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Journal of Biomedicine and Biotechnology
Volume 2007 (2007), Article ID 64870, 10 pages
http://dx.doi.org/10.1155/2007/64870
Research Article

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

1College of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, China
2College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China
3Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, Santiago de Campostela 15782, Spain
4Departamento de Psiquiatría, Radiología y Salud Pública, Facultad de Medicina, Universidad de Santiago de Compostela, Santiago de Campostela 15782, Spain

Received 12 November 2006; Revised 5 April 2007; Accepted 25 May 2007

Academic Editor: Halima Bensmail

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.

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.