| 一类具有垂直传播的SEIRS捕食传染病模型的全局分析 |
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| 引用本文： | 刘烁,马丽娜,李建全.一类具有垂直传播的SEIRS捕食传染病模型的全局分析[J].生物数学学报,2010(1):104-112. |
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| 作者姓名： | 刘烁 马丽娜 李建全 |
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| 作者单位： | 第四军医大学生物医学工程系;陕西师范大学数学与信息科学学院;空军工程大学理学院应用数学物理系; |
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| 基金项目： | 国家自然科学基金(10671209)项目资助; 陕西省自然科学基金(SJ08-ZT13)项目资助 |
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| 摘 要： | 通过假设捕食系统中疾病只在食饵种群中传播,被传染的易惑者经过一段潜伏期后才具有传染性,潜伏者与染病者均具有垂直传播能力,染病者恢复后对该病不具有终身免疫力,建立了一类具有垂直传播的SEIRS捕食传染病模型,运用极限系统理论,分两种情形讨论了系统平衡点的存在性及局部稳定性,利用Lyapunov函数和二次复合矩阵等方法,得到了平衡点全局渐近稳定的条件.
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| 关 键 词： | 垂直传播 潜伏期 捕食系统 传染病模型 平衡点 稳定性 |
Global Analysis of an SEIRS Eco-Epidemiological System with Vertical Transmission |
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| LIU Shuo MA Li-na LI Jian-quan.Global Analysis of an SEIRS Eco-Epidemiological System with Vertical Transmission[J].Journal of Biomathematics,2010(1):104-112. |
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| Authors: | LIU Shuo MA Li-na LI Jian-quan |
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| Institution: | LIU Shuo~1 MA Li-na~2 LI Jian-quan~3 (1 Faculty of Biomedical Engineering,The Fourth Military Medical University,Xi\'an Shanxi 710032 China,2 College of Mathematics , Information Science,Shaanxi Normal University,Xi\'an Shanxi 710062 China,3 Department of Applied Mathematics , Physics,Air Force Engineering University,Xi\'an Shanxi 710051 China) |
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| Abstract: | By assuming that disease only exists in the prey species,a susceptible individual infected by infective becomes infectious individual after a latent period,the infectives and the latent individuals have the ability of vertical transmission,and the infectives can be cured but the recovered have temporary immunity,an SEIRS predator-prey epidemic model with vertical transmission is investigated.Through the limiting system theory,the existence and the local stability of the equilibria for two cases are discusse... |
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| Keywords: | Vertical transmission Latent period Predator-prey system Epidemic model Equilibrium stability |
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