Download Global Dynamics of HIV Infection of CD4(+) T Cells and

Global Dynamics of HIV Infection of CD4(+) T Cells and Macrophages
Elaiw, AM [ 1,2 ]; Alsheri, AS [ 1,3 ]
DISCRETE DYNAMICS IN NATURE AND SOCIETY
Article Number: 264759, DOI: 10.1155/2013/264759, Published: 2013, Publisher
HINDAWI PUBLISHING CORPORATION, 410 PARK AVENUE, 15TH FLOOR, #287
PMB, NEW YORK, NY 10022 USA
ISSN: 1026-0226
Abstract
We study the global dynamics of an HIV infection model describing the interaction of the
HIV with CD4(+) T cells and macrophages. The incidence rate of virus infection and the
growth rate of the uninfected CD4(+) T cells and macrophages are given by general
functions. We have incorporated two types of distributed delays into the model to account
for the time delay between the time the uninfected cells are contacted by the virus particle
and the time for the emission of infectious (matures) virus particles. We have established
a set of conditions which are sufficient for the global stability of the steady states of the
model. Using Lyapunov functionals and LaSalle's invariant principle, we have proven that
if the basic reproduction number R-0 is less than or equal to unity, then the uninfected
steady state is globally asymptotically stable (GAS), and if the infected steady state
exists, then it is GAS.
Keywords
KeyWords Plus:DISTRIBUTED INTRACELLULAR DELAYS; VIRAL DYNAMICS;
DIFFERENTIAL EQUATIONS; MATHEMATICAL-ANALYSIS; LYAPUNOV
FUNCTIONALS; COMBINATION THERAPY; NONLINEAR INCIDENCE; IN-VIVO;
MODEL; STABILITY
Author Information
Reprint Address: Elaiw, AM E-mail Addresses:[email protected]
King Abdulaziz Univ, Fac Sci, Dept Math, POB 80203, Jeddah 21589, Saudi Arabia.
Organization-Enhanced Name(s)
King Abdulaziz University
Addresses:
[ 1 ] King Abdulaziz Univ, Fac Sci, Dept Math, Jeddah 21589, Saudi Arabia
Organization-Enhanced Name(s)
King Abdulaziz University
[ 2 ] Al Azhar Univ, Fac Sci, Dept Math, Assiut 71511, Egypt
Organization-Enhanced Name(s)
Al Azhar University
Assiut University
[ 3 ] King Khalid Univ, Sci & Literature Coll Namas, Dept Math, Abha 61431, Saudi Arabia