| 一类含多时滞和扩散项的非标准离散模型 |
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| 引用本文： | 廖书,方章英,杨炜明. 一类含多时滞和扩散项的非标准离散模型[J]. 工程数学学报, 2022, 39(1): 79-92. DOI: 10.3969/j.issn.1005-3085.2022.01.006 |
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| 作者姓名： | 廖书 方章英 杨炜明 |
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| 作者单位： | 重庆工商大学数学与统计学院，重庆 400067 |
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| 基金项目： | 重庆市基础研究与前沿探索项目;经济社会应用统计重庆市重点实验室开放课题;重庆市教委科学技术研究项目 |
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| 摘 要： | 建立了一类以媒体效应作为主要预防传染病传播手段、并且含有多时滞和扩散项的传染病连续模型，并证明了该连续模型平衡点的全局稳定性。其次，利用非标准有限差分方法对该连续模型进行离散，离散后的模型具有和原连续模型一致的动力学性质。通过构造适当的李雅普诺夫函数，证明离散模型的平衡点在一定条件下也都是全局渐近稳定的。最后，数值模拟验证了理论结果。
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| 关 键 词： | 媒体效应 反应扩散 时滞 非标准有限差分 全局稳定 |
A Nonstandard Numerical Methods for a Mathematical Model for Cholera with Multiply Delays and Dispersal |
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| LIAO Shu,FANG Zhangying,YANG Weiming. A Nonstandard Numerical Methods for a Mathematical Model for Cholera with Multiply Delays and Dispersal[J]. Chinese Journal of Engineering Mathematics, 2022, 39(1): 79-92. DOI: 10.3969/j.issn.1005-3085.2022.01.006 |
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| Authors: | LIAO Shu FANG Zhangying YANG Weiming |
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| Affiliation: | School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067 |
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| Abstract: | A spatial and delayed epidemic model with media coverage is studied, and the global asymptotically stability of the equilibria is proved. Furthermore, a discreted edition of this model is established by applying a nonstandard finite difference scheme which has the same dynamics as the original system. Moveover, it is shown that the global stability of the disease-free equilibrium, and the globally asymptotically stability of the endemic equilibrium is studied by constructing a suitable Lyapunov function. Finally, the NSFD scheme can be well simulated to support the theoretical results. |
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| Keywords: | media coverage reaction diffusion delay nonstandard finite difference scheme global stability |
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