Dynamics of a delayed epidemic model with non-monotonic incidence rate

A delayed epidemic model with non-monotonic incidence rate which describes the psychological effect of certain serious on the community when the number of infectives is getting larger is studied. The disease-free equilibrium is globally asymptotically stable when R0<1R0<1 and is globally attractive when R0=1R0=1 are derived. On the other hand, The disease is permanent when R0>1R0>1 is also obtained. Numerical simulation results are given to support the theoretical predictions.