一类非连续治疗饱和传染率的传染病模型研究  

A Model Study of Infectious Diseases for Discontinuous Treatment with Saturated Infection Rates

作　　者：陶龙 赵妍[1] TAO Long;ZHAO Yan(School of Common Courses,Wannan Medical College,Wuhu Anhui 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：《上饶师范学院学报》2021年第6期18-25,共8页Journal of Shangrao Normal University

基　　金：皖南医学院科学研究项目(WK2018Z08,WK202117)。

摘　　要：研究了一类具有饱和传染率的传染病模型,探讨了非连续免疫治疗对其的影响;运用不连续微分方程的理论和微分包含的相关结论,定义了模型的Filippov解;证明了模型的地方病平衡点和无病平衡点的存在性和唯一性。建立Lyapunov函数证明了:当R_(0)>1时,满足初值条件的所有解都在有限时间内收敛于地方病平衡点;当R_(0)<1时,所有解收敛于无病平衡点。运用Matlab软件对整个理论推导过程进行了数值模拟,进一步验证了结论的正确性。This paper mainly researches the model of a class of infectious disease with saturated infection rates and explores the impact of discontinuous immunity treatment on them. By using the theory of discontinuous differential equations and related conclusions of differential inclusion, the paper defines the solutions of Filippov, and proves the existence and uniqueness of equilibrium. Based on the Lyapunov function, the paper shows that the solutions are convergent to the disease equilibrium in finite time when R_(0)>1. Similarly, it also can prove that solutions all arrive at the free disease equilibrium when R_(0)<1.The numerical simulation is carried out by Matlab, which verifies the correctness of the theoretical derivation.

关 键 词：传染病模型 非连续治疗 饱和传染率 有限时间全局收敛 

分 类 号：TU352.11[建筑科学—结构工程]