一类具有媒体影响的媒介传染病模型的分析

孙传成,邱志鹏,杨晓敏

系统科学与数学 ›› 2017, Vol. 37 ›› Issue (9) : 2028-2038.

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PDF(405 KB)
系统科学与数学 ›› 2017, Vol. 37 ›› Issue (9) : 2028-2038. DOI: 10.12341/jssms13245
论文

一类具有媒体影响的媒介传染病模型的分析

    孙传成,邱志鹏,杨晓敏
作者信息 +

The Analysis of a Vector-Borne Disease Model with Media Impact

    SUN Chuancheng, QIU Zhipeng, YANG Xiaomin
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文章历史 +

摘要

建立了一类媒体报道对媒介传染病传播影响的数学模型, 研究了该传染病模型的动力学性态. 通过求再生矩阵谱半径的方法得到基本再生数, 并给出了地方病平衡点的存在性和局部稳定性. 理论分析的结果表明, 系统可能存在Hopf分支. 进一步, 由全局Lyapunov函数的方法得到了无病平衡点和地方病平衡点全局稳定的充分条件.

Abstract

In this paper, a mathematical model is proposed to describe the transmission dynamics of vector-borne diseases with media impact. By using the method of next generation matrix the reproduction number is derived, which determines the existence of endemic equilibrium, and then the local stability of the endemic equilibrium is investigated. The theoretical results show that the system may undergo the Hopf bifurcation. Sufficient conditions for the global stability are further obtained by a global Lyapunov function.

关键词

时滞 /   / 无病平衡点 /   / Lyapunov函数 /   / 地方病平衡点 /   / 全局稳定性.

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孙传成 , 邱志鹏 , 杨晓敏. 一类具有媒体影响的媒介传染病模型的分析. 系统科学与数学, 2017, 37(9): 2028-2038. https://doi.org/10.12341/jssms13245
SUN Chuancheng , QIU Zhipeng , YANG Xiaomin. The Analysis of a Vector-Borne Disease Model with Media Impact. Journal of Systems Science and Mathematical Sciences, 2017, 37(9): 2028-2038 https://doi.org/10.12341/jssms13245
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