一类疾病在食饵中传播的生态-传染病模型分析  

Analysis of an Eco-epidemiological Model with the Disease in the Prey

作　　者：李毅红[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》2008年第11期139-144,共6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);山西省高校科技研究开发项目(20061025)

摘　　要：分析并建立疾病在食饵中传播的生态-传染病模型,且考虑易感食饵具有常数输入,捕食者种群以Logistic模型增长,讨论了系统解的有界性和各平衡点的存在性,以及局部渐近稳定性,通过构造适当的Lyapunov函数分析了各平衡点的全局渐近稳定性,并运用比较定理证明了系统的持久性.We formulate and analyze the eco-epidemiological model with the disease in the prey, considering the prey population with the constant recruitment （including newborns and migratory） and the growth rate of the predator population is governed by the Logistic model. And we study the boundedness of solutions and the existence of the equilibria, obtain the sufficient conditions of locally asymptotically stable of the equilibria by the Routh-Hurwitz criterion, analyze the global stability of the equilibria by constructing appropriate Lyapunov functions, that is the conditions of the disease existent or not. Furthermore, we study the permanence of the system by comparison theorem.

关 键 词：生态-传染病模型 局部渐近稳定 全局稳定 持久性 

分 类 号：O242.1[理学—计算数学] O175.13[理学—数学]