BIOMD0000000294
type: SBMLModel
rule: 264726
has version: A37
rule: 264742
parameter: metaid_0000004
reaction: 264660
rule: 264729
reaction: 264662
reaction: 264659
species: 264640
units def: metaid_0000073
reaction: 264670
reaction: 264669
reaction: 264690
species: 264643
parameter: 264759
parameter: 264758
parameter: 264765
volume units: volume
species: 264651
reaction: 264664
species: 264646
rule: 264732
reaction: 264666
rule: 264738
parameter: 264749
parameter: 264766
parameter: 264760
units def: metaid_0000071
rule: 264728
reaction: 264674
reaction: 264673
substance units: metaid_0000071
area units: area
parameter: 264751
rule: 264725
parameter: 264750
reaction: 264692
occurs in: http://identifiers.org/taxonomy/9606
reaction: 264691
reaction: 264694
length unit: length
reaction: 264681
parameter: metaid_0000005
reaction: 264687
species: 264650
species: 264642
rule: 264734
reaction: 264678
reaction: 264677
compartment: 264638
parameter: 264767
parameter: 264761
reaction: 264696
reaction: 264695
species: 264647
species: 264654
reaction: 264685
species: 264658
units def: metaid_0000072
rule: 264737
is: MODEL1012210000
occurs in: http://identifiers.org/taxonomy/520
parameter: 264762
rule: 264727
is described by: http://identifiers.org/pubmed/17210532
parameter: metaid_0000003
reaction: 264682
reaction: 264661
parameter: metaid_0000006
reaction: 264693
parameter: 264757
rule: 264739
species: 264641
units def: metaid_0000074
curated: true
parameter: metaid_0000007
name: Restif2007_Vaccination_Invasion
parameter: 264764
notes: This is the model described in the article: Vaccination and the dynamics of immune evasion. Restif O, Grenfell BT. J R Soc Interface. 2007 Feb 22;4(12):143-53. PMID: 17210532 , doi: 10.1098/rsif.2006.0167 ; Abstract: Vaccines exert strong selective pressures on pathogens, favouring the spread of antigenic variants. We propose a simple mathematical model to investigate the dynamics of a novel pathogenic strain that emerges in a population where a previous strain is maintained at low endemic level by a vaccine. We compare three methods to assess the ability of the novel strain to invade and persist: algebraic rate of invasion; deterministic dynamics; and stochastic dynamics. These three techniques provide complementary predictions on the fate of the system. In particular, we emphasize the importance of stochastic simulations, which account for the possibility of extinctions of either strain. More specifically, our model suggests that the probability of persistence of an invasive strain (i) can be minimized for intermediate levels of vaccine cross-protection (i.e. immune protection against the novel strain) and (ii) is lower if cross-immunity acts through a reduced infectious period rather than through reduced susceptibility. This version of the model can be used for both the stochastic and the deterministic simulations described in the article. For deterministic interpretations with infinite population sizes, set the population size N = 1. The model does reproduces the deterministic time course. The initial values are set to the steady state values for a latent infection with strain 1 with an invading infection of strain 2 (I2=1e-06), 100 percent vaccination with a susceptibility reduction τ=0.7 at birth (p=1), and all other parameters as in figure 3 of the publication. To be compatible with older software tools, the english letter names instead of the greek symbols were used for parameter names: parameter symbol name transmission rate β beta recovery rate γ gamma bir…

metaid_0000004
type: Parameter
is: SBO:0000348
constant: true
units: metaid_0000072
value: 50.0
name: life expectancy

metaid_0000072
type: SBMLUnitsDef
unit: 313411
name: years

313411
type: SBMLUnit
exponent: 1.0
scale: 0
multipler: 3.1536E7
kind: SECOND

264660
type: Reaction
kinetic law: 313508
modifier: 313496
product: 313484
is version of: GO:0007567
is: SBO:0000375
fast: false
reversible: false
name: Birth V (vaccinated)

264640
type: Species
notes: total target population size
is version of: http://identifiers.org/taxonomy/9606
has only substance units: true
in compartment: 264638
is: SBO:0000240
boundary condition: false
initial amount: 1.0
initial concentration: NaN
constant: false

264638
type: Compartment
is: SBO:0000290
constant: true
size: 1.0
spatial dimensions: 3.0
name: environment

313484
type: SpeciesReference
stoichiometry: 1.0
species: 264650

264650
type: Species
is version of: http://identifiers.org/taxonomy/9606
is: SBO:0000240
constant: false
boundary condition: false
has only substance units: true
initial concentration: NaN
initial amount: 0.9
in compartment: 264638

