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Stability of a delayed SIRS epidemic model with a nonlinear incidence rate. (English) Zbl 1198.34098

Summary: An SIRS epidemic model with a nonlinear incidence rate and a time delay is investigated. By analyzing the corresponding characteristic equations, the local stability of an endemic equilibrium and a disease-free equilibrium is discussed. By comparison arguments, it is proved that if the basic reproductive number R 0 <1, the disease-free equilibrium is globally asymptotically stable. If R 0 >1, by means of an iteration technique, sufficient conditions are derived for the global asymptotic stability of the endemic equilibrium.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.


MSC:
34D23Global stability of ODE
92D30Epidemiology
34K20Stability theory of functional-differential equations
34K60Qualitative investigation and simulation of models