Global stability of a discrete multigroup SIR model with nonlinear incidence rate |
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| Authors: | Jinling Zhou Yu Yang Tonghua Zhang |
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| Affiliation: | 1. School of Science and Technology, Zhejiang International Studies University, Hangzhou, China;2. Department of Mathematics, Swinburne University of Technology, Melbourne, Victoria, Australia |
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| Abstract: | In this paper, by applying nonstandard finite difference scheme, we propose a discrete multigroup Susceptible‐Infective‐Removed (SIR) model with nonlinear incidence rate. Using Lyapunov functions, it is shown that the global dynamics of this model are completely determined by the basic reproduction number  . If  , then the disease‐free equilibrium is globally asymptotically stable; if  , then there exists a unique endemic equilibrium and it is globally asymptotically stable. Example and numerical simulations are presented to illustrate the results. Copyright © 2017 John Wiley & Sons, Ltd. |
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| Keywords: | multigroup model nonlinear incidence rate nonstandard finite difference globally stability Lyapunov function |
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. If 
, then the disease‐free equilibrium is globally asymptotically stable; if 
, then there exists a unique endemic equilibrium and it is globally asymptotically stable. Example and numerical simulations are presented to illustrate the results. Copyright © 2017 John Wiley & Sons, Ltd.