一类病菌与免疫系统作用模型的定性分析  

Qualitative Analysis of a Model with the Action Between Immune System and Bacteria

作　　者：赵君平[1] 于育民[2] 

机构地区：[1]西安建筑科技大学理学院,陕西西安710055 [2]南阳理工学院应用数学系,河南南阳473004

出　　处：《四川师范大学学报（自然科学版）》2012年第2期202-208,共7页Journal of Sichuan Normal University（Natural Science）

基　　金：陕西省自然科学基金(2009JM1002)资助项目

摘　　要：考虑病菌的一种信息交流机理,建立了一类时滞传染病模型.分析了模型平衡点的存在性、渐近稳定性及Hopf分歧的存在性及方向.最后,运用计算机数值模拟验证所得理论结果,为传染病的控制和预防提供了理论基础和数值依据.Taking into account an exchanging information mechanism of bacteria,an epidemic model with time delay is formulated.The existence and stability of positive equilibrium of the model are investigated,and the length of delay preserving the stability of the positive equilibrium is estimated.Moreover,the existence and direction of Hopf bifurcation are discussed.At last,numerical simulations are curried out to verify the theory results.The results obtained in this paper provide a theoretical and numerical basis to control and prevent the epidemic disease.

关 键 词：传染病模型 稳定性 HOPF分歧 时滞 免疫 

分 类 号：O175[理学—数学]