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

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

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

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

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

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

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

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

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

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

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

550739
type: SBMLUnitsDef
unit: 550751
name: day

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

550811
type: SBMLUnitsDef
unit: 550823
name: per_mm3

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

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

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

550908
type: SBMLUnitsDef
unit: 550920
name: time

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

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

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

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

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

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

550787
type: SBMLUnitsDef
unit: 550799
name: mm3

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

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

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

550763
type: SBMLUnitsDef
unit: 550775
name: per_day

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

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

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