Bifurcation analysis of HIV infection model with antibody and cytotoxic T-lymphocyte immune responses and Beddington-DeAngelis functional response

2014 ◽  
Vol 38 (7) ◽  
pp. 1330-1341 ◽  
Author(s):  
P. Balasubramaniam ◽  
P. Tamilalagan ◽  
M. Prakash
Keyword(s):  
Immune Responses ◽  
Hiv Infection ◽  
Functional Response ◽  
T Lymphocyte ◽  
Bifurcation Analysis ◽  
Cytotoxic T Lymphocyte ◽  
Infection Model ◽  
Hiv Infection Model

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.

scholarly journals Dynamics of a Fractional Order HIV Infection Model with Specific Functional Response and Cure Rate

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Adnane Boukhouima ◽  
Khalid Hattaf ◽  
Noura Yousfi
Keyword(s):  
Hiv Infection ◽  
Functional Response ◽  
Fractional Order ◽  
Infection Model ◽  
Cure Rate ◽  
Order Model ◽  
Immunodeficiency Virus ◽  
Hiv Infection Model ◽  
Well Posed ◽  
Theoretical Results

We propose a fractional order model in this paper to describe the dynamics of human immunodeficiency virus (HIV) infection. In the model, the infection transmission process is modeled by a specific functional response. First, we show that the model is mathematically and biologically well posed. Second, the local and global stabilities of the equilibria are investigated. Finally, some numerical simulations are presented in order to illustrate our theoretical results.

scholarly journals Control of HIV-1 Pathogenesis in Viremic Nonprogressors Is Independent of Gag-Specific Cytotoxic T Lymphocyte Responses

2018 ◽  
Vol 92 (12) ◽  
Author(s):  
Maria Salgado ◽  
Albert Garcia-Minambres ◽  
Judith Dalmau ◽  
Esther Jiménez-Moyano ◽  
Pompeyo Viciana ◽  
...  
Keyword(s):  
T Cell ◽  
Immune Responses ◽  
Hiv Infection ◽  
T Lymphocyte ◽  
Cytotoxic T Lymphocyte ◽  
Viral Pathogenesis ◽  
Elite Controllers ◽  
Cell Counts ◽  
Hiv 1 ◽  
Ctl Responses

ABSTRACT Viremic nonprogressors (VNPs) constitute a very scarce group of untreated human immunodeficiency virus type 1 (HIV-1)-infected individuals who maintain stable CD4 + T cell counts despite high levels of HIV-1 replication. The specific factors associated with this atypical control of the HIV infection have been poorly described. Since specific T cell responses seem to be one of the main causes of HIV-1 control in elite controllers, we studied whether HIV-1 Gag-specific cytotoxic T lymphocyte (CTL) responses could also modulate disease control in VNPs. We characterized the immune responses from four VNPs compared to those of five standard progressors (SPs) during the first years of HIV-1 infection. We observed no differences in the breadth and frequency of Gag-specific cellular responses. Furthermore, we obtained 217 HIV-1 Gag clonal sequences in which the viral variability of Gag increased over 3 years of infection for synonymous and nonsynonymous mutations in both VNPs and SPs. VNPs evolution rates in gag were comparable to SPs. This observation is in line with a similar accumulation of CTL putative escape mutations in Gag epitopes targeted by CTL responses. Altogether, the absence of viral pathogenesis in VNP individuals seems to be independent of HIV-Gag-specific CTL responses. This novel information guides to the study of alternative mechanism of HIV-1 pathogenesis control. IMPORTANCE Control of HIV infection has been widely studied in elite controllers or long-term nonprogressor models. However, there is a less-known group of individuals, termed viremic nonprogressors (VNPs), who maintain stable CD4 + T cell counts despite high plasma viremia. The mechanisms involved in this remarkable control of HIV-1 pathogenesis clearly have implications for the development of new drugs and vaccines. We show here for the first time that VNPs have immune responses and HIV-gag evolution similar to those of standard progressors. Remarkably, we demonstrate that the mechanism of pathogenesis control in these individuals differs from some elite controllers that are reported to have improved immune control. This is noteworthy since it opens the door to new, as-yet-unknown mechanisms for HIV control. Our novel results advance the understanding of mechanisms involved in viremic nonprogression and suggest that there are alternative mechanisms to the adaptive immune responses for an effective control of viral pathogenesis.

Effects of delay in immunological response of HIV infection

2018 ◽  
Vol 11 (06) ◽  
pp. 1850076
Author(s):  
Saroj Kumar Sahani ◽  
Yashi
Keyword(s):  
Immune Response ◽  
Steady State ◽  
Immune Responses ◽  
Hiv Infection ◽  
Killer Cell ◽  
Immunological Response ◽  
Infection Model ◽  
Combination Drug ◽  
Hiv Infection Model

In this paper, a human immunodeficiency virus (HIV) infection model with both the types of immune responses, the antibody and the killer cell immune responses has been introduced. The model has been made more logical by including two delays in the activation of both the immune responses, along with the combination drug therapy. The inclusion of both the delayed immune responses provides a greater understanding of long-term dynamics of the disease. The dependence of the stability of the steady states of the model on the reproduction number [Formula: see text] has been explored through stability theory. Moreover, the global stability analysis of the infection-free steady state and the infected steady state has been proved with respect to [Formula: see text]. The bifurcation analysis of the infected steady state with respect to both delays has been performed. Numerical simulations have been carried out to justify the results proved. This model is capable of explaining the long-term dynamics of HIV infection to a greater extent than that of the existing model as it captures some basic parameters involved in the system such as immunological delay and immune response. Similarly, the model also explains the basic understanding of the disease dynamics as a result of activation of the immune response toward the virus.

scholarly journals Threshold dynamics and threshold analysis of HIV infection model with treatment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Zhimin Chen ◽  
Xiuxiang Liu ◽  
Liling Zeng
Keyword(s):  
Hiv Infection ◽  
Time Delays ◽  
Dynamical Behavior ◽  
Infection Model ◽  
Threshold Dynamics ◽  
Positive Equilibrium ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Immunodeficiency Virus ◽  
Hiv Infection Model

Abstract In this paper, a human immunodeficiency virus (HIV) infection model that includes a protease inhibitor (PI), two intracellular delays, and a general incidence function is derived from biologically natural assumptions. The global dynamical behavior of the model in terms of the basic reproduction number $\mathcal{R}_{0}$ R 0 is investigated by the methods of Lyapunov functional and limiting system. The infection-free equilibrium is globally asymptotically stable if $\mathcal{R}_{0}\leq 1$ R 0 ≤ 1 . If $\mathcal{R}_{0}>1$ R 0 > 1 , then the positive equilibrium is globally asymptotically stable. Finally, numerical simulations are performed to illustrate the main results and to analyze thre effects of time delays and the efficacy of the PI on $\mathcal{R}_{0}$ R 0 .

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