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Global analysis of an epidemic model with nonmonotone incidence rate. (English) Zbl 1119.92042
Summary: We study an epidemic model with nonmonotonic incidence rate, which describes the psychological effect of certain serious diseases on the community when the number of infectives is getting larger. By carrying out a global analysis of the model and studying the stability of the disease-free equilibrium and the endemic equilibrium, we show that either the number of infective individuals tends to zero as time evolves or the disease persists.

MSC:
92C60Medical epidemiology
37N25Dynamical systems in biology
34C60Qualitative investigation and simulation of models (ODE)