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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.
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##### 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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##### References:
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