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Extinction and permanence for a pulse vaccination delayed SEIRS epidemic model. (English) Zbl 1197.34090
Summary: 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 $\theta ^{*}$ and the disease is uniformly persistent if the vaccination rate is less than $\theta _{*}$. Our results indicate that a long latent period of the disease or a large pulse vaccination rate will lead to eradication of the disease. Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

MSC:
34D05Asymptotic stability of ODE
34K45Functional-differential equations with impulses
92D30Epidemiology
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References:
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