Dynamic Behavior in a HIV Infection Model for the Delayed Immune Response

2011 ◽  
Author(s):  
Yongzhao Wang ◽  
Shuangde Zhang ◽  
Dongwei Huang ◽  
Hongjie Liu
Keyword(s):  
Immune Response ◽  
Hiv Infection ◽  
Dynamic Behavior ◽  
Infection Model ◽  
Hiv Infection Model

Global properties of a cell mediated immunity in HIV infection model with two classes of target cells and distributed delays

2014 ◽  
Vol 07 (05) ◽  
pp. 1450055 ◽  
Author(s):  
A. M. Elaiw ◽  
R. M. Abukwaik ◽  
E. O. Alzahrani
Keyword(s):  
Immune Response ◽  
Steady State ◽  
Hiv Infection ◽  
Infection Model ◽  
Target Cells ◽  
Cell Mediated Immunity ◽  
Globally Asymptotically Stable ◽  
Global Properties ◽  
Hiv Infection Model ◽  
Ctl Immune Response

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.

scholarly journals Analysis of an HIV infection model with treatments and delayed immune response

2016 ◽  
Vol 40 (4) ◽  
pp. 3081-3089 ◽  
Author(s):  
Dongwei Huang ◽  
Xiao Zhang ◽  
Yongfeng Guo ◽  
Hongli Wang
Keyword(s):  
Immune Response ◽  
Hiv Infection ◽  
Infection Model ◽  
Hiv Infection Model
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