Network percolation of the disease transmission based on bipartite networks

Abstract

In this paper, considered heterogeneous infectivity and susceptibility, a general stochastic Susceptible-Infectious-Removed (SIR) epidemic model with the cumulative distribution functions (CDFS) of the infectious contact rate and the infectious period based on bipartite networks is discussed. It is isomorphic to a semidirected random network called the bipartite epidemic percolation network. The epidemic threshold corresponds to the phase transition where a giant strongly connected component appears. It is obtained by using the method of the probability generation function. We show that the critical value of the transmissibility predicted by the bond percolation model is larger than that predicted by the epidemic percolation network. We analyze the influences of the network structure and individual heterogeneity on the epidemic threshold by numerical simulations.