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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 σ is identified which determines the outcome of the disease; if σ1, the infected fraction of the population disappears so the disease dies out, while if σ>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 σ ' and σ ¯ 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