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The effect of constant and pulse vaccination on an SIR epidemic model with infectious period. (English) Zbl 1221.37206

Summary: We investigate two delayed SIR models with vaccination and a generalized nonlinear incidence and obtain sufficient conditions for eradication and permanence of the disease, respectively. Our results indicate that a larger vaccination rate will lead to the eradication of a disease. Furthermore, theoretical results show that constant vaccination strategy can lead to disease eradication at relatively low values of vaccination than pulse vaccination strategy. In addition, numerical simulations indicate that pulse vaccination strategy or a longer infectious period will make a larger fraction of population infected by disease.

MSC:

37N25 Dynamical systems in biology
92D30 Epidemiology
34K20 Stability theory of functional-differential equations
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