Stability preserving NSFD scheme for a multi‐group SVIR epidemic model |
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| Authors: | Yan Geng Jinhu Xu |
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| Institution: | 1. School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China;2. School of Science, Xi'an University of Technology, Xi'an, China |
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| Abstract: | A discrete multi‐group SVIR epidemic model with general nonlinear incidence rate and vaccination is investigated by utilizing Mickens' nonstandard finite difference scheme to a corresponding continuous model. Mathematical analysis shows that the global asymptotic stability of the equilibria is fully determined by the basic reproduction number  by constructing Lyapunov functions. The results imply that the discretization scheme can efficiently preserves the global asymptotic stability of the equilibria for corresponding continuous model, and numerical simulations are carried out to illustrate the theoretical results. Copyright © 2017 John Wiley & Sons, Ltd. |
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| Keywords: | multi‐group NSFD scheme general nonlinear incidence Lyapunov functions global asymptotic stability subclass 34D23 31C20 39A30 |
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by constructing Lyapunov functions. The results imply that the discretization scheme can efficiently preserves the global asymptotic stability of the equilibria for corresponding continuous model, and numerical simulations are carried out to illustrate the theoretical results. Copyright © 2017 John Wiley & Sons, Ltd.