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Global behavior of an SEIRS epidemic model with time delays. (English) Zbl 1015.92033
Summary: This is a study of the dynamic behavior of an SEIRS epidemic model with time delays. It is shown that a disease-free equilibrium is globally stable if the reproduction number is not greater than one. When the reproduction number is greater than 1, it is proved that the disease is uniformly persistent in the population, and explicit formulae are obtained by which the eventual lower bound of the fraction of infectious individuals can be computed. Local stability of an endemic equilibrium is also discussed.

MSC:
92D30 Epidemiology
34K20 Stability theory of functional-differential equations
34K60 Qualitative investigation and simulation of models involving functional-differential equations
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