  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.
