一类具有B-D非线性传染率的传染病模型的全局稳定性分析 |
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引用本文: | 马方强,冯孝周,马晓丽.一类具有B-D非线性传染率的传染病模型的全局稳定性分析[J].纺织高校基础科学学报,2016(3):312-318. |
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作者姓名: | 马方强 冯孝周 马晓丽 |
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作者单位: | 西安工业大学 理学院,陕西 西安,710032 |
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基金项目: | 陕西省自然科学基金资助项目(2013JC2-31),西安工业大学校长基金资助项目(XAGDJJ14023;1323),西安工业大学大学生创新创业训练计划项目(201410702008) |
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摘 要: | 对一类具有B-D非线性传染率的传染病模型的全局稳定性进行研究.利用分析计算技巧与李雅谱诺夫函数构造,得到阈值R及无病平衡点和地方病平衡点的存在条件,证明了无病平衡点和地方病平衡点的局部与全局稳定性.结果表明,具有B-D非线性传染率的传染病模型的平衡解局部稳定性与全局稳定性由含模型参数的阀值来决定.
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关 键 词: | 非线性传染率 阈值 平衡点 全局稳定性 |
Global dynamics of the SIQ epidemic model with the B-D nonlinear incidence rate |
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Abstract: | The global stability of the SIQ epidemics model with the B-D nonlinear incidence rate is researched.The threshold value R have been obtained and it shows that there is only a dis-easefree equilibrium point when R<1 ,and there is also an endemic equilibrium point if R>1 . With the help of Lyapunov function,some results about the global stability of disease free and endemic equilibrium points have been established,which are applicable for non-monotone,non-concave incidence rate. |
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Keywords: | nonlinear incidence rate threshold value equilibrium point globally stable |
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