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

Gao, Shujing; Teng, Zhidong; Nieto, Juan J.; Torres, Angela

doi:https://doi.org/10.1155/2007/64870

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Research Article | Open Access

Volume 2007 | Article ID 064870 | https://doi.org/10.1155/2007/64870

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

Shujing Gao,^1,2Zhidong Teng,²Juan J. Nieto,³and Angela Torres⁴

Academic Editor: Halima Bensmail

Received12 Nov 2006

Revised05 Apr 2007

Accepted25 May 2007

Published03 Oct 2007

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.

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Copyright © 2007 Shujing Gao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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