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Pulse vaccination on SEIR epidemic model with nonlinear incidence rate. (English) Zbl 1162.92323
Summary: We consider an SEIR epidemic model with two time delays and nonlinear incidence rate, and study the dynamical behavior of the model with pulse vaccination. By using the Floquet theorem and comparison theorem, we prove that the infection-free periodic solution is globally attractive when \(R^{*}<1\), and using a new modelling method, we obtain a sufficient condition for the permanence of the epidemic model with pulse vaccination when \(R_{*}>1\).

MSC:
92D30 Epidemiology
34K45 Functional-differential equations with impulses
34K13 Periodic solutions to functional-differential equations
34K20 Stability theory of functional-differential equations
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