Perelson1993  HIVinfection_CD4Tcells_ModelA
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):81125 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 Tcell 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 Tcell 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 quasisteadystate
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
quasisteadystate 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 Tcell 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 Tcell 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) 20052011 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 NovĂ¨re N, Laibe C (2010) BioModels Database: An enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol., 4:92.
 Dynamics of HIV infection of CD4+ T cells.
 Perelson AS, Kirschner DE, De Boer R
 Mathematical biosciences , 3/ 1993 , Volume 114 , pages: 81125 , PubMed ID: 8096155
 Theoretical Division, Los Alamos National Laboratory, New Mexico.
 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 Tcell 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 Tcell 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 quasisteadystate 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 quasisteadystate 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 Tcell 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 Tcell precursors.(ABSTRACT TRUNCATED AT 400 WORDS)
Submitter of this revision: Mohammad Umer Sharif Shohan
Modellers: Camille Laibe, Mohammad Umer Sharif Shohan
Metadata information
isDescribedBy (1 statement)
hasTaxon (1 statement)
isVersionOf (2 statements)
occursIn (1 statement)
Connected external resources
Name  Description  Size  Actions 

Model files 

Perelson1993.xml  SBML L2V4 representation of Perelson1993_HIVinfection_CD4Tcells_ModelA  43.16 KB  Preview  Download 
Additional files 

MODEL1006230079biopax2.owl  Autogenerated BioPAX (Level 2)  1.06 KB  Preview  Download 
MODEL1006230079biopax3.owl  Autogenerated BioPAX (Level 3)  2.02 KB  Preview  Download 
MODEL1006230079.m  Autogenerated Octave file  2.94 KB  Preview  Download 
MODEL1006230079.pdf  Autogenerated PDF file  141.14 KB  Preview  Download 
MODEL1006230079.png  Autogenerated Reaction graph (PNG)  5.04 KB  Preview  Download 
MODEL1006230079.sci  Autogenerated Scilab file  200.00 Bytes  Preview  Download 
MODEL1006230079.svg  Autogenerated Reaction graph (SVG)  851.00 Bytes  Preview  Download 
MODEL1006230079.vcml  Autogenerated VCML file  900.00 Bytes  Preview  Download 
MODEL1006230079.xpp  Autogenerated XPP file  1.79 KB  Preview  Download 
MODEL1006230079_url.xml  old xml file  13.57 KB  Preview  Download 
MODEL1006230079_urn.xml  Autogenerated SBML file with URNs  14.19 KB  Preview  Download 
Perelson1993.cps  COPASI version 4.24 (Build 197) representation of Perelson1993_HIVinfection_CD4Tcells_ModelA  74.03 KB  Preview  Download 
Perelson1993.sedml  SEDML L1V2 representation of Perelson1993_HIVinfection_CD4Tcells_ModelA  3.70 KB  Preview  Download 
 Model originally submitted by : Camille Laibe
 Submitted: Jun 23, 2010 10:12:28 AM
 Last Modified: Nov 25, 2019 2:10:39 PM
Revisions

Version: 5
 Submitted on: Nov 25, 2019 2:10:39 PM
 Submitted by: Mohammad Umer Sharif Shohan
 With comment: Automatically added model identifier BIOMD0000000874

Version: 2
 Submitted on: Jun 25, 2010 2:37:31 PM
 Submitted by: Camille Laibe
 With comment: Current version of Perelson1993_HIVinfection_CD4Tcells_ModelA

Version: 1
 Submitted on: Jun 23, 2010 10:12:28 AM
 Submitted by: Camille Laibe
 With comment: Original import of Perelson1993_HIVinfection_CD4Tcells_ModelA
(*) You might be seeing discontinuous revisions as only public revisions are displayed here. Any private revisions of this model will only be shown to the submitter and their collaborators.
: Variable used inside SBML models
Species  Initial Concentration/Amount 

T 1 P01730 
0.0 mol 
T P01730 
1000.0 mol 
T 2 P01730 
0.0 mol 
V  0.001 mol 
Reactions  Rate  Parameters 

=> T_1; V, T  COMpartment*k_1*V*T  k_1 = 2.4E5 
=> T  COMpartment*(s+r*T)  s = 10.0; r = 0.03 
T_1 =>  COMpartment*(mu_T*T_1+k_2*T_1)  mu_T = 0.02; k_2 = 0.003 
T => ; V, T_1, T_2  COMpartment*(mu_T*T+k_1*V*T+r*T*(T+T_1+T_2)/T_max)  k_1 = 2.4E5; mu_T = 0.02; T_max = 1500.0; r = 0.03 
=> T_2; T_1  COMpartment*k_2*T_1  k_2 = 0.003 
T_2 =>  COMpartment*mu_b*T_2  mu_b = 0.24 
=> V; T_2  COMpartment*N*mu_b*T_2  N = 1000.0; mu_b = 0.24 
V => ; T  COMpartment*(k_1*V*T+mu_V*V)  k_1 = 2.4E5; mu_V = 2.4 
(added: 25 Nov 2019, 14:09:21, updated: 25 Nov 2019, 14:09:21)