Permanence of a delayed SIR epidemic model with general nonlinear incidence rate |
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| Authors: | Zhichao Jiang Wanbiao Ma |
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| Affiliation: | 1. Department of Applied Mathematics, School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, 100083, China;2. Fundamental Science Department, North China Institute of Astronautic Engineering, Langfang, Hebei, 065000, China |
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| Abstract: | In this paper, a SIR model with two delays and general nonlinear incidence rate is considered. The local and global asymptotical stabilities of the disease‐free equilibrium are given. The local asymptotical stability and the existence of Hopf bifurcations at the endemic equilibrium are also established by analyzing the distribution of the characteristic values. Furthermore, the sufficient conditions for the permanence of the system are given. Some numerical simulations to support the analytical conclusions are carried out. At last, some conclusions are given. Copyright © 2014 John Wiley & Sons, Ltd. |
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| Keywords: | SIR model Lyapunov functional stability switches Hopf bifurcation permanence |
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