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.

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.

EFFECTS OF ECLIPSE PHASE AND DELAY ON THE DYNAMICS OF HIV INFECTION

2018 ◽  
Vol 26 (03) ◽  
pp. 421-454 ◽  
Author(s):  
SAROJ KUMAR SAHANI ◽  
YASHI
Keyword(s):  
Immune Response ◽  
Stability Analysis ◽  
Hiv Infection ◽  
Equilibrium Points ◽  
Latency Period ◽  
Immunological Response ◽  
Infection Model ◽  
Humoral Immune ◽  
Eclipse Phase ◽  
Hiv Infection Model

In this paper, an HIV infection model with eclipse phase, humoral immune response and immunological delay has been discussed. By studying the characteristic equations of the model, the local stability analysis of various equilibrium points has been explored. Treating the delay as the bifurcation parameter, it has been shown that the delay can destabilize the stability of the infected steady-state leading to Hopf bifurcation and periodic solutions. By using Lyapunov functionals and LaSalle’s invariance principle, the global stability analysis of the boundary equilibrium points has also been explored. It has also been shown numerically that the inclusion of the drug therapy in the model generates sporadic outbursts of virus called viral blips. In the end, numerical simulations have been employed to justify the analytical results proved in the paper. Biologically, the proposed model can explain the presence of viral blips in the system, during the introduction of HAART, as observed in the HIV-infected patient. These blips could mark the viral advancement in the system, thus resulting in complete immunological failure. One of the reasons for these viral blips can be the presence of delay in the activation of immunological response. But the development of drug-resistive virus could also be the reason for this sudden rise in viral loads. Moreover, the incorporation of the delay in the model generates oscillations and periodicity in the model, thus validating the long latency period seen in most HIV-infected patients. Also, a longer delay in the activation of immune response marks a viral advancement in the viral timeline resulting in viral blips, which signify the evolution of the virus.

Asymptotic Analysis of an Age-Structured HIV Infection Model with Logistic Target-Cell Growth and Two Infecting Routes

2020 ◽  
Vol 30 (04) ◽  
pp. 2050059
Author(s):  
Dongxue Yan ◽  
Xianlong Fu
Keyword(s):  
Steady State ◽  
Hiv Infection ◽  
Logistic Growth ◽  
Infection Model ◽  
Target Cells ◽  
Cell Infection ◽  
Numerical Examples ◽  
Distribution Of Eigenvalues ◽  
Age Structured ◽  
Hiv Infection Model

This paper deals with an age-structured HIV infection model with logistic growth for target cells and both virus-to-cell and cell-to-cell infection routes. Based on the existence of the infection-free and infection equilibria and some rigorous analyses for the considered model, we study the asymptotic stability of these equilibria via determining the distribution of eigenvalues. We also address the persistence of the solution semi-flow by proving the existence of a global attractor. Furthermore, Hopf bifurcation occurring at the positive steady state is exploited. At last, some numerical examples are provided to illustrate the obtained results.

scholarly journals Global Dynamics of an HIV Infection Model with Two Classes of Target Cells and Distributed Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
A. M. Elaiw
Keyword(s):  
T Cells ◽  
Steady State ◽  
Hiv Infection ◽  
Infection Model ◽  
Target Cells ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Hiv Infection Model ◽  
Nonlinear Delay

We investigate the global dynamics of an HIV infection model with two classes of target cells and multiple distributed intracellular delays. The model is a 5-dimensional nonlinear delay ODEs that describes the interaction of the HIV with two classes of target cells, CD4+T cells and macrophages. The incidence rate of infection is given by saturation functional response. The model has two types of distributed time delays describing time needed for infection of target cell and virus replication. This model can be seen as a generalization of several models given in the literature describing the interaction of the HIV with one class of target cells, CD4+T cells. Lyapunov functionals are constructed to establish the global asymptotic stability of the uninfected and infected steady states of the model. We have proven that if the basic reproduction numberR0is less than unity then the uninfected steady state is globally asymptotically stable, and ifR0>1then the infected steady state exists and it is globally asymptotically stable.

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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