Modeling and stability analysis for SIRS model with nonlinear infection rate

To improve the existing SIRS (susceptible-infected-recovered-susceptible) model in which the infection rate is not considered, we propose an improved model by taking into account additionally the probability of infection range. The threshold and threshold conditions are derived based on the main-field theory on uniform networks and scale-free networks. We analyze the stability of the system near the equilibrium point by using Lyapunov stability theory and obtain the conclusion that the virus transmission process is not only related to the topology of networks but also on the infection probability and the immunity probability.