264662
type: Reaction
kinetic law: 313557
reactant: 313545
is version of: GO:0016265
is: SBO:0000375
fast: false
reversible: false
name: Death in V

313545
type: SpeciesReference
stoichiometry: 1.0
species: 264650

264659
type: Reaction
kinetic law: 313472
modifier: 313460
product: 313447
is version of: GO:0007567
is: SBO:0000375
fast: false
reversible: false
name: Birth S (unvaccinated)

313447
type: SpeciesReference
stoichiometry: 1.0
species: 264641

264641
type: Species
is version of: http://identifiers.org/taxonomy/9606
is: SBO:0000240
constant: false
boundary condition: false
has only substance units: true
initial concentration: NaN
initial amount: 0.0588235
in compartment: 264638

metaid_0000073
type: SBMLUnitsDef
unit: 313423
name: days

313423
type: SBMLUnit
exponent: 1.0
scale: 0
multipler: 86400.0
kind: SECOND

264670
type: Reaction
kinetic law: 313702
reactant: 313690
is version of: GO:0016265
is: SBO:0000375
fast: false
reversible: false
name: Death in J1

313690
type: SpeciesReference
stoichiometry: 1.0
species: 264655

264655
type: Species
initial amount: 0.0
has version: http://identifiers.org/taxonomy/9606
initial concentration: NaN
constant: false
boundary condition: false
has version: http://identifiers.org/taxonomy/520
is: SBO:0000240
in compartment: 264638
has only substance units: true

264669
type: Reaction
kinetic law: 313678
reactant: 313666
is version of: GO:0016265
is: SBO:0000375
fast: false
reversible: false
name: Death in R2

313666
type: SpeciesReference
stoichiometry: 1.0
species: 264647

264647
type: Species
is version of: http://identifiers.org/taxonomy/9606
is: SBO:0000240
constant: false
boundary condition: false
has only substance units: true
initial concentration: NaN
initial amount: 0.0
in compartment: 264638

264690
type: Reaction
kinetic law: 314199
product: 314187
reactant: 314175
is: SBO:0000375
fast: false
reversible: false
name: Recovery (J1)

314187
type: SpeciesReference
stoichiometry: 1.0
species: 264658

264658
type: Species
is version of: http://identifiers.org/taxonomy/9606
is: SBO:0000240
constant: false
boundary condition: false
has only substance units: true
initial concentration: NaN
initial amount: 0.0
in compartment: 264638

314175
type: SpeciesReference
stoichiometry: 1.0
species: 264655

264643
type: Species
has version: http://identifiers.org/taxonomy/9606
has version: http://identifiers.org/taxonomy/520
in compartment: 264638
initial amount: 1.0E-6
has only substance units: true
is: SBO:0000240
boundary condition: false
constant: false
initial concentration: NaN

264759
type: Parameter
is: SBO:0000348
constant: true
units: metaid_0000072
value: 20.0
name: immune period (yr)

264758
type: Parameter
is: SBO:0000348
constant: true
units: metaid_0000073
value: 21.0
name: infectious period (d)

264765
type: Parameter
notes: fraction of individuals immune against strain 1 exclusively after infection
is: SBO:0000360
constant: false
units: dimensionless
value: NaN

264651
type: Species
initial amount: 0.5
initial concentration: NaN
boundary condition: false
is: SBO:0000240
is version of: http://identifiers.org/taxonomy/520
has only substance units: true
is version of: http://identifiers.org/taxonomy/9606
in compartment: 264638
constant: false

264664
type: Reaction
kinetic law: 313606
reactant: 313593
is version of: GO:0016265
is: SBO:0000375
fast: false
reversible: false
name: Death in I2

313593
type: SpeciesReference
stoichiometry: 1.0
species: 264643

264646
type: Species
is version of: http://identifiers.org/taxonomy/9606
is: SBO:0000240
constant: false
boundary condition: false
has only substance units: true
initial concentration: NaN
initial amount: 0.439407
in compartment: 264638

264666
type: Reaction
kinetic law: 313654
reactant: 313642
is version of: GO:0016265
is: SBO:0000375
fast: false
reversible: false
name: Death in R1

313642
type: SpeciesReference
stoichiometry: 1.0
species: 264646

264749
type: Parameter
notes: fraction of individuals vaccinated at birth
is: SBO:0000380
constant: true
units: dimensionless
value: 1.0

264766
type: Parameter
notes: fraction of individuals immune against strain 2 exclusively after infection
is: SBO:0000360
constant: false
units: dimensionless
value: NaN

