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The effects of pulse vaccination on SEIR model with two time delays. (English) Zbl 1143.92024
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:
 92C60 Medical epidemiology 34K60 Qualitative investigation and simulation of models 34K45 Functional-differential equations with impulses 92D30 Epidemiology 34K13 Periodic solutions of functional differential equations