Global dynamics of delay-distributed HIV infection models with differential drug efficacy in cocirculating target cells

2015 ◽  
Vol 39 (1) ◽  
pp. 4-31 ◽  
Author(s):  
A. M. Elaiw ◽  
N. A. Almuallem
Keyword(s):  
Hiv Infection ◽  
Drug Efficacy ◽  
Target Cells ◽  
Global Dynamics ◽  
Infection Models

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.

GLOBAL ANALYSIS OF AN EXTENDED HIV DYNAMICS MODEL WITH GENERAL INCIDENCE RATE

2015 ◽  
Vol 23 (03) ◽  
pp. 401-421
Author(s):  
AHMED ELAIW ◽  
NADA. ALMUALLEM ◽  
XIA WANG
Keyword(s):  
Global Stability ◽  
Incidence Rate ◽  
Global Analysis ◽  
Drug Efficacy ◽  
Target Cells ◽  
Qualitative Behavior ◽  
Global Dynamics ◽  
Dynamics Model ◽  
Hiv Dynamics ◽  
Infected Cells

The objective of this work is to investigate the qualitative behavior of an Human Immunodeficiency Virus (HIV) dynamics model with two types of cocirculating target cells and under the effect of anti-viral drug therapy. The model takes into account both short-lived infected cells and long-lived chronically infected cells. In the two types of target cells, the drug efficacy is assumed to be different. The incidence rate of virus infection is given by general functional response. We have derived the basic reproduction number which determines the global dynamics of the model. We have established a set of conditions which are sufficient to investigate the global stability of the equilibria of the model. The global stability analysis of the model has been established using the Lyapunov method. Numerical simulations have been performed for the model with a specific form of the incidence rate function. We have shown that the numerical and theoretical results are consistent.

scholarly journals Viral Dynamics of Acute HIV-1 Infection

1999 ◽  
Vol 190 (6) ◽  
pp. 841-850 ◽  
Author(s):  
Susan J. Little ◽  
Angela R. McLean ◽  
Celsa A. Spina ◽  
Douglas D. Richman ◽  
Diane V. Havlir
Keyword(s):  
Antiretroviral Therapy ◽  
Hiv Infection ◽  
Doubling Time ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Target Cells ◽  
Viral Dynamics ◽  
Acute Hiv Infection ◽  
Acute Hiv ◽  
The Mean

Viral dynamics were intensively investigated in eight patients with acute HIV infection to define the earliest rates of change in plasma HIV RNA before and after the start of antiretroviral therapy. We report the first estimates of the basic reproductive number (R0), the number of cells infected by the progeny of an infected cell during its lifetime when target cells are not depleted. The mean initial viral doubling time was 10 h, and the peak of viremia occurred 21 d after reported HIV exposure. The spontaneous rate of decline (α) was highly variable among individuals. The phase 1 viral decay rate (δI = 0.3/day) in subjects initiating potent antiretroviral therapy during acute HIV infection was similar to estimates from treated subjects with chronic HIV infection. The doubling time in two subjects who discontinued antiretroviral therapy was almost five times slower than during acute infection. The mean basic reproductive number (R0) of 19.3 during the logarithmic growth phase of primary HIV infection suggested that a vaccine or postexposure prophylaxis of at least 95% efficacy would be needed to extinguish productive viral infection in the absence of drug resistance or viral latency. These measurements provide a basis for comparison of vaccine and other strategies and support the validity of the simian immunodeficiency virus macaque model of acute HIV infection.

scholarly journals Stability of an HIV/AIDS Treatment Model with Different Stages

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Hai-Feng Huo ◽  
Rui Chen
Keyword(s):  
Hiv Infection ◽  
Hiv Positive ◽  
Global Dynamics ◽  
Asymptotically Stable ◽  
Treatment Model ◽  
Globally Asymptotically Stable ◽  
Asymptomatic Stage ◽  
Mathematical Analyses ◽  
Two Stages ◽  
Hiv Aids

An HIV/AIDS treatment model with different stages is proposed in this paper. The stage of the HIV infection is divided into two stages, that is, HIV-positive in the asymptomatic stage of HIV infection and HIV-positive individuals in the pre-AIDS stage. The fact that some individuals with HIV-positive individuals after the treatment can be transformed into the compartment of HIV-positive individuals in the asymptomatic stage of HIV infection, the compartment of HIV-positive individuals in the pre-AIDS stage, or the compartment of individuals with full-blown AIDS is also considered. Mathematical analyses establish the idea that the global dynamics of the HIV/AIDS model are determined by the basic reproduction numberR0. The disease-free equilibrium is globally asymptotically stable ifR0<1. The endemic equilibrium is globally asymptotically stable ifR0>1for a special case. Numerical simulations are also conducted to support the analytic results.

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