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.


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