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Global stability in some SEIR epidemic models. (English) Zbl 1022.92035

Castillo-Chavez, Carlos (ed.) et al., Mathematical approaches for emerging and reemerging infectious diseases: Models, methods, and theory. Proceedings of a workshop, integral part of the IMA program on mathematics in biology. New York, NY: Springer. IMA Vol. Math. Appl. 126, 295-311 (2002).
Summary: The dynamics of many epidemic models for infectious diseases that spread in a single host population demonstrate a threshold phenomenon. If the basic reproduction number \(R_0\) is below unity, the disease-free equilibrium \(P_0\) is globally stable in the feasible region and the disease always dies out. If \(R_0>1\), a unique endemic equilibrium \(P^*\) is globally asymptotically stable in the interior of the feasible region and the disease will persist at the endemic equilibrium if it is initially present. In this paper, this threshold phenomenon is established for two epidemic models of SEIR type using two recent approaches to the global-stability problem.
For the entire collection see [Zbl 0989.00064].

MSC:

92D30 Epidemiology
34D23 Global stability of solutions to ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
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