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Global asymptotic stability of a delayed SEIRS epidemic model with saturation incidence. (English) Zbl 1142.34384
Summary: In this paper, the asymptotic behavior of solutions of an autonomous SEIRS epidemic model with the saturation incidence is studied. Using the method of Lyapunov-LaSalle invariance principle, we obtain the disease-free equilibrium is globally stable if the basic reproduction number is not greater than one. Moreover, we show that the disease is permanent if the basic reproduction number is greater than one. Furthermore, the sufficient conditions of locally and globally asymptotically stable convergence to an endemic equilibrium are obtained base on the permanence.

MSC:
34K20 Stability theory of functional-differential equations
92D30 Epidemiology
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