However, this is not the case for any initial condition, and the initial growth behavior may be very complex. Numerical simulations are performed to verify our analytical results and further investigate the effect of contact heterogeneity on disease behavior.