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Global stability for a viral infection model with saturated incidence rate. (English) Zbl 1406.92607

Summary: A viral infection model with saturated incidence rate and viral infection with delay is derived and analyzed; the incidence rate is assumed to be a specific nonlinear form \(\beta x v /(1 + \alpha v)\). The existence and uniqueness of equilibrium are proved. The basic reproductive number \(R_0\) is given. The model is divided into two cases: with or without delay. In each case, by constructing Lyapunov functionals, necessary and sufficient conditions are given to ensure the global stability of the models.

MSC:

92D30 Epidemiology
34D23 Global stability of solutions to ordinary differential equations
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