Pulse vaccination, the repeated application ofvaccine over a defined age range, is gaining prominence as aneffective strategy for the elimination of infectious diseases. An SIR epidemic model with pulse vaccination and distributed time delay is proposed in this paper. Using the discrete dynamicalsystem determined by the stroboscopic map, we obtain the exact infection-free periodic solution of the impulsive epidemic systemand prove that the infection-free periodic solution is globally attractive if the vaccination rate is larger enough. Moreover, weshow that the disease is uniformly persistent if the vaccinationrate is less than some critical value. The permanence of the model isinvestigated analytically. Our results indicate that a large pulsevaccination rate is sufficient for the eradication of the disease.
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