Analysis of an SIR Epidemic Model with Pulse Vaccination and Distributed Time Delay

[摘要] Pulse vaccination, the repeated application ofvaccine over a defined age range, is gaining prominence asaneffective strategy for the elimination of infectious diseases. An SIR epidemic model with pulse vaccination and distributed time delay is proposed inthis 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 thata large pulsevaccination rateis sufficient for the eradication of the disease.

[学科分类] 基础医学