An epidemic propagation model with saturated infection rate on a small world network

Abstract

An SIRS model with constant immigration of susceptible and saturated infection rate is established according to the propagation of the infectious viruses in a small world network. By using the mean-field theory and qualitative theory of differential equations, the existence and stability of equilibrium points of the system was analyzed. It also prove that the transmission threshold of this model is not entirely concerned with the topology of networks but also related to other factors such as immunization rate of the susceptible people. By using numerical simulation method to study the different factors which control the viruses, we obtained the conclusion that rewiring probability and the average of the nodes had an evident effect on the computer viruses’ propagation in a small world network.