疾病在食饵中流行的捕食与被捕食模型的分析  

The Dynamic of the Eco-epidemiological Model with the Disease in the Prey

作　　者：康爱花[1] 薛亚奎[1] 

机构地区：[1]中北大学数学系,山西太原030051

出　　处：《数学的实践与认识》2007年第20期77-81,共5页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10471040);山西省青年科学基金(20041004);山西省教育厅科技研究开发项目(20061025)

摘　　要：分析并建立了疾病在食饵中传播的生态-传染病模型,同时考虑到两种群都受密度制约因素的影响,讨论了模型解的有界性和各平衡点的存在性,利用Routh-Hurwitz判据证明了各平衡点的局部渐进稳定性,通过构造Lyapunov函数分析了各平衡点的全局渐进稳定性,得到了疾病存在与否的充分性条件.We analyze and formulate the eco-epidemiologieal 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, and the sufficient conditions of locally asymptotically stable of the equilibria are obtained by the Routh-Hurwitz criterion. Furthermore, we analyze the global stability of the equilibria by using Lyapunov functions, and obtain the conditions of the disease extincting and the disease persistence.

关 键 词：生态-传染病模型 渐进稳定 全局稳定 

分 类 号：O193[理学—数学]