MODEL1006230035
type: SBMLModel
parameter: 140612
creator:
  ORG:
    orgname: The University of Auckland
  n:
    given: Ethan
    family: Choi
parameter: 140602
parameter: 140614
parameter: 140594
rule: 140586
volume units: 290956
parameter: 140599
creator:
  ORG:
    orgname: The University of Auckland
  n:
    given: Ethan
    family: Choi
compartment: 140583
units def: 374739
length unit: 076409
parameter: 140596
notes: 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…
modified:
  W3 CDTF: Fri Jun 25 13:42:21 BST 2010
rule: 140591
units def: 374666
units def: 374812
is described by: http://identifiers.org/pubmed/8096155
units def: 374690
curated: false
rule: 140589
units def: 374776
parameter: 140600
created:
  W3 CDTF: Fri Jun 25 13:42:21 BST 2010
parameter: 140615
units def: 374642
name: Perelson1993_HIVinfection_CD4Tcells_ModelD
parameter: 140610
units def: 374714
area units: 291053
creator:
  ORG:
    orgname: The University of Auckland
  n:
    given: Ethan
    family: Choi
time units: 374812
parameter: 140616
parameter: 140607
modified:
  W3 CDTF: Fri Jun 25 13:42:21 BST 2010
parameter: 140606
rule: 140588
parameter: 140598
parameter: 140608
parameter: 140603
rule: 140587
substance units: 178797
parameter: 140611
parameter: 140595
rule: 140592
parameter: 140618
modified:
  W3 CDTF: Fri Jun 25 13:42:21 BST 2010
parameter: 140604

140612
type: Parameter
constant: true
value: 0.24
name: mu_b

140602
type: Parameter
constant: true
value: 0.023
name: k_3

140614
type: Parameter
constant: false
value: NaN
name: T_2

140594
type: Parameter
constant: true
value: 10.0
name: s

140599
type: Parameter
constant: false
value: 1000.0
name: T

140583
type: Compartment
constant: true
units: litre
size: 1.0
spatial dimensions: 3.0

374739
type: SBMLUnitsDef
unit: 374763
unit: 374751
name: per_day_mm3

374763
type: SBMLUnit
exponent: -3.0
scale: -3
multipler: 1.0
kind: METRE

374751
type: SBMLUnit
exponent: -1.0
scale: 0
multipler: 86400.0
kind: SECOND

140596
type: Parameter
constant: true
value: 2.0E-5
name: gamma

374666
type: SBMLUnitsDef
unit: 374678
name: per_day

374678
type: SBMLUnit
exponent: -1.0
scale: 0
multipler: 86400.0
kind: SECOND

374812
type: SBMLUnitsDef
unit: 374824
name: time

374824
type: SBMLUnit
exponent: 1.0
scale: 0
multipler: 86400.0
kind: SECOND

374690
type: SBMLUnitsDef
unit: 374702
name: mm3

374702
type: SBMLUnit
exponent: 3.0
scale: -3
multipler: 1.0
kind: METRE

374776
type: SBMLUnitsDef
unit: 374800
unit: 374788
name: mm3_per_day

374800
type: SBMLUnit
exponent: -1.0
scale: 0
multipler: 86400.0
kind: SECOND

374788
type: SBMLUnit
exponent: 3.0
scale: -3
multipler: 1.0
kind: METRE

140600
type: Parameter
constant: true
value: 2.4E-5
name: k_1

140615
type: Parameter
constant: true
value: 1000.0
name: N

374642
type: SBMLUnitsDef
unit: 374654
name: day

374654
type: SBMLUnit
exponent: 1.0
scale: 0
multipler: 86400.0
kind: SECOND

140610
type: Parameter
constant: false
value: 0.0
name: T_1

374714
type: SBMLUnitsDef
unit: 374727
name: per_mm3

374727
type: SBMLUnit
exponent: -3.0
scale: -3
multipler: 1.0
kind: METRE

140616
type: Parameter
constant: true
value: 2.4
name: mu_V

140607
type: Parameter
constant: true
value: 2.0
name: t_min

140606
type: Parameter
constant: true
value: 0.001
name: V_0

140598
type: Parameter
constant: false
value: NaN
name: beta

140608
type: Parameter
constant: false
value: NaN
name: T_1_t

140603
type: Parameter
constant: true
value: 2.424
name: k_4

140611
type: Parameter
constant: true
value: 0.003
name: k_2

140595
type: Parameter
constant: true
value: 0.01
name: p

140618
type: Parameter
constant: false
value: NaN
name: V

140604
type: Parameter
constant: true
value: 1000.0
name: T_0