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Global stability of an SIR epidemic model with time delays. (English) Zbl 0811.92019
Summary: An SIR disease transmission model is formulated under the assumption that the force of infection at the present time depends on the number of infectives at the past. It is shown that a disease free equilibrium point is globally stable if no endemic equilibrium point exists. Further the endemic point (if it exists) is globally stable with respect to the whole state space except the neighborhood of the disease free state.

MSC:
92D30 Epidemiology
34D05 Asymptotic properties of solutions to ordinary differential equations
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