Mathematical analysis of the global dynamics of a model for HIV infection of CD4+ T cells

2008 ◽  
Vol 11 (1) ◽  
Author(s):  
TO Oluyo ◽  
R O Ayeni ◽  
O O Ayndokan
Keyword(s):  
T Cells ◽  
Hiv Infection ◽  
Mathematical Analysis ◽  
Global Dynamics

scholarly journals Global Dynamics of an HIV Infection Model with Two Classes of Target Cells and Distributed Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
A. M. Elaiw
Keyword(s):  
T Cells ◽  
Steady State ◽  
Hiv Infection ◽  
Infection Model ◽  
Target Cells ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Hiv Infection Model ◽  
Nonlinear Delay

We investigate the global dynamics of an HIV infection model with two classes of target cells and multiple distributed intracellular delays. The model is a 5-dimensional nonlinear delay ODEs that describes the interaction of the HIV with two classes of target cells, CD4+T cells and macrophages. The incidence rate of infection is given by saturation functional response. The model has two types of distributed time delays describing time needed for infection of target cell and virus replication. This model can be seen as a generalization of several models given in the literature describing the interaction of the HIV with one class of target cells, CD4+T cells. Lyapunov functionals are constructed to establish the global asymptotic stability of the uninfected and infected steady states of the model. We have proven that if the basic reproduction numberR0is less than unity then the uninfected steady state is globally asymptotically stable, and ifR0>1then the infected steady state exists and it is globally asymptotically stable.

Analysis of global dynamics for HIV-infection of CD4+T cells and its treatment

2018 ◽  
Vol 46 (1) ◽  
Author(s):  
Urszula Foryś ◽  
Mariusz Bodzioch ◽  
Marcin Choiński
Keyword(s):  
T Cells ◽  
Hiv Infection ◽  
Cd4 T Cells ◽  
Global Dynamics

scholarly journals Global Dynamics of HIV Infection of CD4+T Cells and Macrophages

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
A. M. Elaiw ◽  
A. S. Alsheri
Keyword(s):  
T Cells ◽  
Steady State ◽  
Hiv Infection ◽  
Reproduction Number ◽  
Infection Model ◽  
Global Dynamics ◽  
Globally Asymptotically Stable ◽  
Virus Particles ◽  
Hiv Infection Model ◽  
Invariant Principle

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 numberR0is 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.

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