204324
constant: true
value: 2.4
name: mu_V
type: Parameter

204320
constant: true
value: 0.003
name: k_2
type: Parameter

531216
exponent: 3.0
scale: -3
multipler: 1.0
kind: METRE
type: SBMLUnit

204330
constant: true
value: 1400.0
name: N_initial
type: Parameter

MODEL1006230075
parameter: 204316
rule: 204300
rule: 204298
modified:
  W3 CDTF: Fri Jun 25 14:33:25 BST 2010
parameter: 204315
rule: 204305
parameter: 204308
time units: 531241
parameter: 204326
parameter: 204327
parameter: 204324
parameter: 204331
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…
creator:
  ORG:
    orgname: The University of Auckland
  n:
    given: Ethan
    family: Choi
volume units: 290956
parameter: 204332
units def: 531095
length unit: 131592
rule: 204301
rule: 204306
parameter: 204319
parameter: 204314
name: Perelson1993_HIVinfection_CD4Tcells_ModelC
modified:
  W3 CDTF: Fri Jun 25 14:33:25 BST 2010
parameter: 204312
units def: 531241
parameter: 204311
type: SBMLModel
parameter: 204330
area units: 291053
creator:
  ORG:
    orgname: The University of Auckland
  n:
    given: Ethan
    family: Choi
is described by: http://identifiers.org/pubmed/8096155
parameter: 204322
parameter: 204323
creator:
  ORG:
    orgname: The University of Auckland
  n:
    given: Ethan
    family: Choi
parameter: 204318
substance units: 178797
rule: 204302
created:
  W3 CDTF: Fri Jun 25 14:33:25 BST 2010
curated: false
units def: 531204
units def: 531071
units def: 531119
parameter: 204310
rule: 204304
units def: 531167
parameter: 204328
parameter: 204320
units def: 531143
compartment: 204294
modified:
  W3 CDTF: Fri Jun 25 14:33:25 BST 2010

531071
unit: 531083
name: day
type: SBMLUnitsDef

204328
constant: true
value: 1096.0
name: tau
type: Parameter

204314
constant: true
value: 1.0
name: theta
type: Parameter

531095
unit: 531107
name: per_day
type: SBMLUnitsDef

531131
exponent: 3.0
scale: -3
multipler: 1.0
kind: METRE
type: SBMLUnit

204310
constant: true
value: 0.03
name: r
type: Parameter

531167
unit: 531191
unit: 531179
name: per_day_mm3
type: SBMLUnitsDef

531241
unit: 531253
name: time
type: SBMLUnitsDef

204331
constant: true
value: 1050.0
name: N_AZT
type: Parameter

204294
constant: true
units: litre
size: 1.0
spatial dimensions: 3.0
type: Compartment

204315
constant: false
value: NaN
name: s_V
type: Parameter

204311
constant: true
value: 1500.0
name: T_max
type: Parameter

531107
exponent: -1.0
scale: 0
multipler: 86400.0
kind: SECOND
type: SBMLUnit

204322
constant: true
value: 0.24
name: mu_b
type: Parameter

204326
constant: false
value: 0.001
name: V
type: Parameter

531143
unit: 531155
name: per_mm3
type: SBMLUnitsDef

531083
exponent: 1.0
scale: 0
multipler: 86400.0
kind: SECOND
type: SBMLUnit

531204
unit: 531229
unit: 531216
name: mm3_per_day
type: SBMLUnitsDef

204332
constant: false
value: NaN
name: N
type: Parameter

204316
constant: false
value: 1000.0
name: T
type: Parameter

204319
constant: false
value: 0.0
name: T_1
type: Parameter

204312
constant: true
value: 0.02
name: mu_T
type: Parameter

204323
constant: false
value: 0.0
name: T_2
type: Parameter

204308
constant: true
value: 10.0
name: s
type: Parameter

531155
exponent: -3.0
scale: -3
multipler: 1.0
kind: METRE
type: SBMLUnit

204327
constant: false
value: NaN
name: T_tot
type: Parameter

531253
exponent: 1.0
scale: 0
multipler: 86400.0
kind: SECOND
type: SBMLUnit

531229
exponent: -1.0
scale: 0
multipler: 86400.0
kind: SECOND
type: SBMLUnit

531119
unit: 531131
name: mm3
type: SBMLUnitsDef

204318
constant: true
value: 2.4E-5
name: k_1
type: Parameter

531191
exponent: -3.0
scale: -3
multipler: 1.0
kind: METRE
type: SBMLUnit

531179
exponent: -1.0
scale: 0
multipler: 86400.0
kind: SECOND
type: SBMLUnit