ABSTRACT:
This a model from the article:
Dynamics of HIV infection of CD4+ T cells.
Perelson AS, Kirschner DE, De Boer R. Math Biosci
1993 Mar;114(1):81-125 8096155
,
Abstract:
We examine a model for the interaction of HIV with CD4+ T cells that considers
four populations: uninfected T cells, latently infected T cells, actively
infected T cells, and free virus. Using this model we show that many of the
puzzling quantitative features of HIV infection can be explained simply. We also
consider effects of AZT on viral growth and T-cell population dynamics. The
model exhibits two steady states, an uninfected state in which no virus is
present and an endemically infected state, in which virus and infected T cells
are present. We show that if N, the number of infectious virions produced per
actively infected T cell, is less a critical value, Ncrit, then the uninfected
state is the only steady state in the nonnegative orthant, and this state is
stable. For N > Ncrit, the uninfected state is unstable, and the endemically
infected state can be either stable, or unstable and surrounded by a stable
limit cycle. Using numerical bifurcation techniques we map out the parameter
regimes of these various behaviors. oscillatory behavior seems to lie outside
the region of biologically realistic parameter values. When the endemically
infected state is stable, it is characterized by a reduced number of T cells
compared with the uninfected state. Thus T-cell depletion occurs through the
establishment of a new steady state. The dynamics of the establishment of this
new steady state are examined both numerically and via the quasi-steady-state
approximation. We develop approximations for the dynamics at early times in
which the free virus rapidly binds to T cells, during an intermediate time scale
in which the virus grows exponentially, and a third time scale on which viral
growth slows and the endemically infected steady state is approached. Using the
quasi-steady-state approximation the model can be simplified to two ordinary
differential equations the summarize much of the dynamical behavior. We compute
the level of T cells in the endemically infected state and show how that level
varies with the parameters in the model. The model predicts that different viral
strains, characterized by generating differing numbers of infective virions
within infected T cells, can cause different amounts of T-cell depletion and
generate depletion at different rates. Two versions of the model are studied. In
one the source of T cells from precursors is constant, whereas in the other the
source of T cells decreases with viral load, mimicking the infection and killing
of T-cell precursors.(ABSTRACT TRUNCATED AT 400 WORDS)
This model was taken from the CellML repository
and automatically converted to SBML.
The original model was:
Perelson AS, Kirschner DE, De Boer R. (1993) - version=1.0
The original CellML model was created by:
Ethan Choi
mcho099@aucklanduni.ac.nz
The University of Auckland
This model originates from BioModels Database: A Database of Annotated Published Models (http://www.ebi.ac.uk/biomodels/). It is copyright (c) 2005-2011 The BioModels.net Team.
To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. Please refer to CC0 Public Domain Dedication
for more information.
In summary, you are entitled to use this encoded model in absolutely any manner you deem suitable, verbatim, or with modification, alone or embedded it in a larger context, redistribute it, commercially or not, in a restricted way or not..
To cite BioModels Database, please use: Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le Novère N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.
Camille Laibe 
