Global dynamics of a multistage SIR model with distributed delays and nonlinear incidence rate |
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| Authors: | Haitao Song Shengqiang Liu Weihua Jiang |
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| Institution: | 1. Complex Systems Research Center, Shanxi University, Taiyuan, China;2. The Academy of Fundamental and Interdisciplinary Science, Harbin Institute of Technology, Harbin, China;3. Department of Mathematics, Harbin Institute of Technology, Harbin, China |
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| Abstract: | In this paper, a multistage susceptible‐infectious‐recovered model with distributed delays and nonlinear incidence rate is investigated, which extends the model considered by Guo et al. H. Guo, M. Y. Li and Z. Shuai, Global dynamics of a general class of multistage models for infectious diseases, SIAM J. Appl. Math., 72 (2012), 261–279]. Under some appropriate and realistic conditions, the global dynamics is completely determined by the basic reproduction number R0. If R0≤1, then the infection‐free equilibrium is globally asymptotically stable and the disease dies out in all stages. If R0>1, then a unique endemic equilibrium exists, and it is globally asymptotically stable, and hence the disease persists in all stages. The results are proved by utilizing the theory of non‐negative matrices, Lyapunov functionals, and the graph‐theoretical approach. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | multistage SIR model distributed delay global stability Lyapunov functional epidemiology |
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