具有接种免疫和联合治疗的HIV传染病模型动力学性态研究  

Study on the Dynamics of a Model of HIV Infectious Disease with Vaccination and Combination Therapy

作　　者：兰美娜 李桂花[1] LAN Mei-na;LI Gui-hua(School of Science,North University of China,Taiyuan 030051,China)

机构地区：[1]中北大学理学院,山西太原030051

出　　处：《数学的实践与认识》2021年第9期270-275,共6页Mathematics in Practice and Theory

基　　金：山西省自然科学基金(201901D111179)。

摘　　要：建立了对HIV同时进行接种免疫和联合治疗的传染病模型并对其动力学性态进行了分析.当基本再生数R_(0)<1时,系统存在两个地方病平衡点且无病平衡点局部渐近稳定;当R_(0)>1时,系统存在唯一的地方病平衡点.进一步构造Lyapunov函数证明了无病平衡点的全局渐近稳定性.通过数值模拟发现系统会发生Hopf分支,当R_(0)<1时,系统存在一个极限环;当R_(0)>1时,系统存在两个极限环.最后对两种抑制剂关于HIV的治疗效果进行模拟,得出接种免疫和联合治疗共同作用对HIV的治疗效果更佳.In this paper,we establish an infectious disease model of vaccination and combined treatment of HIV and study its dynamic behavior.When the basic reproduction number R_(0) is less than 1,the disease-free equilibrium is locally asymptotically stable and the existence conditions of two endemic equilibria are given.Furthermore,by constructing Lyapunov function,we prove that the global asymptotic stability of the disease-free equilibrium.When R_(0) is more than 1,the system always has a unique endemic equilibrium.By numerical simulation we find that the system occurs Hopf bifurcation.If R_(0)<1,there is a limit cycle around a positive equilibrium of large number of infected population;when R_(0)>1,two limit cycles may be happened.By simulating the therapeutic effect of the two inhibitors for HIV,we obtain that the combined effect of vaccination and combined treatment is better.

关 键 词：接种免疫 联合治疗 基本再生数 稳定性 HOPF分支 

分 类 号：O175[理学—数学] R181.3[理学—基础数学]