Stability and Hopf bifurcation analysis of immune response delayed HIV type 1 infection model with two target cells

2014 ◽  
Vol 38 (17) ◽  
pp. 3653-3669 ◽  
Author(s):  
P. Balasubramaniam ◽  
M. Prakash ◽  
P. Tamilalagan
Keyword(s):  
Immune Response ◽  
Hopf Bifurcation ◽  
Bifurcation Analysis ◽  
Infection Model ◽  
Target Cells ◽  
Hiv Type 1

scholarly journals Bifurcation Analysis of an Age Structured HIV Infection Model with Both Virus-to-Cell and Cell-to-Cell Transmissions

2018 ◽  
Vol 28 (09) ◽  
pp. 1850109 ◽  
Author(s):  
Xiangming Zhang ◽  
Zhihua Liu
Keyword(s):  
T Cells ◽  
Hopf Bifurcation ◽  
Hiv Infection ◽  
Bifurcation Analysis ◽  
Dynamical Behavior ◽  
Infection Model ◽  
Positive Equilibrium ◽  
Semilinear Equations ◽  
Age Structured ◽  
Hiv Infection Model

We make a mathematical analysis of an age structured HIV infection model with both virus-to-cell and cell-to-cell transmissions to understand the dynamical behavior of HIV infection in vivo. In the model, we consider the proliferation of uninfected CD[Formula: see text] T cells by a logistic function and the infected CD[Formula: see text] T cells are assumed to have an infection-age structure. Our main results concern the Hopf bifurcation of the model by using the theory of integrated semigroup and the Hopf bifurcation theory for semilinear equations with nondense domain. Bifurcation analysis indicates that there exist some parameter values such that this HIV infection model has a nontrivial periodic solution which bifurcates from the positive equilibrium. The numerical simulations are also carried out.

Global Stability and Hopf Bifurcation in a Delayed Viral Infection Model with Cell-to-Cell Transmission and Humoral Immune Response

2019 ◽  
Vol 29 (12) ◽  
pp. 1950161 ◽  
Author(s):  
Jinhu Xu ◽  
Yan Geng ◽  
Suxia Zhang
Keyword(s):  
Immune Response ◽  
Hopf Bifurcation ◽  
Viral Infection ◽  
Humoral Immune Response ◽  
Dynamical Behavior ◽  
Infection Model ◽  
Humoral Immune ◽  
Cell Transmission ◽  
Viral Infection Model ◽  
Intracellular Delays

We have developed a class of viral infection model with cell-to-cell transmission and humoral immune response. The model addresses both immune and intracellular delays. We also constructed Lyapunov functionals to establish the global dynamical properties of the equilibria. Theoretical results indicate that considering only two intracellular delays did not affect the dynamical behavior of the model, but incorporating an immune delay greatly affects the dynamics, i.e. an immune delay may destabilize the immunity-activated equilibrium and lead to Hopf bifurcation, oscillations and stability switches. Our results imply that an immune delay dominates the intracellular delays in the model. We also investigated the direction of the Hopf bifurcation and the stability of the periodic solutions by applying normal form and center manifold theory, and investigated the existence of global Hopf bifurcation by regarding the immune delay as a bifurcation parameter. Numerical simulations are carried out to support the analytical conclusions.

Cell-Mediated Immune Response to Human Immunodeficiency Virus (HIV) Type 1 in Seronegative Homosexual Men with Recent Sexual Exposure to HIV-1

1992 ◽  
Vol 165 (6) ◽  
pp. 1012-1019 ◽  
Author(s):  
Mario Clerici ◽  
Janis V. Giorgi ◽  
Chen-Cheng Chou ◽  
Vaheideh K. Gudeman ◽  
Jerome A. Zack ◽  
...  
Keyword(s):  
Immune Response ◽  
Human Immunodeficiency Virus ◽  
Homosexual Men ◽  
Cell Mediated Immune Response ◽  
Immunodeficiency Virus ◽  
Hiv Type 1 ◽  
Hiv 1

scholarly journals Inactivation of Human Immunodeficiency Virus Type 1 by Porphyrins

