Global properties of a class of HIV models

被引:168
作者
Elaiw, A. M. [1 ]
机构
[1] Al Azhar Univ, Fac Sci, Dept Math, Assiut Branch, Assiut, Egypt
关键词
Global stability; Direct Lyapunov method; HIV/AIDS; Controllability; MATHEMATICAL-ANALYSIS; PERIODIC-SOLUTION; FEEDBACK-CONTROL; DYNAMICS; INFECTION; STABILITY; CHEMOTHERAPY;
D O I
10.1016/j.nonrwa.2009.07.001
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this paper, we study the global properties of a class of human immunodeficiency virus (HIV) models. The basic model is a 5-dimensional nonlinear ODEs that describes the interaction of the HIV with two target cells, CD4(+) T cells and macrophages. An HIV model with exposed state and a model with nonlinear incidence rate are also analyzed. Lyapunov functions are constructed to establish the global asymptotic stability of the uninfected and infected steady states. We have proven that if the basic reproduction number R-0 is less than unity, then the uninfected steady state is globally asymptotically stable. If R-0 > 1 (or if the infected steady state exists), then the infected steady state is globally asymptotically stable. In a control system framework, we have shown that the HIV model incorporating the effect of Highly Active AntiRetroviral Therapy (HAART) is globally asymptotically controllable to the uninfected steady state. (C) 2009 Elsevier Ltd. All rights reserved.
引用
收藏
页码:2253 / 2263
页数:11
相关论文
共 29 条
[1]   HIV dynamics: Modeling, data analysis, and optimal treatment protocols [J].
Adams, BM ;
Banks, HT ;
Davidian, M ;
Kwon, HD ;
Tran, HT ;
Wynne, SN ;
Rosenberg, ES .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2005, 184 (01) :10-49
[2]  
Adams BM, 2004, MATH BIOSCI ENG, V1, P223
[3]   Feedback control of the chemotherapy of HIV [J].
Alvarez-Ramirez, J ;
Meraz, M ;
Velasco-Hernandez, JX .
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2000, 10 (09) :2207-2219
[4]   A state-dependent Riccati equation-based estimator approach for HIV feedback control [J].
Banks, HT ;
Kwon, HD ;
Toivanen, JA ;
Tran, HT .
OPTIMAL CONTROL APPLICATIONS & METHODS, 2006, 27 (02) :93-121
[5]   Feedback control of a biodynamical model of HIV-1 [J].
Brandt, ME ;
Chen, GR .
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, 2001, 48 (07) :754-759
[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]   Optimal HIV treatment by maximising immune response [J].
Culshaw, RV ;
Ruan, S ;
Spiteri, RJ .
JOURNAL OF MATHEMATICAL BIOLOGY, 2004, 48 (05) :545-562
[8]   Virus dynamics: A global analysis [J].
De Leenheer, P ;
Smith, HL .
SIAM JOURNAL ON APPLIED MATHEMATICS, 2003, 63 (04) :1313-1327
[9]   Global stability of a deterministic model for HIV infection in vivo [J].
Dehghan, Mehdi ;
Nasri, Mostafa ;
Razvan, Mohammad Reza .
CHAOS SOLITONS & FRACTALS, 2007, 34 (04) :1225-1238
[10]   Stabilization of HIV/aids model by receding horizon control [J].
Elaiw A.M. ;
Kiss K. ;
Caetano M.A.L. .
Journal of Applied Mathematics and Computing, 2005, 18 (1-2) :95-112