Modeling HIV Infection of CD4+ T-cell Subpopulations

Essunger, Paulina; Perelson, Alan S.

doi:10.1006/jtbi.1994.1199

Cited by 114 publications

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“…(See, for example, [1] and [2].) Although this could alternatively be achieved by assuming that RTI-resistant virions have higher fitness than PI-resistant virions (i.e., that η RTI < η PI ), our simulations favor the former assumption, namely that µ 01 < µ 10 .…”

mentioning

confidence: 85%

“…We numerically compute the other possible fixed points, W 1 , W 2 , W 3 , and W 4 , using the parameter values in Table 1. To do this, we first compute the eigenvalues and eigenvectors σ 1 , σ 2 , σ 3 , and σ 4 and V 1 , V 2 , V 3 , and V 4 , respectively, of the matrix C = B −1 A, where A and B are defined as in (9) and (10). We plug these into equation (36) and then compute the equilibrium solutions W k as in (37).…”

Section: Stability Analysismentioning

confidence: 99%

“…We start with the estimate in [35] that the ratio of virions to infected T cells in the peripheral blood is approximately 112. We make very rough estimates of mass-action encounter rates, as in other T cell-pathogen models, such as [10]. Finally, we incorporate the estimated infectivity rate of 3.43 × 10 −8 in [35].…”

mentioning

confidence: 99%

“…With this assumption, the pressure for forward mutations occurs because of the increased fitness of the drug-resistant strains under treatment conditions. We also assume that µ 01 < µ 10 . There is some evidence that mutations resistant to RTIs are more prevalent than mutations resistant to PIs.…”

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confidence: 99%

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A mathematical model for treatment-resistant mutations of HIV

Moore

2005

Mathematical Biosciences and Engineering

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Abstract. In this paper, we propose and analyze a mathematical model, in the form of a system of ordinary differential equations, governing mutated strains of human immunodeficiency virus (HIV) and their interactions with the immune system and treatments. Our model incorporates two types of resistant mutations: strains that are not responsive to protease inhibitors, and strains that are not responsive to reverse transcriptase inhibitors. It also includes strains that do not have either of these two types of resistance (wildtype virus) and strains that have both types. We perform our analysis by changing the system of ordinary differential equations (ODEs) to a simple single-variable ODE, then identifying equilibria and determining stability. We carry out numerical calculations that illustrate the behavior of the system. We also examine the effects of various treatment regimens on the development of treatment-resistant mutations of HIV in this model.

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confidence: 85%

Section: Stability Analysismentioning

confidence: 99%

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confidence: 99%

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confidence: 99%

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A mathematical model for treatment-resistant mutations of HIV

Moore

2005

Mathematical Biosciences and Engineering

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“…The elementary properties of such systems of equations are well understood and numerical solution proceeds routinely with software such as Matlab. Constituting a special case because the infected cells are those of the immune system itself, dynamical models for HIV-1 usually consist of systems of differential equations which range from the simple two-component models (Bonhoeffer et al, 1997), to three-component (Herz et al, 1996) and four-component models (McLean et al, 1991;Phillips, 1996;Le Corfec and Tuckwell, 1998) and possibly as many as ten components (Essunger and Perelson, 1994). The basic components consist of the densities (in units, for example, of numbers per cubic mm of plasma) of uninfected (activated) CD4+ T-cells, infected such cells and HIV-1 virions.…”

Section: The Elements Of Viral Reproductionmentioning

confidence: 99%

On the behavior of solutions in viral dynamical models

Tuckwell

Wan

2004

Biosystems

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We consider simple mathematical models for the early population dynamics of the human immunodefficiency type 1 virus (HIV-1). Although these systems of differential equations may be solved by numerical methods, few general theoretical results are available due to nonlinearities. We analyze a model whose components are plasma densities of uninfected CD4+ T-cells and infected cells (assumed in this model to be proportional to virion density). In addition to analyzing the nature of the equilibrium points, we show that there are no periodic or limit-cycle solutions. Depending on the values of the parameters, solutions either tend without oscillation to an equilibrium point with zero virion density or to an equilibrium point in which there are a nonzero number of virions. In the latter case the approach to equilibrium may be through damped oscillations or without oscillation.

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HIV-1 dynamics after transient antiretroviral therapy: Implications for pathogenesis and clinical management

et al. 1997

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Simple models of CD4 lymphocyte interactions with human immunodeficiency virus (HIV) lead to the hypothesis that progression of HIV infection involves an increase in viral replicative capacity, due either to changes in the virus or in the host environment, or both. In order to consider how changes in plasma virus load after transient, potent antiretroviral therapy can be used to test the above hypothesis--a simple mathematical model that encompasses the processes of (1) arrival of new CD4 lymphocytes, (2) death/removal of these cells by HIV-independent mechanisms, (3) infection of susceptible CD4 lymphocytes by HIV, and (4) death/removal of infected cells was investigated. This showed that the in vivo rate of increase in plasma virus load immediately after transient therapy provides a measure of the viral replicative capacity. Thus, the hypothesis that progression of HIV infection involves an increase in viral replicative capacity can be tested by measuring this viral growth rate in patients with high CD4 counts and in patients with low CD4 counts. Studies should thus investigate dynamics of changes in virus levels after stopping antiretroviral therapy and, in particular, measure rates of increase in virus in patients at high and low CD4 counts. In practice, such data may assist in therapeutic management of patients with HIV infection.

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Modeling HIV Infection of CD4+ T-cell Subpopulations

Cited by 114 publications

References 0 publications

A mathematical model for treatment-resistant mutations of HIV

A mathematical model for treatment-resistant mutations of HIV

On the behavior of solutions in viral dynamical models

HIV-1 dynamics after transient antiretroviral therapy: Implications for pathogenesis and clinical management

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