Bistability in a SIRS model with general nonmonotone and saturated incidence rate

Abstract

In this paper, we consider a SIRS model with general nonmonotone and saturated incidence rate and perform stability and bifurcation analysis. We show that the system has saddle-node bifurcation and displays bistable behavior. We obtain the critical thresholds that characterize the dynamical behaviors of the model. We find with surprise that the system always admits a disease free equilibrium E0 which is always asymptotically stable. Numerical simulations are carried out to verify our results.