考虑治疗的离散HIV病毒模型的动力学性态（英文）  

Threshold Dynamics of Discrete HIV Virus Model with Therapy

作　　者：马霞 曹慧[2] MA Xia;CAO Hui(Department of Science,Taiyuan Institute of Technology,Taiyuan 030008,China;College of Science,Shaanxi University of Science and Technology,Xi'an 710021,China)

机构地区：[1]太原工业学院理学系,山西太原030008 [2]陕西科技大学理学院,陕西西安710021

出　　处：《应用数学》2020年第1期1-11,共11页Mathematica Applicata

基　　金：Supported by the National Natural Science Foundation of China(11301314);Program for the Reserved Discipline Leaders of Taiyuan Institute of Technology(2018008)

摘　　要：本文主要研究一类带有治疗的离散HIV模型的持续性和全局稳定性.通过定义基本再生数,我们得到当R0<1时,模型的非感染平衡点是全局渐近稳定的,病毒将会消失.当R0>1时,病毒将会持续存在.通过构造李雅普诺夫函数证明了当1<R0<N时,模型的感染平衡点是全局渐近稳定的.模型的阈值动力学性态和对应的连续模型是一致的.In the paper,we mainly investigate the permanence and the global stability of the discrete HIV model with therapy.By defining the basic reproduction number R0,we conclude the uninfected state P^0 is globally stable when R0<1,therefore the virus will be extinct.However,the virus will be persistent when R0>1.we also obtain the infected state P^* is globally stable when 1<R0<N by constructing Lyapunov function.The threshold dynamical behavior is in agreement with the continuous differential model.

关 键 词：离散HIV病毒模型 基本再生数 持续性 全局稳定性 李雅普诺夫函数 

分 类 号：O175[理学—数学]