Global dynamics of a delayed HTLV-I infection model with Beddington-DeAngelis incidence and immune impairment

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.

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Analysis of a viral infection model with immune impairment, intracellular delay and general non-linear incidence rate

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2014.08.009 ◽

2014 ◽

Vol 69 ◽

pp. 1-9 ◽

Cited By ~ 4

Author(s):

Eric Avila-Vales ◽

Noé Chan-Chí ◽

Gerardo García-Almeida

Keyword(s):

Viral Infection ◽

Incidence Rate ◽

Infection Model ◽

Intracellular Delay ◽

Non Linear ◽

Immune Impairment ◽

Viral Infection Model

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GLOBAL DYNAMICS OF A DELAYED HIV-1 INFECTION MODEL WITH ABSORPTION AND SATURATION INFECTION

International Journal of Biomathematics ◽

10.1142/s1793524512600121 ◽

2012 ◽

Vol 05 (03) ◽

pp. 1260012 ◽

Cited By ~ 9

Author(s):

RUI XU

Keyword(s):

Viral Entry ◽

Chronic Infection ◽

Infection Model ◽

Global Dynamics ◽

Asymptotically Stable ◽

Basic Reproduction Ratio ◽

Globally Asymptotically Stable ◽

Reproduction Ratio ◽

Virus Particles ◽

Hiv 1

In this paper, an HIV-1 infection model with absorption, saturation infection and an intracellular delay accounting for the time between viral entry into a target cell and the production of new virus particles is investigated. By analyzing the characteristic equations, the local stability of an infection-free equilibrium and a chronic-infection equilibrium of the model is established. By using suitable Lyapunov functionals and LaSalle's invariance principle, it is proved that if the basic reproduction ratio is less than unity, the infection-free equilibrium is globally asymptotically stable; and if the basic reproduction ratio is greater than unity, sufficient condition is derived for the global stability of the chronic-infection equilibrium.

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