具有功能性反应且捕食者有病的生态-流行病模型  

Eco-epidemiological model with epidemic and response function in the predator

作　　者：郭中凯[1] 李文龙[2] 程雷虎[1] 李自珍[1,3] 

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

出　　处：《兰州大学学报（自然科学版）》2009年第3期117-121,共5页Journal of Lanzhou University(Natural Sciences)

基　　金：国家自然科学基金项目(30700100);教育部博士点青年基金项目(2007);甘肃省"十一五"科技支撑重点项目

摘　　要：建立并研究了一个捕食者具有传染病的生态-流行病(SI)模型,考虑了捕食者具有HollingⅡ功能性反应及食饵具有Logistic增长,且染病的捕食者会因病死亡,以及只有健康的捕食者才具有捕食能力,但这种疾病一旦染上就不再康复。应用特征方程的方法以及构造Liapunov函数的知识,得到了平衡点局部渐近稳定的充分条件,进一步分析了平衡点的全局稳定性,得到了边界平衡点全局稳定的充分条件。A predator-prey （SI） model of predator with epidemic was formulated and analyzed and predator with Holling Ⅱ response function and prey with logistic growth were considered. It was found that the infectious predator would die of diseases and only the healthy predator had predation capacity, but once infected with the disease, the predator would not be able to recover. By using characteristic equation and Liapunov function, we obtained the sufficient condition of locally asymptotical stability of the equilibria. Furthermore, we analyzed the global stability of the equilibria, and obtained the sufficient condition of global stability of the boundary equilibria.

关 键 词：捕食者-食饵系统 功能性反应 生态-流行病模型 渐近稳定 传染病 

分 类 号：O175.13[理学—数学] Q141[理学—基础数学]