一类含媒体效应和多扩散项的非标准离散模型的全局稳定性分析

廖书,杨炜明

系统科学与数学 ›› 2020, Vol. 40 ›› Issue (5) : 857-870.

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PDF(5289 KB)
系统科学与数学 ›› 2020, Vol. 40 ›› Issue (5) : 857-870. DOI: 10.12341/jssms13896
论文

一类含媒体效应和多扩散项的非标准离散模型的全局稳定性分析

    廖书,杨炜明
作者信息 +

The Global Stability of Nonstandard Finite Difference Scheme for a Diffusive Dynamics Model with Media Coverage

    LIAO Shu ,YANG Weiming
Author information +
文章历史 +

摘要

文章旨在建立一类含媒体效应和多扩散项的传染 病模型, 并利用非标准有限差分方法(NSFD)进行离散, 该离散模型具有和对应的原连续模型一致的动力学性质. 其次文章证明当基本再生数小于1时, 离散模型的无病平衡点是全局渐近稳定的; 当基本再生数大于1时, 通过构造适当的Lyapunov函数, 证明地方病平衡点也是全局渐近稳定的. 最后将离散模型研究结果应用于苏格兰小儿肺炎中, 验证媒体效应和扩散项对疫情控制起到的重要作用.

Abstract

In this paper, we aim to construct a spatial epidemic model with media coverage, the model can be discretized by applying a nonstandard finite difference scheme (NSFD). This NSFD scheme has the same dynamics as the original system. Moveover, we prove the global stability of the disease-free equilibrium when R0<1; when R0>1, it is proved that the endemic equilibrium point is globally asymptotically stable by constructing an appropriate Lyapunov function. Finally, the NSFD scheme can be well suited to numerically solve the Pneumococcus amongst children under two in Scotland.

关键词

媒体效应 / 偏微分方程 / 非标准有限差分 / 全局稳定 / 苏格兰小儿肺炎.

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廖书 , 杨炜明. 一类含媒体效应和多扩散项的非标准离散模型的全局稳定性分析. 系统科学与数学, 2020, 40(5): 857-870. https://doi.org/10.12341/jssms13896
LIAO Shu , YANG Weiming. The Global Stability of Nonstandard Finite Difference Scheme for a Diffusive Dynamics Model with Media Coverage. Journal of Systems Science and Mathematical Sciences, 2020, 40(5): 857-870 https://doi.org/10.12341/jssms13896
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