A delayed SIRS epidemic model with pulse vaccination

A delayed SIRS epidemic model with pulse vaccination and saturated contact rate is investigated. By using the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic solution of the system. Further, by using the comparison theorem, we prove that under the condition that R0 < 1 the infection-free periodic solution is globally attractive, and that under the condition that R′ > 1 the disease is uniformly persistent, which means that after some period of time the disease will become endemic.