Dynamics of a network-based SIS epidemic model with nonmonotone incidence rate

•A network-based SIS epidemic model with non-monotone incidence rate is proposed.•A threshold value for the transmission rate is obtained.•The threshold value determines the dynamics of the proposed model.•Numerical experiments for a finite scale-free network are presented.•The effect of the nonlinear incidence on the epidemic dynamics is also considered.

This paper studies the dynamics of a network-based SIS epidemic model with nonmonotone incidence rate. This type of nonlinear incidence can be used to describe the psychological effect of certain diseases spread in a contact network at high infective levels. We first find a threshold value for the transmission rate. This value completely determines the dynamics of the model and interestingly, the threshold is not dependent on the functional form of the nonlinear incidence rate. Furthermore, if the transmission rate is less than or equal to the threshold value, the disease will die out. Otherwise, it will be permanent. Numerical experiments are given to illustrate the theoretical results. We also consider the effect of the nonlinear incidence on the epidemic dynamics.