314394
stoichiometry: 1.0
species: 264650
type: SpeciesReference

313714
stoichiometry: 1.0
species: 264654
type: SpeciesReference

314175
stoichiometry: 1.0
species: 264655
type: SpeciesReference

313593
stoichiometry: 1.0
species: 264643
type: SpeciesReference

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

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

314054
stoichiometry: 1.0
species: 264655
type: SpeciesReference

264681
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
type: Reaction
reactant: 313898

314212
stoichiometry: 1.0
species: 264654
type: SpeciesReference

264643
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
type: Species
is: SBO:0000240
boundary condition: false
constant: false
initial concentration: NaN

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

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

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

313618
stoichiometry: 1.0
species: 264651
type: SpeciesReference

313690
stoichiometry: 1.0
species: 264655
type: SpeciesReference

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

264655
initial amount: 0.0
type: Species
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

313763
stoichiometry: 1.0
species: 264641
type: SpeciesReference

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

313837
stoichiometry: 1.0
species: 264643
type: SpeciesReference

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

313520
stoichiometry: 1.0
species: 264641
type: SpeciesReference

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

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

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

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

314357
stoichiometry: 1.0
species: 264658
type: SpeciesReference

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

314296
stoichiometry: 1.0
species: 264641
type: SpeciesReference

264658
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
type: Species

314224
stoichiometry: 1.0
species: 264658
type: SpeciesReference

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

metaid_0000072
unit: 313411
name: years
type: SBMLUnitsDef

264650
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
type: Species

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

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

313776
stoichiometry: 1.0
species: 264642
type: SpeciesReference

313447
stoichiometry: 1.0
species: 264641
type: SpeciesReference

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

313545
stoichiometry: 1.0
species: 264650
type: SpeciesReference

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

313982
stoichiometry: 1.0
species: 264646
type: SpeciesReference

314018
stoichiometry: 1.0
species: 264647
type: SpeciesReference

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

313898
stoichiometry: 1.0
species: 264650
type: SpeciesReference

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

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

313642
stoichiometry: 1.0
species: 264646
type: SpeciesReference

metaid_0000071
unit: 313399
name: individuals
type: SBMLUnitsDef

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

314284
stoichiometry: 1.0
species: 264646
type: SpeciesReference

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

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

264646
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
type: Species

313825
stoichiometry: 1.0
species: 264641
type: SpeciesReference

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

314103
stoichiometry: 1.0
species: 264646
type: SpeciesReference

metaid_0000074
unit: 313435
name: per_year
type: SBMLUnitsDef

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

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

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

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

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

264647
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
type: Species

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

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

313970
stoichiometry: 1.0
species: 264642
type: SpeciesReference

313738
stoichiometry: 1.0
species: 264658
type: SpeciesReference

314406
stoichiometry: 1.0
species: 264641
type: SpeciesReference

313910
stoichiometry: 1.0
species: 264651
type: SpeciesReference

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

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

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

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

264640
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
type: Species
initial concentration: NaN
constant: false

metaid_0000073
unit: 313423
name: days
type: SBMLUnitsDef

314370
stoichiometry: 1.0
species: 264641
type: SpeciesReference

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

314006
stoichiometry: 1.0
species: 264643
type: SpeciesReference

BIOMD0000000294
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
type: SBMLModel
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…

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

264651
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
type: Species
in compartment: 264638
constant: false

314333
stoichiometry: 1.0
species: 264641
type: SpeciesReference

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

314248
stoichiometry: 1.0
species: 264651
type: SpeciesReference

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

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

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

314042
stoichiometry: 1.0
species: 264647
type: SpeciesReference

314115
stoichiometry: 1.0
species: 264654
type: SpeciesReference

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

264641
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
type: Species

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

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

264654
has only substance units: true
has version: http://identifiers.org/taxonomy/9606
type: Species
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

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

314187
stoichiometry: 1.0
species: 264658
type: SpeciesReference

313666
stoichiometry: 1.0
species: 264647
type: SpeciesReference

314260
stoichiometry: 1.0
species: 264658
type: SpeciesReference

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

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

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

264642
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
type: Species
constant: false
initial amount: 0.00176967
initial concentration: NaN

314320
stoichiometry: 1.0
species: 264647
type: SpeciesReference

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

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

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

313569
stoichiometry: 1.0
species: 264642
type: SpeciesReference

313484
stoichiometry: 1.0
species: 264650
type: SpeciesReference

orgname: EMBL-EBI

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

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

n:
  given: Lukas
  family: Endler