264760
type: Parameter
is: SBO:0000348
constant: true
units: metaid_0000072
value: 50.0
name: vaccine immune period (yr)

metaid_0000071
type: SBMLUnitsDef
unit: 313399
name: individuals

313399
type: SBMLUnit
exponent: 1.0
scale: 0
multipler: 1.0
kind: ITEM

264674
type: Reaction
kinetic law: 313750
reactant: 313738
is version of: GO:0016265
is: SBO:0000375
fast: false
reversible: false
name: Death in Rp

313738
type: SpeciesReference
stoichiometry: 1.0
species: 264658

264673
type: Reaction
kinetic law: 313726
reactant: 313714
is version of: GO:0016265
is: SBO:0000375
fast: false
reversible: false
name: Death in J2

313714
type: SpeciesReference
stoichiometry: 1.0
species: 264654

264654
type: Species
has only substance units: true
has version: http://identifiers.org/taxonomy/9606
initial concentration: NaN
in compartment: 264638
constant: false
is: SBO:0000240
boundary condition: false
has version: http://identifiers.org/taxonomy/520
initial amount: 0.0

264751
type: Parameter
is: SBO:0000380
constant: true
units: dimensionless
value: 0.5

264750
type: Parameter
is: SBO:0000380
constant: true
units: dimensionless
value: 0.7

264692
type: Reaction
kinetic law: 314272
product: 314260
reactant: 314248
is: SBO:0000375
fast: false
reversible: false
name: Recovery (Iv2)

314260
type: SpeciesReference
stoichiometry: 1.0
species: 264658

314248
type: SpeciesReference
stoichiometry: 1.0
species: 264651

264691
type: Reaction
kinetic law: 314236
product: 314224
reactant: 314212
is: SBO:0000375
fast: false
reversible: false
name: Recovery (J2)

314224
type: SpeciesReference
stoichiometry: 1.0
species: 264658

314212
type: SpeciesReference
stoichiometry: 1.0
species: 264654

264694
type: Reaction
kinetic law: 314345
product: 314333
reactant: 314320
is: SBO:0000375
fast: false
reversible: false
name: Loss of Immunity (R2)

314333
type: SpeciesReference
stoichiometry: 1.0
species: 264641

314320
type: SpeciesReference
stoichiometry: 1.0
species: 264647

264681
type: Reaction
product: 313910
modifier: 313946
modifier: 313922
reversible: false
name: Primary Infection of V with strain 2
is: SBO:0000375
kinetic law: 313958
fast: false
modifier: 313934
reactant: 313898

313910
type: SpeciesReference
stoichiometry: 1.0
species: 264651

313898
type: SpeciesReference
stoichiometry: 1.0
species: 264650

metaid_0000005
type: Parameter
notes: transmission rate
is: SBO:0000023
constant: false
units: metaid_0000074
value: NaN

metaid_0000074
type: SBMLUnitsDef
unit: 313435
name: per_year

313435
type: SBMLUnit
exponent: -1.0
scale: 0
multipler: 3.1536E7
kind: SECOND

264687
type: Reaction
name: Secondary Infection with strain 2
modifier: 314127
is: SBO:0000375
product: 314115
fast: false
reactant: 314103
modifier: 314151
reversible: false
modifier: 314139
kinetic law: 314163

314115
type: SpeciesReference
stoichiometry: 1.0
species: 264654

314103
type: SpeciesReference
stoichiometry: 1.0
species: 264646

264642
type: Species
has version: http://identifiers.org/taxonomy/520
is: SBO:0000240
has only substance units: true
in compartment: 264638
has version: http://identifiers.org/taxonomy/9606
boundary condition: false
constant: false
initial amount: 0.00176967
initial concentration: NaN

264678
type: Reaction
modifier: 313862
modifier: 313849
reversible: false
modifier: 313874
product: 313837
is: SBO:0000375
name: Primary Infection with strain 2
fast: false
reactant: 313825
kinetic law: 313886

313837
type: SpeciesReference
stoichiometry: 1.0
species: 264643

313825
type: SpeciesReference
stoichiometry: 1.0
species: 264641

264677
type: Reaction
modifier: 313788
modifier: 313800
fast: false
reactant: 313763
product: 313776
reversible: false
name: Primary Infection with strain 1
is: SBO:0000375
kinetic law: 313813

313763
type: SpeciesReference
stoichiometry: 1.0
species: 264641

313776
type: SpeciesReference
stoichiometry: 1.0
species: 264642

264767
type: Parameter
notes: fraction of individuals immune to both strains
is: SBO:0000360
constant: false
units: dimensionless
value: NaN