2002 ◽  
Vol 46 (12) ◽  
pp. 3917-3925 ◽  
Author(s):  
Andrei N. Vzorov ◽  
Dabney W. Dixon ◽  
Jenna S. Trommel ◽  
Luigi G. Marzilli ◽  
Richard W. Compans
Keyword(s):  
Human Immunodeficiency Virus ◽  
Target Cells ◽  
Copper Chelate ◽  
Active Compounds ◽  
Sexually Transmitted ◽  
Immunodeficiency Virus ◽  
Hiv Type 1 ◽  
Env Protein ◽  
Cd4 Cell

ABSTRACT We have evaluated the anti-human immunodeficiency virus (HIV) activity of a series of natural and synthetic porphyrins to identify compounds that could potentially be used as microbicides to provide a defense against infection by sexually transmitted virus. For assays we used an epithelial HeLa-CD4 cell line with an integrated long terminal repeat-β-galactosidase gene. For structure-activity analysis, we divided the porphyrins tested into three classes: (i) natural porphyrins, (ii) metallo-tetraphenylporphyrin tetrasulfonate (metallo-TPPS4) derivatives, and (iii) sulfonated tetra-arylporphyrin derivatives. None of the natural porphyrins studied reduced infection by more than 80% at a concentration of 5 μg/ml in these assays. Some metal chelates of TPPS4 were more active, and a number of sulfonated tetra-aryl derivatives showed significantly higher activity. Some of the most active compounds were the sulfonated tetranaphthyl porphyrin (TNapPS), sulfonated tetra-anthracenyl porphyrin (TAnthPS), and sulfonated 2,6-difluoro-meso-tetraphenylporphine [TPP(2,6-F2)S] and its copper chelate [TPP(2,6-F2)S,Cu], which reduced infection by 99, 96, 94, and 96%, respectively. Our observations indicate that at least some of these compounds are virucidal, i.e., that they render the virus noninfectious. The active compounds were found to inhibit binding of the HIV type 1 gp120 to CD4 and also to completely inhibit the ability of Env proteins expressed from recombinant vectors to induce cell fusion with receptor-bearing target cells. These results support the conclusion that modified porphyrins exhibit substantial activity against HIV and that their target is the HIV Env protein.

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 EFFECT OF TIME DELAY ON SPATIAL PATTERNS IN A AIRAL INFECTION MODEL WITH DIFFUSION

2016 ◽  
Vol 21 (2) ◽  
pp. 143-158
Author(s):  
Jia Liu ◽  
Qunying Zhang ◽  
Canrong Tian
Keyword(s):  
Immune Response ◽  
Hopf Bifurcation ◽  
Time Delay ◽  
Viral Infection ◽  
Spatial Patterns ◽  
Infection Model ◽  
The Stability ◽  
Manifold Theory ◽  
Viral Infection Model ◽  
Theoretical Results

This paper is concerned with the dynamics of a viral infection model with diffusion under the assumption that the immune response is retarded. A time delay is incorporated into the model described the delayed immune response after viral infection. Based upon a stability analysis, we demonstrate that the appearance, or the absence, of spatial patterns is determined by the delay under some conditions. Moreover, the spatial patterns occurs as a consequence of Hopf bifurcation. By applying the normal form and the center manifold theory, the direction as well as the stability of the Hopf bifurcation is explored. In addition, a series of numerical simulations are performed to illustrate our theoretical results.

Plasma and Mucosal Fluid from HIV Type 1-Infected Patients But Not from HIV Type 1-Exposed Uninfected Subjects Prevent HIV Type 1-Exposed DC from Infecting Other Target Cells

2007 ◽  
Vol 23 (1) ◽  
pp. 101-106 ◽  
Author(s):  
Johan Söderlund ◽  
Taha Hirbod ◽  
Anna Smed-Sörensen ◽  
Ulrika Johansson ◽  
Joshua Kimani ◽  
...  
Keyword(s):  
Target Cells ◽  
Hiv Type 1 ◽  
Exposed Uninfected
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