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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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