一类疾病垂直感染的生态-流行病模型的动力学研究  

Dynamics of eco-epidemiological model with the vertical infection

作　　者：赵丽萍[1] 李自珍[1,2] 王文婷[1] 马智慧[3] 

机构地区：[1]兰州大学数学与统计学院,兰州730000 [2]兰州大学干旱与草地农业生态教育部重点实验室,兰州730000 [3]兰州大学生命科学学院,兰州730000

出　　处：《兰州大学学报（自然科学版）》2009年第4期127-132,共6页Journal of Lanzhou University(Natural Sciences)

基　　金：国家自然科学基金项目(30700100);高等学校博士点青年基金项目(2007)

摘　　要：研究了捕食者-食饵模型中食饵染病且能垂直感染的具有密度制约因素的生态-流行病模型,分析了解的有界性,讨论了非负平衡点的存在性,得到了平衡点局部渐进稳定的充分条件.进一步分析了非负平衡点的全局稳定性,分别得到了捕食者绝灭、疾病消失和疾病成为地方病的充分条件.A density-dependent predator-prey model of prey with epidemic infected vertically was formulated in this paper. The boundness of solutions to the proposed system and the existence of equilibrium were studied; then the sufficient condition of equilibria existing, the sufficient conditions for locally asymptotically stability of the equilibrium were obtained. Furthermore, the sufficient conditions for the extinction of infective prey population, disease disappearance and epidemic persistence were obtained through analyzing the global stability of the equilibrium.

关 键 词：生态-流行病模型 垂直感染 平衡点 稳定性 

分 类 号：O175[理学—数学] Q141[理学—基础数学]