Global stability of a delayed SEIRS epidemic model with saturation incidence rate. (English) Zbl 1204.34096

Summary: An SEIRS epidemic model with a saturation incidence rate and a time delay describing a latent period is investigated. By analyzing the corresponding characteristic equations, the local stability of an endemic equilibrium and a disease-free equilibrium is established. When the basic reproduction number is greater than unity, by means of an iteration technique, sufficient conditions are obtained for the global asymptotic stability of the endemic equilibrium. By comparison arguments, it is proved that if the basic reproduction number is less than unity, the disease-free equilibrium is globally asymptotically stable. Numerical simulations are carried out to illustrate the main theoretical results.


34K20 Stability theory of functional-differential equations
34D23 Global stability of solutions to ordinary differential equations
37N25 Dynamical systems in biology
92D30 Epidemiology
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