A delay-differential equation model of HIV infection of CD4+ T-cells

Culshaw, Rebecca V.; Ruan, Shigui

doi:10.1016/s0025-5564(00)00006-7

Cited by 557 publications

(345 citation statements)

References 26 publications

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“…Although not many models have been implemented as DDE, delays occur naturally in biological phenomena and a DDE formulation is often more biologically intuitive than its counterpart ODE model. Examples can be found in the context of HIV modeling (Tam, 1999;Culshaw and Ruan, 2000), glucose insulin regulatory system (De Gaetano and Arino, 2000), gene expression Figure 8. Antral gastrin depletion.…”

Section: Discussionmentioning

confidence: 99%

The importance of an inter-compartmental delay in a model for human gastric acid secretion

Marino

Ganguli

Joseph

et al. 2003

Bulletin of Mathematical Biology

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In this work we re-examine an existing model of gastric acid secretion. The model is a 2-compartment model of the human stomach accounting for regions where relevant cells (D, G, ECL and parietal cells) and proteins and acid they secrete (somatostatin, gastrin, histamine, and gastric acid, respectively) are found. These proteins compose a positive and negative feedback system that controls the secretion of gastric acid by parietal cells. The original model consists of 18 ordinary differential equations and yields a stable 3-period limit cycle solution. We modify the existing model by introducing a delay into the system and assuming that the cell populations are in steady state over a short-time window (<300 h) and are able to reduce the system to an 8-equation delay differential equation model. In addition to demonstrating congruency between the two models, we also show that a similar stability is only reproducible when the delay in gastrin transport is approximately 30 min. This suggests that gastric acid secretion homeostasis likely depends strongly on the delay in gastrin transport from the antrum to the corpus.

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Section: Discussionmentioning

confidence: 99%

The importance of an inter-compartmental delay in a model for human gastric acid secretion

Marino

Ganguli

Joseph

et al. 2003

Bulletin of Mathematical Biology

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“…The basic class of ODE HIV models (Culshaw and Ruan, 2000;Nelson and Perelson, 2002;Nelson et al, 2000;Perelson and Nelson, 1999) generally includes variables that represent the healthy cells T, infected cells T Ã , and the viral load V. The viral load is an integral part of the system of equations that influences the dynamics of the healthy and infected cells.…”

Section: Viral Loadmentioning

confidence: 99%

A viral load-based cellular automata approach to modeling HIV dynamics and drug treatment

Shi¹,

Tridane²,

Kuang³

2008

Journal of Theoretical Biology

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“…It also incorporated the feature that production of virus was delayed from the time of initial infection. Later Culshaw and Ruan [7] simplified the model proposed in the work of Perelson et al [23] by considering only three components: the uninfected CD4+ T-cells, infected CD4+ T-cells, and free virus. The reduced model is thus more mathematically tractable, allowing theoretical analysis using the delay as the bifurcation parameter.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we provide a detailed analytical study of a mathematical model of the interaction between infective virus, CD4+ T-cells, and CTL, which incorporates a discrete intracellular delay in time between infection of a CD4+ T-cell and the emission of viral particles on a cellular level as proposed in, say, Herz et al [14], Tam [30], Nelson et al [19], and Culshaw and Ruan [7].…”

Section: Introductionmentioning

confidence: 99%

An Intracellular Delay-Differential Equation Model of the HIV Infection and Immune Control

Dumrongpokaphan

Lenbury

Ouncharoen

et al. 2007

Math. Model. Nat. Phenom.

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Abstract. Previous work has shown that intracellular delay needs to be taken into account to accurately determine the half-life of free virus from drug perturbation experiments [1]. The delay also effects the estimated value for the infected T-cell loss rate when we assume that the drug is not completely effective [19]. Models of virus infection that include intracellular delay are more accurate representations of the biological data.We analyze a non-linear model of the human immunodeficiency virus (HIV) infection that considers the interaction between a replicating virus, CD4+ T-cell and the cytotoxic-lymphocytes (CTL). We then investigate the intracellular delay effect on the stability of the endemically infected steady state. Criteria are given to ensure that the infected steady state is asymptotically stable for all delays. Model analysis also allows the prediction of a critical delay τ c below which the effector CTL can play a significant role in the immune control mechanism even when the basic reproduction number is high.

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A delay-differential equation model of HIV infection of CD4+ T-cells

Cited by 557 publications

References 26 publications

The importance of an inter-compartmental delay in a model for human gastric acid secretion

The importance of an inter-compartmental delay in a model for human gastric acid secretion

A viral load-based cellular automata approach to modeling HIV dynamics and drug treatment

An Intracellular Delay-Differential Equation Model of the HIV Infection and Immune Control

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