MODEL1006230093
type: SBMLModel
volume units: 290956
modified:
  W3 CDTF: Fri Jun 25 14:46:19 BST 2010
creator:
  ORG:
    orgname: The University of Auckland
  n:
    given: Ethan
    family: Choi
substance units: 178797
modified:
  W3 CDTF: Fri Jun 25 14:46:19 BST 2010
units def: 621562
is described by: http://identifiers.org/pubmed/8096155
parameter: 978547
curated: false
units def: 621647
rule: 978526
parameter: 978544
compartment: 978514
area units: 237671
rule: 978517
units def: 621586
parameter: 978540
parameter: 978556
parameter: 978555
rule: 978522
parameter: 978548
time units: 621683
rule: 978525
parameter: 978528
created:
  W3 CDTF: Fri Jun 25 14:46:19 BST 2010
units def: 621538
parameter: 978551
parameter: 978532
parameter: 978531
length unit: 821056
rule: 978521
modified:
  W3 CDTF: Fri Jun 25 14:46:19 BST 2010
units def: 621611
parameter: 978559
creator:
  ORG:
    orgname: The University of Auckland
  n:
    given: Ethan
    family: Choi
parameter: 978552
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…
parameter: 978539
creator:
  ORG:
    orgname: The University of Auckland
  n:
    given: Ethan
    family: Choi
parameter: 978543
name: Perelson1993_HIVinfection_CD4Tcells_ModelB
units def: 621683
rule: 978518
units def: 621513
parameter: 978536
parameter: 978535

621562
type: SBMLUnitsDef
unit: 621574
name: mm3

621574
type: SBMLUnit
exponent: 3.0
scale: -3
multipler: 1.0
kind: METRE

978547
type: Parameter
constant: true
value: 0.003
name: k_2

621647
type: SBMLUnitsDef
unit: 621671
unit: 621659
name: mm3_per_day

621671
type: SBMLUnit
exponent: -1.0
scale: 0
multipler: 86400.0
kind: SECOND

621659
type: SBMLUnit
exponent: 3.0
scale: -3
multipler: 1.0
kind: METRE

978544
type: Parameter
constant: false
value: 0.0
name: T_1

978514
type: Compartment
constant: true
units: litre
size: 1.0
spatial dimensions: 3.0

621586
type: SBMLUnitsDef
unit: 621598
name: per_mm3

621598
type: SBMLUnit
exponent: -3.0
scale: -3
multipler: 1.0
kind: METRE

978540
type: Parameter
constant: false
value: 1000.0
name: T

978556
type: Parameter
constant: false
value: 0.001
name: V

978555
type: Parameter
constant: true
value: 1400.0
name: N

978548
type: Parameter
constant: true
value: 0.24
name: mu_b

621683
type: SBMLUnitsDef
unit: 621695
name: time

621695
type: SBMLUnit
exponent: 1.0
scale: 0
multipler: 86400.0
kind: SECOND

978528
type: Parameter
constant: true
value: 10.0
name: s

621538
type: SBMLUnitsDef
unit: 621550
name: per_day

621550
type: SBMLUnit
exponent: -1.0
scale: 0
multipler: 86400.0
kind: SECOND

978551
type: Parameter
constant: false
value: 0.0
name: T_2

978532
type: Parameter
constant: true
value: 1500.0
name: T_max

978531
type: Parameter
constant: true
value: 0.03
name: r

621611
type: SBMLUnitsDef
unit: 621635
unit: 621623
name: per_day_mm3

621635
type: SBMLUnit
exponent: -3.0
scale: -3
multipler: 1.0
kind: METRE

621623
type: SBMLUnit
exponent: -1.0
scale: 0
multipler: 86400.0
kind: SECOND

978559
type: Parameter
constant: false
value: NaN
name: T_tot

978552
type: Parameter
constant: true
value: 2.4
name: mu_V

978539
type: Parameter
constant: false
value: NaN
name: s_V

978543
type: Parameter
constant: true
value: 2.4E-5
name: k_1

621513
type: SBMLUnitsDef
unit: 621525
name: day

621525
type: SBMLUnit
exponent: 1.0
scale: 0
multipler: 86400.0
kind: SECOND

978536
type: Parameter
constant: true
value: 1.0
name: theta

978535
type: Parameter
constant: true
value: 0.02
name: mu_T