一类具有饱和传染率的垂直传染的肺结核病动力学分析  

Dynamic Analysis of Vertical Infected Pulmonary Tuberculosis with Saturated Infection Rate

作　　者：陶龙 TAO Long(School of Common Courses,Wannan Medical College,Wuhu 241000,China)

机构地区：[1]皖南医学院公共基础学院,安徽芜湖241000

出　　处：《宿州学院学报》2021年第9期47-50,共4页Journal of Suzhou University

基　　金：皖南医学院质量工程项目(2018iyxm45);皖南医学院科学研究项目(WK202117)。

摘　　要：建立了一个具有垂直传染的肺结核传染病动力学模型。运用微分方程动力系统的相关内容,证明了模型平衡点的存在唯一性并计算得到了基本再生数R_(0)。通过构造恰当的Lyapunov函数,证明了当R_(0)>1时,满足初值条件的解全局收敛到地方病平衡点;当R_(0)<1时,满足初值条件的解全局收敛到无病平衡点;运用Matlab进行了数值模拟,验证了理论结果的正确性。It is to establish a dynamic model of vertical infected pulmonary tuberculosis.By using differential equations in dynamical systems,it proves the existence and uniqueness of equilibrium and calculates the basic reproduction number R_(0).By constructing the appropriate Lyapunov function,it proves that the solution satisfying the initial condition converges to the global endemic equilibrium point when R_(0)>1.Similarly,it also shows that the solutionsatisfying the initial condition converges to the free disease equilibrium when R_(0)<1.Finally,Matlab is used for numerical simulation to verify the theoretical results.

关 键 词：垂直传染 饱和传染率 全局收敛 数值模拟 

分 类 号：O175.15[理学—数学]