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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.

##### MSC:
 92D30 Epidemiology 34D23 Global stability of ODE 37N25 Dynamical systems in biology
##### Keywords:
endemic equilibrium; latent period; compound matrices
Full Text:
##### References:
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