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

Mahiéddine Kouche; Bedr'eddine Ainseba

International Journal of Applied Mathematics and Computer Science (2010)

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

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topMahiéddine 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 -

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