title: Analysis of an SIR epidemic model with pulse vaccination and distributed time delay.
abstract: Pulse vaccination, the repeated application of vaccine over a defined age range, is gaining prominence as an effective 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 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 enough. Moreover, we show that the disease is uniformly persistent if the vaccination rate is less than some critical value. The permanence of the model is investigated analytically. Our results indicate that a large pulse vaccination rate is sufficient for the eradication of the disease.
authors.affiliation: College of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China. gaosjmath@tom.com
authors.forename: Shujing
authors.initials: S
authors.lastname: Gao
authors.forename: Zhidong
authors.initials: Z
authors.lastname: Teng
authors.forename: Juan J
authors.initials: JJ
authors.lastname: Nieto
authors.forename: Angela
authors.initials: A
authors.lastname: Torres