考虑CTL免疫饱和作用及自我增殖的HIV模型的性态分析  

Analysis of an HIV Model with Immune Saturation and Self-proliferation of CTL

作　　者：姜翠翠 姚苗然 田妍妮 JIANG Cui-cui;YAO Miao-ran;TIAN Yan-ni(Department of Mathematics,College of Basic Medicine,Army Medical University,Chongqing 400038,China;School of Mathematics and Statistics,Henan University of Science and Technology,Luoyang 471000,China;Three Gorges Mathematical Research Center,China Three Gorges University,Yichang 443000,China)

机构地区：[1]中国人民解放军陆军军医大学基础医学院数学教研室,重庆400038 [2]河南科技大学数学与统计学院,河南洛阳471000 [3]三峡大学三峡数学研究中心,湖北宜昌443000

出　　处：《数学的实践与认识》2023年第7期169-175,共7页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11901576)。

摘　　要：建立了具有CTL免疫饱和作用及自我增殖的病毒动力学模型,通过构造Lyapunov函数,得到了模型的全局稳定性.特别地,当CTL自我增殖率比较大时,如果基本再生数小于阈值,无感染但免疫激活平衡点始终存在且全局渐近稳定,这意味着在HIV感染中虽然病毒被清除,但免疫效应始终存在.而当CTL自我增殖率不足时,免疫饱和效应可能导致免疫功能受到抑制.进一步通过数值模拟发现,忽略免疫饱和作用会过高估计免疫效应.A virus dynamics model with CTL immune saturation and self-proliferation is established,and the global stabilities of the model are obtained by constructing the Lyapunov functions.In particular,when the per capita self-proliferation rate of CTL is sufficient,infection-free but immunity-activated equilibrium always exists and is globally asymptotically stable if the basic reproduction number of virus is less than a specific threshold,which means that although the virus is eliminated,the immune effect always exists.However,immune saturation effect may lead to suppression of immune function if the per capita self-proliferation rate of CTL is insufficient.Furthermore,numerical simulations show that ignoring the immune saturation effect overestimates the immune effect.

关 键 词：免疫饱和 CTL增殖 LYAPUNOV函数 全局稳定性 

分 类 号：R512.91[医药卫生—内科学] O175[医药卫生—临床医学]