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Global stability of an SEIS epidemic model with recruitment and a varying total population size. (English) Zbl 1005.92030
Summary: This paper considers an SEIS epidemic model that incorporates constant recruitment, disease-caused death and disease latency. The incidence term is of the bilinear mass-action form. It is shown that the global dynamics is completely determined by the basic reproduction number \(R_0\). If \(R_0\geq 1\), the disease-free equilibrium is globally stable and the disease dies out. If \(R_0>1\), a unique endemic equilibrium is globally stable in the interior of the feasible region and the disease persists at the endemic equilibrium.

MSC:
92D30 Epidemiology
34D23 Global stability of solutions to ordinary differential equations
34D20 Stability of solutions to ordinary differential equations
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