Extinction and permanence for a pulse vaccination delayed SEIRS epidemic model

Tailei Zhang and Zhidong Teng

Chaos, Solitons & Fractals, 2009, vol. 39, issue 5, 2411-2425

Abstract: A delayed SEIRS epidemic model with pulse vaccination and bilinear incidence rate is investigated. Using Krasnoselskii’s fixed-point theorem, we obtain the existence of disease-free periodic solution (DFPS for short) of the delayed impulsive epidemic system. Further, using the comparison method, we prove that under the condition R∗<1, the DFPS is globally attractive, and that R∗>1 implies that the disease is permanent. Theoretical results show that the disease will be extinct if the vaccination rate is larger than θ∗ and the disease is uniformly persistent if the vaccination rate is less than θ∗. Our results indicate that a long latent period of the disease or a large pulse vaccination rate will lead to eradication of the disease.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:39:y:2009:i:5:p:2411-2425

DOI: 10.1016/j.chaos.2007.07.012

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