Dynamics of a Saturation Incidence SIRS Epidemic Model with Pulses at Different Moments

In this paper, the dynamical behavior of a saturation incidence SIRS epidemic model with birth pulse, pulse treatment, and pulse vaccination is studied. By using discrete map, the existence and stability of the infection-free periodic solution are investigated. A threshold for a disease to be extinct or endemic is established. The Poincaré map and center manifold theorem are used to discuss flip bifurcation of endemic periodic solution. Moreover, numerical simulations are in good agreement with the theoretical analysis.