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Global stability for the SEIR model in epidemiology. (English) Zbl 0821.92022
Summary: The SEIR model with nonlinear incidence rates in epidemiology is studied. Global stability of the endemic equilibrium is proved using a general criterion for the orbital stability of periodic orbits associated with higher-dimensional nonlinear autonomous systems as well as the theory of competitive systems of differential equations.

MSC:
92D30 Epidemiology
37C75 Stability theory for smooth dynamical systems
37N99 Applications of dynamical systems
34C25 Periodic solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
37G99 Local and nonlocal bifurcation theory for dynamical systems
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