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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.

This paper studies a two-strain SIS epidemic model with a competing mechanism and a saturating incidence rate on complex networks. This type of incidence rate could be used to reflect the crowding effect of the infective individuals. We first obtain the associated reproduction numbers for each of the two strains which determine the existence of the boundary equilibria. Stability of the disease-free and boundary equilibria are further examined. Besides, we also show that the two competing strains can coexist under certain conditions. Interestingly, the saturating incidence rate can have specific effects on not only the stability of the boundary equilibria, but also the existence of the coexistence equilibrium. Numerical simulations are presented to support the theoretical results.