一类具有两个离散时滞的HTLV-1病毒模型动力学分析  

Dynamical analysis of a class of HTLV-1 virus model with two discrete time delays

作　　者：连颖颖[1] LIAN Yingying(School of Mathematics and Statistics, Anyang Normal University, Anyang 455000, China)

机构地区：[1]安阳师范学院数学与统计学院,河南安阳455000

出　　处：《暨南大学学报（自然科学与医学版）》2018年第6期547-552,共6页Journal of Jinan University(Natural Science & Medicine Edition)

基　　金：国家自然科学基金项目(U1604157);河南省高等学校重点科研项目(18A630001)

摘　　要：目的:研究一类具有细胞内时滞和CTL免疫时滞的HTLV-1病毒动力学行为.方法:定义依赖于时滞的基本再生数R0,建立一个李雅普诺夫函数研究未感染平衡点稳定性,利用特征方程根是否穿越虚轴判断感染平衡点的稳定性.结论:当R0<1时,未感染平衡点是全局稳定的;当R0> 1时,非感染平衡点存在,存在以下两类情形:(a)仅考虑细胞内时滞,非感染平衡点在一定条件下是局部渐近稳定的;(b)仅考虑免疫时滞,系统会产生Hopf分岔.结论:数值模拟验证模型结论有效,可为HTLV-1药物研发提供依据.Objective: To investigate the dynamic behavior of a class of HTLV-1 viral kinetic models with intracellular delays and CTL immune delays. Methods: The basic regenerative number R 0, which is dependent on the time delay, was defined. A Lyapunov function is established to study the stability of the uninfected equilibrium, and whether the root of the characteristic equation crosses the virtual axis to determine the stability of the infection equilibrium. Results: When R 0<1, uninfected equilibrium is globally stable; when R 0>1, the non-infective equilibrium exists, and two types of situations are investigated:(a) Only intracellular delays are considered, non-infection The equilibrium point is locally asymptotically stable under certain conditions;(b) Only the immune delay is considered and the system generates Hopf bifurcation. Conclusion: Numerical simulations verify the validity of the model conclusions, which provides an important basis for HTLV-1 drug development.

关 键 词：HTLV-1 时滞 渐近稳定性 HOPF分岔 

分 类 号：O193[理学—数学]