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Zbl 1021.92040
Zhang, Juan; Ma, Zhien
Global dynamics of an SEIR epidemic model with saturating contact rate. (English)
[J] Math. Biosci. 185, No.1, 15-32 (2003). ISSN 0025-5564

Summary: {\it J. A. P. Heesterbeek} and {\it J. A. P. Metz} [J. Math. Biol. 31, 529-539 (1993; Zbl 0770.92021)] derived an expression for the saturating contact rate of individual contacts in an epidemiological model. In this paper, the SEIR model with this saturating contact rate is studied. The basic reproduction number $R_0$ is proved to be a sharp threshold which completely determines the global dynamics and the outcome of the disease. If $R_0\leq 1$, the disease-free equilibrium is globally stable and the disease always dies out. If $R_0>1$, there exists a unique endemic equilibrium which is globally stable and the disease persists at an endemic equilibrium state if it initially exists. The contribution of the saturating contact rate to the basic reproduction number and the level of the endemic equilibrium are also analyzed.

MSC 2000:: *92D30 Epidemiology
34D23 Global stability
34D05 Asymptotic stability of ODE

Keywords: SEIR model; saturating contact rate; asymptotically autonomous system; competitive system; orbital asymptotical stability

Citations: Zbl 0770.92021

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