# A mathematical model of HIV-1 infection including the saturation effect of healthy cell proliferation

• Volume: 20, Issue: 3, page 601-612
• ISSN: 1641-876X

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## Abstract

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In this paper we derive a model describing the dynamics of HIV-1 infection in tissue culture where the infection spreads directly from infected cells to healthy cells trough cell-to-cell contact. We assume that the infection rate between healthy and infected cells is a saturating function of cell concentration. Our analysis shows that if the basic reproduction number does not exceed unity then infected cells are cleared and the disease dies out. Otherwise, the infection is persistent with the existence of an infected equilibrium. Numerical simulations indicate that, depending on the fraction of cells surviving the incubation period, the solutions approach either an infected steady state or a periodic orbit.

## How to cite

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Mahiéddine Kouche, and Bedr'eddine Ainseba. "A mathematical model of HIV-1 infection including the saturation effect of healthy cell proliferation." International Journal of Applied Mathematics and Computer Science 20.3 (2010): 601-612. <http://eudml.org/doc/208011>.

@article{MahiéddineKouche2010,
abstract = {In this paper we derive a model describing the dynamics of HIV-1 infection in tissue culture where the infection spreads directly from infected cells to healthy cells trough cell-to-cell contact. We assume that the infection rate between healthy and infected cells is a saturating function of cell concentration. Our analysis shows that if the basic reproduction number does not exceed unity then infected cells are cleared and the disease dies out. Otherwise, the infection is persistent with the existence of an infected equilibrium. Numerical simulations indicate that, depending on the fraction of cells surviving the incubation period, the solutions approach either an infected steady state or a periodic orbit.},
author = {Mahiéddine Kouche, Bedr'eddine Ainseba},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {HIV; periodic oscillations; persistence; stability; tissue culture},
language = {eng},
number = {3},
pages = {601-612},
title = {A mathematical model of HIV-1 infection including the saturation effect of healthy cell proliferation},
url = {http://eudml.org/doc/208011},
volume = {20},
year = {2010},
}

TY - JOUR
AU - Mahiéddine Kouche
AU - Bedr'eddine Ainseba
TI - A mathematical model of HIV-1 infection including the saturation effect of healthy cell proliferation
JO - International Journal of Applied Mathematics and Computer Science
PY - 2010
VL - 20
IS - 3
SP - 601
EP - 612
AB - In this paper we derive a model describing the dynamics of HIV-1 infection in tissue culture where the infection spreads directly from infected cells to healthy cells trough cell-to-cell contact. We assume that the infection rate between healthy and infected cells is a saturating function of cell concentration. Our analysis shows that if the basic reproduction number does not exceed unity then infected cells are cleared and the disease dies out. Otherwise, the infection is persistent with the existence of an infected equilibrium. Numerical simulations indicate that, depending on the fraction of cells surviving the incubation period, the solutions approach either an infected steady state or a periodic orbit.
LA - eng
KW - HIV; periodic oscillations; persistence; stability; tissue culture
UR - http://eudml.org/doc/208011
ER -

## References

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