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Global stability of an SEIR epidemic model with constant immigration. (English) Zbl 1142.34352
Summary: An SEIR epidemic model with the infectious force in the latent (exposed), infected and recovered period is studied. It is assumed that susceptible and exposed individuals have constant immigration rates. The model exhibits a unique endemic state if the fraction $p$ of infectious immigrants is positive. If the basic reproduction number ${R}_{0}$ is greater than 1, sufficient conditions for the global stability of the endemic equilibrium are obtained by the compound matrix theory.
##### MSC:
 34D23 Global stability of ODE 92D30 Epidemiology