Global stability for the SEIR model in epidemiology.

*(English)*Zbl 0821.92022Summary: 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 |

##### Keywords:

omega limit sets; global stability; SEIR model; nonlinear incidence rates; endemic equilibrium; orbital stability; periodic orbits; higher- dimensional nonlinear autonomous systems; competitive systems
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\textit{M. Y. Li} and \textit{J. S. Muldowney}, Math. Biosci. 125, No. 2, 155--164 (1995; Zbl 0821.92022)

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