具有饱和发生率和恢复率的HIV模型稳定性分析  

Stability Analysis of HIV Models with Saturation Occurrence and Recovery Rate

作　　者：张馨予 王丽媛 ZHANG Xinyu;WANG Liyuan(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《江苏海洋大学学报（自然科学版）》2022年第4期89-94,共6页Journal of Jiangsu Ocean University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11801243)。

摘　　要：建立了一类具有饱和发生率和饱和恢复率的HIV模型,构造了正定的Lyapunov函数,并利用Hurwitz判据和LaSalle不变集原理分析了无病平衡点和正平衡点的稳定性。可以得到,当基本再生数R_(0)<1时,无病平衡点是局部渐近稳定和全局渐近稳定的;当基本再生数R_(0)>1时,正平衡点是全局渐近稳定的。最后通过数值模拟验证了结果。A class of HIV models with saturation occurrence rate and saturation recovery rate were established. The Lyapunov function of positive definite was constructed, and the stability of disease-free and positive equilibrium points was analyzed by using Hurwitz criterion and LaSalle invariant set principle. It can be obtained that when the basic regeneration number R_(0)<1, the disease-free equilibrium point is locally asymptotically stable and globally asymptotically stable. When the basic regeneration number R_(0)>1, the positive equilibrium point is globally asymptotically stable. The results are also verified by numerical simulations.

关 键 词：饱和发生率 饱和恢复率 LYAPUNOV函数 稳定性 

分 类 号：O175.13[理学—数学]