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一类具非线性发生率和时滞的SIQS传染病模型的全局稳定性 被引量：13

Global stability of a SIQS epidemic model with nonlinear incidence rate and time delay
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摘要 提出了一类具有非线性发生率和时滞的SIQS传染病模型,定义了基本再生数R0。利用特征根法、函数分析法、微分方程比较原理、迭代原理,对该模型的动力学特性进行分析。证明了当R0<1时,无病平衡点P0是全局渐近稳定的;当R0>1时,无病平衡点P0不稳定,地方病平衡点P*是全局渐近稳定的。 In this paper,a SIQS epidemic model with nonlinear incidence rate and time delay is proposed and analyzed. We have defined the basic reproductive number R0 . By using eigenvalue,function analysis,comparison principle and iterative methods,the dynamic characteristics of model is analyzed. It is proved that the disease free equilibrium point P0 is globally stable if R0 ﹤1,it is unstable if R0 ﹥1,and the endemic equilibrium point P＊is globally stable if R0 ﹥1.
作者 杨俊仙 徐丽
机构地区 安徽农业大学理学院
出处 《山东大学学报（理学版）》 CAS CSCD 北大核心 2014年第5期67-74,共8页 Journal of Shandong University(Natural Science)
基金 国家自然科学基金资助项目(11201002 70271062) 安徽农业大学数学学科资助项目(XKXWD2013020 XK2013029)
关键词 非线性发生率 时滞 平衡点 基本再生数 全局稳定性 nonlinear incidence rate time delay equilibrium point reproductive number global stability
分类号 O175.13 [理学—基础数学]
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参考文献18

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二级参考文献19

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共引文献13

同被引文献82

引证文献13

二级引证文献19

山东大学学报（理学版）
2014年 第5期

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