右端不连续免疫对非线性出生率和医院容纳的影响  

Effects of Right-end Discontinuous Treatment on Nonlinear Birth Rate and Hospital Capacity Models

作　　者：李迅 陶龙 LI Xun;TAO Long(Nanjing Health School,Jiangsu Union Technical Institute,Nanjing 210038,China;School of Common Courses,Wannan Medical College,Wuhu 241000,China)

机构地区：[1]江苏联合职业技术学院南京卫生分院,江苏南京210038 [2]皖南医学院

出　　处：《通化师范学院学报》2022年第10期31-39,共9页Journal of Tonghua Normal University

基　　金：皖南医学院科学研究项目(WK202117)。

摘　　要：文章研究了一类右端不连续的微分方程动力系统传染病模型,同时考虑了模型对非线性出生率和医院容纳量的影响;利用不连续微分方程的理论解的性质,证明了无病平衡点和有病平衡点的存在唯一性.通过计算模型的基本再生数R和构造Lyapunov函数,证明当R>1时,满足初值条件的所有解曲线都在有限时间内全局渐近稳定于有病平衡点;当R<1时,满足初值条件的所有解曲线都在有限时间内全局渐近稳定于无病平衡点.在文章的最后,利用Matlab仿真实验验证了理论结果的正确性.In this paper,we study a class of right-hand discontinuous differential equation dynamic system infectious disease model,and consider the effects of nonlinear birth rate and hospital capacity.By using the properties of theoretical solutions of discontinuous differential equations,the existence and uniqueness of disease-free equilibrium points and diseased equilibrium points are proved.By calculating the basic reproduction number of the model and constructing the Lyapunov function,it is proved that all solution curves satisfying the initial value condition are globally asymptotically stable at the diseased equilibrium point in finite time.All solution curves satisfying the initial value condition are globally asymptotically stable at the disease-free equilibrium point in finite time.At the end of the article,matlab simulation is used to verify the correctness of the theoretical results.

关 键 词：非线性出生率 右端不连续 微分包含 LYAPUNOV函数 有限时间全局稳定 

分 类 号：O175[理学—数学]