一类具有标准发生率的媒介传染病模型的稳定性  

Stability analysis of a kind of host-vector epidemic model with standard incidence rate

作　　者：肖亚男[1] 薛亚奎[1] 

机构地区：[1]中北大学理学院,山西太原030051

出　　处：《高师理科学刊》2015年第3期11-14,共4页Journal of Science of Teachers＇College and University

基　　金：国家自然科学基金资助项目(10901145)

摘　　要：建立并研究了一类具有标准发生率的媒介传染病模型,给出疾病流行与否的阈值并讨论了平衡点的存在性.证明了当基本再生数R0<1时,无病平衡点是局部渐近稳定的;当R0>1时,存在唯一的地方病平衡点且是局部渐近稳定的.并通过计算机数值模拟发现,无病平衡点和地方病平衡点都是全局渐近稳定的.The host-vector epidemic model with standard incidence rate was formulated and studied.The threshold is identified which determines the outcome of disease and the existence of the equilibrium was discussed.The model is shown that the disease free equilibrium is locally stability when R0〈1.For the basic reproductive number R0〉1,a unique endemic equilibrium exists and is locally asymptotically stable.The numerical simulations are carried out to find the disease free equilibrium and endemic equilibrium are globally asymptotically stable.

关 键 词：媒介传染 动力学系统 基本再生数 平衡点 稳定性 

分 类 号：O175.1[理学—数学]