Article ID Journal Published Year Pages File Type
1140600 Mathematics and Computers in Simulation 2014 14 Pages PDF
Abstract

The paper discusses the dynamical behaviors of a discrete-time SIR epidemic model. The local stability of the disease-free equilibrium and endemic equilibrium is obtained. It is shown that the model undergoes flip bifurcation and Hopf bifurcation by using center manifold theorem and bifurcation theory. Numerical simulations not only illustrate our results, but also exhibit the complex dynamical behaviors, such as the period-doubling bifurcation in period-2, 4, 8, quasi-periodic orbits and the chaotic sets. These results reveal far richer dynamical behaviors of the discrete epidemic model compared with the continuous epidemic models although the discrete epidemic model is easy.

Related Topics
Physical Sciences and Engineering Engineering Control and Systems Engineering
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