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

T. Dumrongpokaphan; Y. Lenbury; R. Ouncharoen; Y. Xu

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 2, Issue: 1, page 84-112
- ISSN: 0973-5348

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topDumrongpokaphan, T., et al. "An Intracellular Delay-Differential Equation Model of the HIV Infection and Immune Control." Mathematical Modelling of Natural Phenomena 2.1 (2010): 84-112. <http://eudml.org/doc/222283>.

@article{Dumrongpokaphan2010,

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 $\tau_c$ below which the effector
CTL can play a significant role in the immune control mechanism even when the basic reproduction
number is high.
},

author = {Dumrongpokaphan, T., Lenbury, Y., Ouncharoen, R., Xu, Y.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {delay system; CD4+T-cell; the HIV infection and immune control},

language = {eng},

month = {3},

number = {1},

pages = {84-112},

publisher = {EDP Sciences},

title = {An Intracellular Delay-Differential Equation Model of the HIV Infection and Immune Control},

url = {http://eudml.org/doc/222283},

volume = {2},

year = {2010},

}

TY - JOUR

AU - Dumrongpokaphan, T.

AU - Lenbury, Y.

AU - Ouncharoen, R.

AU - Xu, Y.

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

JO - Mathematical Modelling of Natural Phenomena

DA - 2010/3//

PB - EDP Sciences

VL - 2

IS - 1

SP - 84

EP - 112

AB -
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 $\tau_c$ below which the effector
CTL can play a significant role in the immune control mechanism even when the basic reproduction
number is high.

LA - eng

KW - delay system; CD4+T-cell; the HIV infection and immune control

UR - http://eudml.org/doc/222283

ER -

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