2,779 research outputs found

    Global dynamics of cell mediated immunity in viral infection models with distributed delays

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    In this paper, we investigate global dynamics for a system of delay differential equations which describes a virus-immune interaction in \textit{vivo}. The model has two distributed time delays describing time needed for infection of cell and virus replication. Our model admits three possible equilibria, an uninfected equilibrium and infected equilibrium with or without immune response depending on the basic reproduction number for viral infection R0R_{0} and for CTL response R1R_{1} such that R1<R0R_{1}<R_{0}. It is shown that there always exists one equilibrium which is globally asymptotically stable by employing the method of Lyapunov functional. More specifically, the uninfected equilibrium is globally asymptotically stable if R0≤1R_{0}\leq1, an infected equilibrium without immune response is globally asymptotically stable if R1≤1<R0R_{1}\leq1<R_{0} and an infected equilibrium with immune response is globally asymptotically stable if R1>1R_{1}>1. The immune activation has a positive role in the reduction of the infection cells and the increasing of the uninfected cells if R1>1R_{1}>1.Comment: 16 pages, accepted by Journal of Mathematical Analysis and Application

    HIV-infected sex workers with beneficial HLA-variants are potential hubs for selection of HIV-1 recombinants that may affect disease progression

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    Cytotoxic T lymphocyte (CTL) responses against the HIV Gag protein are associated with lowering viremia; however, immune control is undermined by viral escape mutations. The rapid viral mutation rate is a key factor, but recombination may also contribute. We hypothesized that CTL responses drive the outgrowth of unique intra-patient HIV-recombinants (URFs) and examined gag sequences from a Kenyan sex worker cohort. We determined whether patients with HLA variants associated with effective CTL responses (beneficial HLA variants) were more likely to carry URFs and, if so, examined whether they progressed more rapidly than patients with beneficial HLA-variants who did not carry URFs. Women with beneficial HLA-variants (12/52) were more likely to carry URFs than those without beneficial HLA variants (3/61) (p &lt; 0.0055; odds ratio = 5.7). Beneficial HLA variants were primarily found in slow/standard progressors in the URF group, whereas they predominated in long-term non-progressors/survivors in the remaining cohort (p = 0.0377). The URFs may sometimes spread and become circulating recombinant forms (CRFs) of HIV and local CRF fragments were over-represented in the URF sequences (p &lt; 0.0001). Collectively, our results suggest that CTL-responses associated with beneficial HLA variants likely drive the outgrowth of URFs that might reduce the positive effect of these CTL responses on disease progression

    Viral Dynamics of Delayed CTL-inclusive HIV-1 Infection Model With Both Virus-to-cell and Cell-to-cell Transmissions

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    We consider a mathematical model that describes a viral infection of HIV-1 with both virus-tocell and cell-to-cell transmission, CTL response immune and four distributed delays, describing intracellular delays and immune response delay. One of the main features of the model is that it includes a constant production rate of CTLs export from thymus, and an immune response delay. We derive the basic reproduction number and show that if the basic reproduction number is less than one, then the infection free equilibrium is globally asymptotically stable; whereas, if the basic reproduction number is greater than one, then there exist a chronic infection equilibrium, which is globally asymptotically stable in absence of immune response delay. Furthermore, for the special case with only immune response delay, we determine some conditions for stability switches of the chronic infection equilibrium. Numerical simulations indicate that the intracellular delays and immune response delay can stabilize and/or destabilize the chronic infection equilibrium

    Global Analysis for an HIV Infection Model with CTL Immune Response and Infected Cells in Eclipse Phase

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    abstract: A modified mathematical model describing the human immunodeficiency virus (HIV) pathogenesis with cytotoxic T-lymphocytes (CTL) and infected cells in eclipse phase is presented and studied in this paper. The model under consideration also includes a saturated rate describing viral infection. First, the positivity and boundedness of solutions for nonnegative initial data are proved. Next, the global stability of the disease free steady state and the endemic steady states are established depending on the basic reproduction number R[subscript 0] and the CTL immune response reproduction number R[subscript CTL]. Moreover, numerical simulations are performed in order to show the numerical stability for each steady state and to support our theoretical findings. Our model based findings suggest that system immunity represented by CTL may control viral replication and reduce the infection.The final version of this article, as published in Applied Sciences, can be viewed online at: http://www.mdpi.com/2076-3417/7/8/86

    Stability of delayed virus infection model with a general incidence rate and adaptive immune response

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    We present the dynamical behaviors of a virus infection model with general infection rate, immune responses and two intracellular delays which describe the interactions of the HIV virus, target cells, CTL cells and antibodies within host. Three factors are incorporated in this model: (1) the intrinsic growth rate of uninfected cells, (2) a nonlinear incidence rate function considering both virus-tocell infection and cell-to-cell transmission, and (3) a nonlinear productivity and removal function. By the method of Lyapunov functionals and LaSalle’s invariance principle, we show that the global dynamics of the model is determined by the reproductive numbers for viral infection R0, for antibody immune response R1, for CTL immune response R2, for CTL immune competition R3 and for antibody immune competition R4. The numerical simulations are given to illustrate our theoretical results

    Modeling the dynamics of viral–host interaction during treatment of productively infected cells and free virus involving total immune response

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    Virus dynamics models are useful in interpreting and predicting the change in viral load over the time and the effect of treatment in emerging viral infections like HIV/AIDS, hepatitis B virus (HBV).We propose a mathematical model involving the role of total immune response (innate, CTL, and humoral) and treatment for productively infected cells and free virus to understand the dynamics of virus–host interactions. A threshold condition for the extinction or persistence of infection, i.e. basic reproductive number, in the presence of immune response (RI ) is established. We study the global stability of virus-free equilibrium and interior equilibrium using LaSalle’s principle and Lyapunov’s direct method. The global stability of virus-free equilibrium ensures the clearance of virus from the body, which is independent of initial status of subpopulations. Central manifold theory is used to study the behavior of equilibrium points at RI = 1, i.e. when the basic reproductive number in the presence of immune response is one. A special case, when the immune response (IR) is not present, has also been discussed. Analysis of special case suggests that the basic reproductive number in the absence of immune response R0 is greater than that of in the presence of immune response RI , i.e. R0&gt; RI . It indicates that infection may be eradicated if RI &nbsp;&lt; 1. Numerical simulations are performed to illustrate the analytical results using MatLab and Mathematica

    Hopf Bifurcation and Stability of Periodic Solutions for Delay Differential Model of HIV Infection of CD4 +

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    This paper deals with stability and Hopf bifurcation analyses of a mathematical model of HIV infection of CD4+ T-cells. The model is based on a system of delay differential equations with logistic growth term and antiretroviral treatment with a discrete time delay, which plays a main role in changing the stability of each steady state. By fixing the time delay as a bifurcation parameter, we get a limit cycle bifurcation about the infected steady state. We study the effect of the time delay on the stability of the endemically infected equilibrium. We derive explicit formulae to determine the stability and direction of the limit cycles by using center manifold theory and normal form method. Numerical simulations are presented to illustrate the results
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