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.