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Global stability of an SEIR epidemic model with general nonlinear incidence rate. (Chinese. English summary) Zbl 1349.34185

Summary: An SEIR epidemic model with general nonlinear incidence rate \(g(S)h(I)\) is studied. By using the Liapunov function method, it is proved that the disease-free equilibrium \(P_0\) is globally asymptotically stable in \(G\) if \(R_0 \leq 1\) and the disease always dies out eventually. By the Poincaré-Bendixson theory, it is proved that the endemic equilibrium \(P^*\) is globally asymptotically stable in the interior of \(G\) if \(R_0 > 1\), and the disease spreads to the endemic equilibrium.

MSC:

34C60 Qualitative investigation and simulation of ordinary differential equation models
34D23 Global stability of solutions to ordinary differential equations
92D30 Epidemiology
34D05 Asymptotic properties of solutions to ordinary differential equations
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