264761
type: Parameter
notes: fraction of individuals infected with strain 1
is: SBO:0000360
constant: false
units: dimensionless
value: NaN

264696
type: Reaction
kinetic law: 314418
product: 314406
reactant: 314394
is: SBO:0000375
fast: false
reversible: false
name: Loss of Immunity (V)

314406
type: SpeciesReference
stoichiometry: 1.0
species: 264641

314394
type: SpeciesReference
stoichiometry: 1.0
species: 264650

264695
type: Reaction
kinetic law: 314382
product: 314370
reactant: 314357
is: SBO:0000375
fast: false
reversible: false
name: Loss of Immunity (Rp)

314370
type: SpeciesReference
stoichiometry: 1.0
species: 264641

314357
type: SpeciesReference
stoichiometry: 1.0
species: 264658

264685
type: Reaction
kinetic law: 314030
product: 314018
reactant: 314006
is: SBO:0000375
fast: false
reversible: false
name: Recovery (I2)

314018
type: SpeciesReference
stoichiometry: 1.0
species: 264647

314006
type: SpeciesReference
stoichiometry: 1.0
species: 264643

264762
type: Parameter
notes: fraction of individuals infected with strain 2
is: SBO:0000360
constant: false
units: dimensionless
value: NaN

metaid_0000003
type: Parameter
notes: birth/death rate
is: SBO:0000022
constant: false
units: metaid_0000074
value: NaN

264682
type: Reaction
kinetic law: 313994
product: 313982
reactant: 313970
is: SBO:0000375
fast: false
reversible: false
name: Recovery (I1)

313982
type: SpeciesReference
stoichiometry: 1.0
species: 264646

313970
type: SpeciesReference
stoichiometry: 1.0
species: 264642

264661
type: Reaction
kinetic law: 313532
reactant: 313520
is version of: GO:0016265
is: SBO:0000375
fast: false
reversible: false
name: Death in S

313520
type: SpeciesReference
stoichiometry: 1.0
species: 264641

metaid_0000006
type: Parameter
notes: basic reproductive ratio (beta/(gamma+mu))
is: SBO:0000002
constant: true
units: dimensionless
value: 17.0

264693
type: Reaction
kinetic law: 314308
product: 314296
reactant: 314284
is: SBO:0000375
fast: false
reversible: false
name: Loss of Immunity (R1)

314296
type: SpeciesReference
stoichiometry: 1.0
species: 264641

314284
type: SpeciesReference
stoichiometry: 1.0
species: 264646

264757
type: Parameter
notes: rate of immunity loss of vacinated individuals
is: SBO:0000022
constant: false
units: metaid_0000074
value: NaN

metaid_0000007
type: Parameter
notes: recovery rate
is: SBO:0000022
constant: false
units: metaid_0000074
value: NaN

264764
type: Parameter
notes: fraction of vaccinated uninfected individuals
is: SBO:0000360
constant: false
units: dimensionless
value: NaN

metaid_0000013
type: Parameter
notes: rate of immunity loss
is: SBO:0000022
constant: false
units: metaid_0000074
value: NaN

264663
type: Reaction
kinetic law: 313581
reactant: 313569
is version of: GO:0016265
is: SBO:0000375
fast: false
reversible: false
name: Death in I1

313569
type: SpeciesReference
stoichiometry: 1.0
species: 264642

264686
type: Reaction
reactant: 314042
fast: false
modifier: 314078
kinetic law: 314090
product: 314054
reversible: false
is: SBO:0000375
modifier: 314066
name: Secondary Infection with strain 1

314042
type: SpeciesReference
stoichiometry: 1.0
species: 264647

314054
type: SpeciesReference
stoichiometry: 1.0
species: 264655

264665
type: Reaction
kinetic law: 313630
reactant: 313618
is version of: GO:0016265
is: SBO:0000375
fast: false
reversible: false
name: Death in Iv2

313618
type: SpeciesReference
stoichiometry: 1.0
species: 264651

264752
type: Parameter
is: SBO:0000380
constant: true
units: dimensionless
value: 0.5

264755
type: Parameter
is: SBO:0000380
constant: true
units: dimensionless
value: 0.5

264763
type: Parameter
notes: fraction of susceptible individuals
is: SBO:0000360
constant: false
units: dimensionless
value: NaN

W3 CDTF: Wed Apr 21 00:54:23 BST 2010

W3 CDTF: Tue May 15 22:55:51 BST 2012

ORG:
  orgname: EMBL-EBI
n:
  given: Lukas
  family: Endler