一类具有垂直传播的SIS捕食传染病模型的全局分析  

Global analysis of an SIS predator-prey epidemic model with vertical transmission

作　　者：马丽娜[1] 刘烁[2] 李建全[3] 赵清波[2] 

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710062 [2]第四军医大学生物医学工程学院数理教研室,陕西西安710032 [3]空军工程大学应用数学物理系,陕西西安710051

出　　处：《西北大学学报（自然科学版）》2011年第4期582-586,共5页Journal of Northwest University（Natural Science Edition）

基　　金：国家自然科学基金青年科学基金资助项目(61005046);陕西省自然科学基础研究计划基金资助项目(2010JQ8020)

摘　　要：目的研究具有垂直传播的传染病在捕食系统两种群之间的传播规律。方法假设捕食系统中疾病只在捕食者种群中存在,建立了一类具有垂直传播的SIS捕食传染病模型,分析了平衡点的存在条件,运用Hurwitz判据、极限系统理论和LaSalle不变性原理,分析了平衡点的稳定性。结果得到了平衡点局部渐近稳定的充要条件和无病平衡点全局渐近稳定的条件。结论表明可以通过减小传染率和增大恢复率来控制疾病的流行。Aim To investigate the pattern of the infectious disease with vertical transmission spread between the two species of the predator-prey system. Methods A predator-prey model with an SIS type of disease spreads in the predator species only is established and the existence conditions of the equilibria are studied. In addition, use of the Hurwitz criterion, the limit system theory and LaSalle＇s Invariance Principle, the stability of the equilibria is analysized. Results The sufficient and necessary conditions of the local stability of the equilibria and the conditions of the global stability of the disease-free equilibria are obtained. Conclusion The results imply that decreasing the incidence term and increasing the rate constant for recovery can contribnte to control the spread of the infectious disease.

关 键 词：垂直传播 传染病模型 平衡点 稳定性 

分 类 号：O175.1[理学—数学]