具有非溶解免疫抑制及免疫时滞的病毒动力学模型  

A Virus Dynamics Model with Nonlytic Inhibition and Immune Delay

作　　者：王颖 刘贤宁[1] WANG Ying;LIU Xian-ning(School of Mathematics and Statistic of Southwest University, Chongqing 400715, China)

机构地区：[1]西南大学数学与统计学院,重庆400715

出　　处：《西南师范大学学报（自然科学版）》2021年第3期101-110,共10页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11671327).

摘　　要：为了研究非溶解免疫活动在病毒感染中的影响,提出了包含非溶解效应机制的体液免疫反应的病毒动力学模型,同时也考虑了体液免疫时滞对平衡点稳定性的影响.通过构建Lyapunov函数以及应用LaSalle不变原理证明了:当R_(0)<1时,无病平衡点E_(0)是全局渐近稳定的;当R_(0)>1,τ=0时,正平衡点E^(*)是全局渐近稳定的.通过理论分析及数值模拟表明体液免疫时滞会改变正平衡点的稳定性,当免疫时滞超过某个临界值时,E^(*)变得不稳定并且产生了Hopf分支.最后,通过数值模拟表明非溶解体液免疫抑制机制在病毒感染中发挥着重要的作用.In this paper,to study the effect of nonlytic in the viral infection,we analyzed a virus dynamics model of the humoral immune response with nonlytic effect mechanism,at the same time,we also considered the effect of humoral immunity delay on the stability of the equilibrium point.By constructing Lyapunov functional and using the LaSalle's invariance principle,we proved that when R_(0)<1,the disease-free equilibrium E_(0)is globally asymptotically stable and when R_(0)>1,τ=0,the positive equilibrium point E^(*)is globally asymptotically stable.Through the theoretical analysis and numerical simulation show that the humoral immune delay can change the stability of the positive equilibrium point.When the immune delay exceeds a critical value,E^(*)becomes unstable and Hopf bifurcation occurs.Finally,through the numerical simulation shows that the nonlytic humoral immune suppression mechanisms play an important role in the viral infection.

关 键 词：体液免疫 时滞 稳定性 LYAPUNOV函数 HOPF分支 

分 类 号：O175[理学—数学]