<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>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.</p></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.

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

Laboratory of Applied Mathematics, Badji-Mokhtar University, BP 12, Annaba 23000, Algeria

Institute of Mathematics of Bordeaux, UMR CNRS 52 51, Case 36 Université Victor Segalen Bordeaux 2, 3 ter place de la Victoire, F 33076 Bordeaux Cedex, France

International Journal of Applied Mathematics and Computer Science

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...

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

Published Online: Sep 27, 2010

Page range: 601 - 612

DOI: https://doi.org/10.2478/v10006-010-0045-z

Keywords
HIV, periodic oscillations, persistence, stability, tissue culture

This content is open access.

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

Published Online: Sep 27, 2010

Page range: 601 - 612

DOI: https://doi.org/10.2478/v10006-010-0045-z

KeywordsHIV, periodic oscillations, persistence, stability, tissue culture

This content is open access.

Keywords
HIV, periodic oscillations, persistence, stability, tissue culture