基于密度影响的生态-传染病模型  

The Dynamic of the Eco-epidemiological Model with Density-dependent

作　　者：康爱花[1] 

机构地区：[1]山西大同大学朔州师范分校数学系,山西朔州036000

出　　处：《淮阴师范学院学报（自然科学版）》2012年第4期342-345,共4页Journal of Huaiyin Teachers College;Natural Science Edition

摘　　要：分析并建立了疾病在被捕食者中传播的捕食与被捕食模型,且两种群都受密度制约因素的影响,讨论了系统的有界性和各平衡点存在的条件.首先计算各平衡点对应的雅哥比矩阵,利用Routh-Hurwitz判据分析各平衡点的局部渐进稳定性;其次通过构造Lyapunov函数,由LaSalle不变原理证明了正平衡点的全局渐进稳定性;再次利用比较定理证明了系统的持久性.In the paper,we analyzed and formulated the prey-predator model with the disease in the prey,considering density-dependent of two species.The boundness of solutions and the existence of the equilibria are studied.First,we calculate the Jacobian matrix,and obtain the sufficient conditions of locally asymptotically stable of the equilibra by the Routh-Hurwitz criterion.Second,we analyze the global stability of the equilibria by using Lyapunov functions and LaSalle invariance principle.At last,the permanence of the system is discussed in term of comparison theorem.

关 键 词：模型 捕食与被捕食 局部稳定 全局稳定 持久性 

分 类 号：O157.13[理学—数学]