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Global dynamics of a SEIR model with varying total population size. (English) Zbl 0974.92029
Summary: A SEIR model for the transmission of an infectious disease that spreads in a population through direct contact of the hosts is studied. The force of infection is of proportionate mixing type. A threshold $\sigma$ is identified which determines the outcome of the disease; if $\sigma \le 1$, the infected fraction of the population disappears so the disease dies out, while if $\sigma>1$, the infected fraction persists and a unique endemic equilibrium state is shown, under a mild restriction on the parameters, to be globally asymptotically stable in the interior of the feasible region. Two other threshold parameters $\sigma'$ and $\overline\sigma$ are also identified; they determine the dynamics of the population sizes in the cases when the disease dies out and when it is endemic, respectively.

34D23Global stability of ODE
37N25Dynamical systems in biology
Full Text: DOI
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