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

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

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

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

531241
type: SBMLUnitsDef
unit: 531253
name: time

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

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

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

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

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

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

531095
type: SBMLUnitsDef
unit: 531107
name: per_day

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

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

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

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

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

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

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

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

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

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

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

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

531071
type: SBMLUnitsDef
unit: 531083
name: day

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

531119
type: SBMLUnitsDef
unit: 531131
name: mm3

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

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

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

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

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

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

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

531143
type: SBMLUnitsDef
unit: 531155
name: per_mm3

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

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