The effects of CTL immune response on HIV infection model with potent therapy, latently infected cells and cell-to-cell viral transmission

In this paper, we study the global properties of a human immunodeficiency virus (HIV) infection model with cytotoxic T lymphocytes (CTL) immune response. The model is a six-dimensional that describes the interaction of the HIV with two classes of target cells, CD4+ T cells and macrophages. The infection rate is given by saturation functional response. Two types of distributed time delays are incorporated into the model to describe the time needed for infection of target cell and virus replication. Using the method of Lyapunov functional, we have established that the global stability of the model is determined by two threshold numbers, the basic infection reproduction number R0 and the immune response activation number [Formula: see text]. We have proven that if R0 ≤ 1, then the uninfected steady state is globally asymptotically stable (GAS), if [Formula: see text], then the infected steady state without CTL immune response is GAS, and if [Formula: see text], then the infected steady state with CTL immune response is GAS.

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THE ADOMIAN DECOMPOSITION METHOD FOR SOLVING HIV INFECTION MODEL OF LATENTLY INFECTED CELLS

Matrix Science Mathematic ◽

10.26480/msmk.01.2019.05.08 ◽

2019 ◽

Vol 3 (1) ◽

pp. 05-08 ◽

Cited By ~ 1

Author(s):

Nigar Ali, ◽

Saeed Ahmad, ◽

Sartaj Aziz ◽

Gul Zaman

Keyword(s):

Hiv Infection ◽

Decomposition Method ◽

Adomian Decomposition Method ◽

Infection Model ◽

Adomian Decomposition ◽

Latently Infected ◽

Infected Cells ◽

Hiv Infection Model

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Stability and Hopf Bifurcation in an HIV-1 Infection Model with Latently Infected Cells and Delayed Immune Response

Discrete Dynamics in Nature and Society ◽

10.1155/2013/169427 ◽

2013 ◽

Vol 2013 ◽

pp. 1-12

Author(s):

Haibin Wang ◽

Rui Xu

Keyword(s):

Immune Response ◽

Infection Model ◽

Asymptotically Stable ◽

Basic Reproduction Ratio ◽

Globally Asymptotically Stable ◽

Reproduction Ratio ◽

Latently Infected ◽

Infected Cells ◽

Ctl Immune Response ◽

Hiv 1

An HIV-1 infection model with latently infected cells and delayed immune response is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria is established and the existence of Hopf bifurcations at the CTL-activated infection equilibrium is also studied. By means of suitable Lyapunov functionals and LaSalle’s invariance principle, it is proved that the infection-free equilibrium is globally asymptotically stable if the basic reproduction ratio for viral infectionR0≤1; if the basic reproduction ratio for viral infectionR0>1and the basic reproduction ratio for CTL immune responseR1≤1, the CTL-inactivated infection equilibrium is globally asymptotically stable. If the basic reproduction ratio for CTL immune responseR1>1, the global stability of the CTL-activated infection equilibrium is also derived when the time delayτ=0. Numerical simulations are carried out to illustrate the main results.

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