Analysis of a delayed epidemic model with pulse vaccination and saturation incidence.

Pulse vaccination is an important strategy for the elimination of infectious diseases. An SEIRS epidemic model with time delays and pulse vaccination is formulated in this paper. Using the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic solution of the impulsive epidemic system and prove that the infection-free periodic solution is globally attractive if the vaccination rate is larger than theta*. Moreover, we show that the disease is uniformly persistent if the vaccination rate is less than theta*. The permanence of the model is investigated analytically. Our results indicate that a long latent period of the disease is sufficient condition for the extinction of the disease.