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Stability analysis in a class of discrete SIRS epidemic models. (English) Zbl 1254.92082

Summary: The dynamical behavior of a class of discrete-time SIRS epidemic models is discussed. Conditions for the existence and local stability of the disease-free equilibrium and endemic equilibrium are obtained. The numerical simulations not only illustrate the validity of our results, but also exhibit more complex dynamical behavior, such as flip bifurcation, Hopf bifurcation and chaos phenomena. These results reveal far richer dynamical behaviors of the discrete epidemic model compared with continuous epidemic models.

MSC:

92D30 Epidemiology
39A30 Stability theory for difference equations
65C60 Computational problems in statistics (MSC2010)
39A60 Applications of difference equations
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