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Global stability of an SEIR epidemic model with vertical transmission and saturating contact rate. (English) Zbl 1197.34077
Summary: 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.

34C60 Qualitative investigation and simulation of ordinary differential equation models
92D30 Epidemiology
34D23 Global stability of solutions to ordinary differential equations
Full Text: DOI
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