550823
exponent: -3.0
scale: -3
multipler: 1.0
kind: METRE
type: SBMLUnit

550908
unit: 550920
name: time
type: SBMLUnitsDef

550872
unit: 550896
unit: 550884
name: mm3_per_day
type: SBMLUnitsDef

450175
constant: false
value: 1000.0
name: T
type: Parameter

550811
unit: 550823
name: per_mm3
type: SBMLUnitsDef

450182
constant: false
value: 0.0
name: T_2
type: Parameter

450173
constant: true
value: 1500.0
name: T_max
type: Parameter

450171
constant: true
value: 0.03
name: r
type: Parameter

450177
constant: true
value: 2.4E-5
name: k_1
type: Parameter

550739
unit: 550751
name: day
type: SBMLUnitsDef

550847
exponent: -1.0
scale: 0
multipler: 86400.0
kind: SECOND
type: SBMLUnit

MODEL1006230079
rule: 450167
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…
curated: false
parameter: 450182
parameter: 450187
modified:
  W3 CDTF: Fri Jun 25 14:37:31 BST 2010
units def: 550872
units def: 550835
rule: 450164
parameter: 450170
parameter: 450179
type: SBMLModel
area units: 237671
name: Perelson1993_HIVinfection_CD4Tcells_ModelA
units def: 550739
units def: 550811
parameter: 450183
creator:
  ORG:
    orgname: The University of Auckland
  n:
    given: Ethan
    family: Choi
parameter: 450177
units def: 550908
rule: 450168
parameter: 450181
creator:
  ORG:
    orgname: The University of Auckland
  n:
    given: Ethan
    family: Choi
time units: 550908
compartment: 450160
modified:
  W3 CDTF: Fri Jun 25 14:37:31 BST 2010
parameter: 450173
created:
  W3 CDTF: Fri Jun 25 14:37:31 BST 2010
parameter: 450175
length unit: 131592
parameter: 450178
modified:
  W3 CDTF: Fri Jun 25 14:37:31 BST 2010
creator:
  ORG:
    orgname: The University of Auckland
  n:
    given: Ethan
    family: Choi
units def: 550787
parameter: 450171
rule: 450165
parameter: 450174
rule: 450163
units def: 550763
is described by: http://identifiers.org/pubmed/8096155
parameter: 450186
volume units: 290956
substance units: 178797
parameter: 450185

550763
unit: 550775
name: per_day
type: SBMLUnitsDef

550884
exponent: 3.0
scale: -3
multipler: 1.0
kind: METRE
type: SBMLUnit

550751
exponent: 1.0
scale: 0
multipler: 86400.0
kind: SECOND
type: SBMLUnit

550835
unit: 550859
unit: 550847
name: per_day_mm3
type: SBMLUnitsDef

550896
exponent: -1.0
scale: 0
multipler: 86400.0
kind: SECOND
type: SBMLUnit

450186
constant: false
value: 0.001
name: V
type: Parameter

550775
exponent: -1.0
scale: 0
multipler: 86400.0
kind: SECOND
type: SBMLUnit

450160
constant: true
units: litre
size: 1.0
spatial dimensions: 3.0
type: Compartment

450174
constant: true
value: 0.02
name: mu_T
type: Parameter

550787
unit: 550799
name: mm3
type: SBMLUnitsDef

550859
exponent: -3.0
scale: -3
multipler: 1.0
kind: METRE
type: SBMLUnit

450181
constant: true
value: 0.24
name: mu_b
type: Parameter

450178
constant: false
value: 0.0
name: T_1
type: Parameter

450187
constant: false
value: NaN
name: T_tot
type: Parameter

450185
constant: true
value: 1400.0
name: N
type: Parameter

550799
exponent: 3.0
scale: -3
multipler: 1.0
kind: METRE
type: SBMLUnit

450179
constant: true
value: 0.003
name: k_2
type: Parameter

450183
constant: true
value: 2.4
name: mu_V
type: Parameter

450170
constant: true
value: 10.0
name: s
type: Parameter

550920
exponent: 1.0
scale: 0
multipler: 86400.0
kind: SECOND
type: SBMLUnit