Modelling of Epidemics with a Generalized Nonlinear Incidence on Complex Networks

In this paper the spreading of epidemic model on complex networks with a generalized nonlinear incidence rate is presented. Firstly the SIS model on homogeneous networks with nonlinear incidence rate is considered, and the existence conditions about the disease-free equilibrium and the endemic equilibrium are given. And then the model on heterogenous scale-free (SF) networks is considered, where the absence of the threshold on SF networks with nonlinear incidence is demonstrated. At last the stability of the disease-free equilibrium on SF networks is obtained. From this paper, it is shown that, while the number of the equilibria is indeed different from the corresponding model with linear incidence rate, the basic reproductive number, which determinate whether the disease is spreading or not, is independent of the functional form of the nonlinear incidence rate.