具有年龄结构的结核病模型平衡解的稳定性  

The Stability of Equilibrium Solution for an Age-Dependent Tuberculosis Model

作　　者：余兰萍[1] 王佳伏 YU Lanping;WANG Jiafu(The Central South University of Forestry and Technology,Changsha 410004,China)

机构地区：[1]中南林业科技大学理学院,湖南长沙410004

出　　处：《应用数学》2018年第4期785-791,共7页Mathematica Applicata

基　　金：湖南省自然科学基金(2017JJ3525);湖南省教育厅科学研究项目(15C1413);中南林业科技大学人才引进项目(101-0662)

摘　　要：结核病是由结核杆菌感染引起的慢性传染病,也是中国发病、死亡人数最多的重大传染病之一,几乎一半的中国人是结核杆菌的带菌者.本文在结核病传播的数学模型的动力学系统基础上,不仅考虑了年龄对结核病的影响,还考虑了处于潜伏期的人群,采用建立数学模型的方法来分析结核病的传播机理,建立了一个具有年龄结构的结核病微分方程模型.利用微分方程理论,对模型的无病平衡解的全局渐近稳定性,结核病平衡解的局部稳定性,做了比较系统的分析研究.得到了具有年龄结构的结核病模型平衡解的存在性和稳定性的阀值,为结核病的控制与治疗提供了理论依据,并展示了方程的应用前景.Tuberculosis, a chronic infectious disease caused by Mycobacterium tuberculosis, is one of the major infectious diseases with the largest number of morbidity and mortality in our country. Almost half of the Chinese are carriers of Tubercle bacillus. In this paper, based on the dynamical system of tuberculosis spread model, the effect of age on TB and the crowd in the incubation period are considered by using method of mathematical model to analyze the propagation mechanism of tuberculosis, and an age-dependent tuberculosis model is established. By using the differential equation theory, the global asymptotic stability of the disease-free equilibrium and the local stability of the local equilibrium are analyzed systematically. The existence and stability threshold of the age-dependent tuberculosis model are obtained, which provides a theoretical basis for the control and treatment of tuberculosis, and shows the application prospect of the model.

关 键 词：结核病 微分方程模型 平衡解 稳定性 

分 类 号：O175.12[理学—数学]