Global Stability of HIV-1 Infection Model with Two Time Delays

被引:3
作者
Miao, Hui [1 ]
Abdurahman, Xamxinur [1 ]
Muhammadhaji, Ahmadjan [1 ]
机构
[1] Xinjiang Univ, Coll Math & Syst Sci, Xinjiang 830046, Urumqi, Peoples R China
基金
中国国家自然科学基金;
关键词
IMMUNE-RESPONSE; INTRACELLULAR DELAY; MATHEMATICAL-ANALYSIS; VIRAL MODEL; DYNAMICS; INCLUDES;
D O I
10.1155/2013/163484
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We investigate global dynamics for a system of delay differential equations which describes a virus-immune interaction in vivo. The model has two time delays describing time needed for infection of cell and CTLs generation. Our model admits three possible equilibria: infection-free equilibrium, CTL-absent infection equilibrium, and CTL-present infection equilibrium. The effect of time delay on stability of the equilibria of the CTL immune response model has been studied.
引用
收藏
页数:12
相关论文
共 20 条
[1]   Geometric stability switch criteria in delay differential systems with delay dependent parameters [J].
Beretta, E ;
Kuang, Y .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2002, 33 (05) :1144-1165
[2]   Periodic solutions and chaos in a non-linear model for the delayed cellular immune response [J].
Canabarro, AA ;
Gléria, IM ;
Lyra, ML .
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2004, 342 (1-2) :234-241
[3]   A delay-differential equation model of HIV infection of CD4+ T-cells [J].
Culshaw, RV ;
Ruan, SG .
MATHEMATICAL BIOSCIENCES, 2000, 165 (01) :27-39
[4]   A mathematical model of cell-to-cell spread of HIV-1 that includes a time delay [J].
Culshaw, RV ;
Ruan, SG ;
Webb, G .
JOURNAL OF MATHEMATICAL BIOLOGY, 2003, 46 (05) :425-444
[5]  
Hale J., 1997, THEORY FUNCTIONAL DI
[6]  
Hale J., 1993, INTRO FUNCTIONAL DIF, DOI [10.1007/978-1-4612-4342-7, DOI 10.1007/978-1-4612-4342-7]
[7]  
Janeway AC TP., 2005, Immunobiology: The immune system in health and disase
[8]  
Kuang Y., 1993, Delay Differential Equations with Applications in Population Dynamics
[9]   Global Dynamics of an In-host Viral Model with Intracellular Delay [J].
Li, Michael Y. ;
Shu, Hongying .
BULLETIN OF MATHEMATICAL BIOLOGY, 2010, 72 (06) :1492-1505
[10]   Mathematical analysis of delay differential equation models of HIV-1 infection [J].
Nelson, PW ;
Perelson, AS .
MATHEMATICAL BIOSCIENCES, 2002, 179 (01) :73-94