Hopf Bifurcation Analysis for a Delayed SIRS Epidemic Model with a Nonlinear Incidence Rate |
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| Institution: | [1]Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, China; [2]School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, China |
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| Abstract: | This paper is concerned with a delayed SIRS epidemic model with a nonlinear incidence rate. The main results are given in terms of local stability and Hopf bifurcation. Sufficient conditions for the local stability of the positive equilibrium and existence of Hopf bifurcation are obtained by regarding the time delay as the bifurcation parameter. Further,the properties of Hopf bifurcation such as the direction and stability are investigated by using the normal form theory and center manifold argument. Finally,some numerical simulations are presented to verify the theoretical analysis. |
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| Keywords: | Hopf bifurcation delay SIRS model stability periodic solution |
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