Global stability of a delayed HIV infection model with nonlinear incidence rate

被引：20

作者：

Yuan, Zhaohui ^{[1
]}

Ma, Zhongjun ^{[2
]}

Tang, Xianhua ^{[3
]}

机构：

[1] Hunan Univ, Coll Math & Econometr, Changsha 410082, Hunan, Peoples R China

[2] Guilin Univ Elect Technol, Sch Math & Comp Sci, Guilin 541004, Guangxi, Peoples R China

[3] Cent S Univ, Sch Math Sci & Comp Technol, Changsha 410083, Hunan, Peoples R China

来源：

NONLINEAR DYNAMICS | 2012年 / 68卷 / 1-2期

基金：

中国国家自然科学基金;

关键词：

Nonlinear incidence rate; Delay; Stability; HIV; CTL; DIFFERENTIAL-EQUATION MODELS; DYNAMICS IN-VIVO; INTRACELLULAR DELAY; IMMUNE-RESPONSE; VIRUS DYNAMICS; CLEARANCE RATE; DRUG-THERAPY; TIME;

D O I：

10.1007/s11071-011-0219-8

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

Under the assumption that the incidence rate of the infection and the removal rate of the infective by cytotoxic T lymphocytes are nonlinear, we study the global dynamics of a HIV infection model with the response of the immune system using characteristic equation, the Fluctuation lemma, and the direct Lyapunov method. The existence of a threshold parameter, i.e., the basic reproduction number or basic reproductive ratio is established and the global stability of the equilibria is discussed.

引用

页码：207 / 214

页数：8

共 29 条

[1]

[Anonymous], 1996, Not AMS, DOI DOI 10.1006/TPBI.1998.1382

[2]

[Anonymous], 1993, INTRO FUNCTIONAL DIF, DOI 10.1007/978-1-4612-4342-7

[3] Virus dynamics and drug therapy [J].

Bonhoeffer, S ;

May, RM ;

Shaw, GM ;

Nowak, MA .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1997, 94 (13) :6971-6976

[4] Human immunodeficiency virus drug therapy and virus load [J].

Bonhoeffer, S ;

Coffin, JM ;

Nowak, MA .

JOURNAL OF VIROLOGY, 1997, 71 (04) :3275-3278

[5] Analysis of an HIV/AIDS treatment model with a nonlinear incidence [J].

Cai, Liming ;

Wu, Jingang .

CHAOS SOLITONS & FRACTALS, 2009, 41 (01) :175-182

[6] HIV-1 infection and low steady state viral loads [J].

Callaway, DS ;

Perelson, AS .

BULLETIN OF MATHEMATICAL BIOLOGY, 2002, 64 (01) :29-64

[7] Estimating kinetic parameters from HIV primary infection data through the eyes of three different mathematical models [J].

Ciupe, MS ;

Bivort, BL ;

Bortz, DM ;

Nelson, PW .

MATHEMATICAL BIOSCIENCES, 2006, 200 (01) :1-27

[8] A delay-differential equation model of HIV infection of CD4+ T-cells [J].

Culshaw, RV ;

Ruan, SG .

MATHEMATICAL BIOSCIENCES, 2000, 165 (01) :27-39

[9] Global stability for a virus dynamics model with nonlinear incidence of infection and removal [J].

Georgescu, Paul ;

Hsieh, Ying-Hen .

SIAM JOURNAL ON APPLIED MATHEMATICS, 2006, 67 (02) :337-353

[10] Viral dynamics in vivo: Limitations on estimates of intracellular delay and virus decay [J].

Herz, AVM ;

Bonhoeffer, S ;

Anderson, RM ;

May, RM ;

Nowak, MA .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1996, 93 (14) :7247-7251

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