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Zbl 1143.92024
Gao, Shujing; Teng, Zhidong; Xie, Dehui
The effects of pulse vaccination on SEIR model with two time delays. (English)
[J] Appl. Math. Comput. 201, No. 1-2, 282-292 (2008). ISSN 0096-3003

Summary: Impulsive vaccination has been applied to control the spread and transmission of an infectious disease. An SEIR epidemic model with two time delays and pulse vaccination is formulated. The exact infection-free periodic solution of the impulsive epidemic system is obtained. Moreover, we show that, if the vaccination rate is larger than $\theta ^{*}$, the infectious population disappears so the disease dies out, while if the vaccination rate is less than $\theta _{*}$, the infectious population persists. Our results indicate that a large vaccination rate or a short period of pulsing or a long latent period of the disease is a sufficient condition for the eradication of the disease.

MSC 2000:: *92C60 Medical epidemiology
34K60 Applications of functional-differential equations
34K45 Equations with impulses
92D30 Epidemiology
34K13 Periodic solutions of functional differential equations

Keywords: SEIR epidemic model; pulse vaccination; time delay; global attractivity; permanence

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