带有胞胞感染和体液免疫及RTI的HIV-1病毒模型  

A HIV-1 Virus Model with Cell-to-cell Viral Transmissions,Discrete Delays,Humoral Immunity and RTI

作　　者：蒲月 刘贤宁[1] PU Yue;LIU Xian-ning(School of Mathematics and Statistics,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：《生物数学学报》2019年第2期181-194,共14页Journal of Biomathematics

基　　金：国家自然科学基金项目(11671327).

摘　　要：本文主要研究带有逆转录酶抑制剂(RTI)的HIV-1病毒模型,该模型同时具有病毒对细胞的感染和胞胞感染以及体液免疫反应和两个离散时滞的影响因素.研究了时滞对平衡点的影响.研究表明,细胞内部的时滞对感染模型的平衡点没有影响.但是,免疫时滞会改变免疫激发平衡点E2的稳定性以及导致Hopf分支的产生.当免疫时滞超过一个临界值时,Hopf分支就产生了.利用合适的李雅普诺夫函数和拉萨尔不变原理,建立了三个边界平衡点的全局稳定性.若R0<1,未感染平衡点E0是全局渐近稳定的;若R1<1<R0,免疫未激发平衡点E1是全局渐进稳定的;若R1>1,τ2=0,免疫激发平衡点E2是全局渐进稳定的.最后,通过数值模拟验证了理论的正确性.In this paper,we investigated the dynamical behavior of an HIV-1 virus model with both virus to cell and cell to cell transmissions and two discrete delay using reverse transcriptase inhibitors.We studied the effect of time delay on stability of the equilibria.The study shows the intracellular delay has no effect for the stability of the equilibria of the infection model.However,the immune delay can change the stability of the immune-activated equilibrium E2 and lead to the existence of Hopf bifurcation.Hopf bifurcation occurs when the immune delay passes a critical value.By using suitable Lyapunov functional and the LaSalle’s invariance principle,we also establish the global stabilities of the two boundary equilibria.If R0<1,the infection-free equilibrium E0 is globally asymptotically stable;if R1<1<R0,the immune-inactivated equilibrium E1 is globally asymptotically stable;if R1>1,τ2=0,the immune-activated equilibrium E2 is globally asymptotically stable.In the end,we check our theorems with numerical simulation.

关 键 词：胞胞感染 病毒感染 体液免疫 时滞 HOPF分支 

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