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Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period. (English) Zbl 1065.92046
Summary: We studied the global dynamics of a SEIR epidemic model in which the latent and immune state were infective. The basic reproductive rate, \(R_0\), is derived. If \(R_0 \leqslant 1\), 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 locally stable. Furthermore, we proved the global stability of the unique endemic equilibrium when \(\alpha_1 = \alpha_2\) = 0 and the disease persists at an endemic equilibrium state if it initially exists.

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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