Global stability of an SEIR epidemic model with vertical transmission and saturating contact rate.

*(English)*Zbl 1197.34077Summary: The SEIR epidemic model with vertical transmission and the saturating contact rate is studied. It is proved that the global dynamics are completely determined by the basic reproduction number \(R_{0}(p, q)\), where \(p\) and \(q\) are fractions of infected newborns from the exposed and infectious classes, respectively. If \(R_{0}(p, q)\leq 1\), the disease-free equilibrium is globally asymptotically stable and the disease always dies out. If \(R_{0}(p, q) > 1\), a unique endemic equilibrium exists and is globally stable in the interior of the feasible region, and the disease persists at the endemic equilibrium state if it initially exists.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.

##### MSC:

34C60 | Qualitative investigation and simulation of ordinary differential equation models |

92D30 | Epidemiology |

34D23 | Global stability of solutions to ordinary differential equations |

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\textit{X.-Z. Li} and \textit{L.-L. Zhou}, Chaos Solitons Fractals 40, No. 2, 874--884 (2009; Zbl 1197.34077)

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