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

2017 ◽  
Vol 7 (8) ◽  
pp. 861 ◽  
Author(s):  
Karam Allali ◽  
Jaouad Danane ◽  
Yang Kuang
Keyword(s):  
Immune Response ◽  
Hiv Infection ◽  
Global Analysis ◽  
Infection Model ◽  
Infected Cells ◽  
Eclipse Phase ◽  
Hiv Infection Model ◽  
Ctl Immune Response

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.

Sign in / Sign up

Export Citation Format

Share Document