metaid_0000006
notes: basic reproductive ratio (beta/gamma) pathogen 1
constant: true
units: dimensionless
value: 17.0
type: Parameter

metaid_0000073
unit: 943345
name: days
type: SBMLUnitsDef

metaid_0000033
is version of: http://identifiers.org/taxonomy/9606
is: SBO:0000240
constant: false
boundary condition: false
has only substance units: true
initial concentration: 0.0
initial amount: NaN
in compartment: metaid_0000027
type: Species

metaid_0000053
kinetic law: 943443
reactant: 943431
is version of: GO:0016265
is: SBO:0000375
fast: false
reversible: false
name: Death in I_1
type: Reaction

943672
stoichiometry: 1.0
species: metaid_0000029
type: SpeciesReference

metaid_0000063
reactant: 943816
modifier: 943852
reversible: false
modifier: 943864
product: 943828
name: Secondary Infection with strain 2
modifier: 943840
fast: false
kinetic law: 943876
is: SBO:0000375
type: Reaction

944045
stoichiometry: 1.0
species: metaid_0000029
type: SpeciesReference

943961
stoichiometry: 1.0
species: metaid_0000034
type: SpeciesReference

metaid_0000054
kinetic law: 943467
reactant: 943455
is version of: GO:0016265
is: SBO:0000375
fast: false
reversible: false
name: Death in I_2
type: Reaction

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

943479
stoichiometry: 1.0
species: metaid_0000032
type: SpeciesReference

943900
stoichiometry: 1.0
species: metaid_0000032
type: SpeciesReference

943816
stoichiometry: 1.0
species: metaid_0000032
type: SpeciesReference

metaid_0000074
unit: 943357
name: per_year
type: SBMLUnitsDef

metaid_0000032
is version of: http://identifiers.org/taxonomy/9606
is: SBO:0000240
constant: false
boundary condition: false
has only substance units: true
initial concentration: 0.93733
initial amount: NaN
in compartment: metaid_0000027
type: Species

943345
exponent: 1.0
scale: 0
multipler: 86400.0
kind: SECOND
type: SBMLUnit

metaid_0000064
kinetic law: 943913
product: 943900
reactant: 943888
is: SBO:0000375
fast: false
reversible: false
name: Recovery (I_1)
type: Reaction

metaid_0000007
notes: recovery rate from disease 1
constant: false
units: metaid_0000074
value: NaN
type: Parameter

943431
stoichiometry: 1.0
species: metaid_0000030
type: SpeciesReference

metaid_0000065
kinetic law: 943949
product: 943937
reactant: 943925
is: SBO:0000375
fast: false
reversible: false
name: Recovery (I_2)
type: Reaction

metaid_0000055
kinetic law: 943491
reactant: 943479
is version of: GO:0016265
is: SBO:0000375
fast: false
reversible: false
name: Death in R_1
type: Reaction

metaid_0000027
is: GO:0043245
is: SBO:0000290
constant: true
size: 1.0
spatial dimensions: 3.0
name: environment
type: Compartment

metaid_0000031
has version: http://identifiers.org/taxonomy/520
has only substance units: true
initial concentration: 1.0E-6
in compartment: metaid_0000027
type: Species
constant: false
initial amount: NaN
is: SBO:0000240
has version: http://identifiers.org/taxonomy/9606
boundary condition: false

metaid_0000012
constant: true
units: metaid_0000073
value: 21.0
name: infectious period 2
type: Parameter

943684
stoichiometry: 1.0
species: metaid_0000031
type: SpeciesReference

metaid_0000018
constant: false
units: dimensionless
value: NaN
type: Parameter

metaid_0000061
type: Reaction
modifier: 943720
modifier: 943708
reactant: 943672
product: 943684
fast: false
modifier: 943696
kinetic law: 943732
is: SBO:0000375
name: Primary Infection with strain 2
reversible: false

metaid_0000008
notes: transmission rate pathogen 2
constant: false
units: metaid_0000074
value: NaN
type: Parameter

metaid_0000021
constant: false
units: dimensionless
value: NaN
type: Parameter

metaid_0000020
constant: false
units: dimensionless
value: NaN
type: Parameter

metaid_0000056
kinetic law: 943515
reactant: 943503
is version of: GO:0016265
is: SBO:0000375
fast: false
reversible: false
name: Death in R_2
type: Reaction

943828
stoichiometry: 1.0
species: metaid_0000035
type: SpeciesReference

943503
stoichiometry: 1.0
species: metaid_0000033
type: SpeciesReference

943973
stoichiometry: 1.0
species: metaid_0000036
type: SpeciesReference

metaid_0000011
constant: true
units: metaid_0000073
value: 21.0
name: infectious period 1
type: Parameter

943575
stoichiometry: 1.0
species: metaid_0000036
type: SpeciesReference

metaid_0000030
has version: http://identifiers.org/taxonomy/520
initial concentration: 0.003775
type: Species
in compartment: metaid_0000027
has version: http://identifiers.org/taxonomy/9606
is: SBO:0000240
boundary condition: false
has only substance units: true
constant: false
initial amount: NaN

metaid_0000028
is version of: http://identifiers.org/taxonomy/9606
is: SBO:0000240
constant: false
boundary condition: false
has only substance units: true
initial concentration: 1.0
initial amount: NaN
in compartment: metaid_0000027
type: Species

metaid_0000019
constant: false
units: dimensionless
value: NaN
type: Parameter

metaid_0000062
modifier: 943780
reversible: false
name: Secondary Infection with strain 1
kinetic law: 943804
modifier: 943768
is: SBO:0000375
product: 943756
fast: false
reactant: 943744
modifier: 943792
type: Reaction

metaid_0000009
notes: basic reproductive ratio (beta/gamma) pathogen 2
constant: true
units: dimensionless
value: 17.0
type: Parameter

943357
exponent: -1.0
scale: 0
multipler: 3.1536E7
kind: SECOND
type: SBMLUnit

metaid_0000029
is version of: http://identifiers.org/taxonomy/9606
is: SBO:0000240
constant: false
boundary condition: false
has only substance units: true
initial concentration: 0.0588912
initial amount: NaN
in compartment: metaid_0000027
type: Species

metaid_0000057
kinetic law: 943539
reactant: 943527
is version of: GO:0016265
is: SBO:0000375
fast: false
reversible: false
name: Death in I_1p
type: Reaction

944081
stoichiometry: 1.0
species: metaid_0000029
type: SpeciesReference

metaid_0000010
notes: recovery rate from disease 2
constant: false
units: metaid_0000074
value: NaN
type: Parameter

metaid_0000023
notes: cross-immunity
constant: true
units: dimensionless
value: 0.2
type: Parameter

943756
stoichiometry: 1.0
species: metaid_0000034
type: SpeciesReference

metaid_0000016
notes: force of infection strain 1
constant: false
units: metaid_0000074
value: NaN
type: Parameter

metaid_0000068
kinetic law: 944057
product: 944045
reactant: 944033
is: SBO:0000375
fast: false
reversible: false
name: Loss of Immunity (R_1)
type: Reaction

BIOMD0000000249
rule: metaid_0000048
units def: metaid_0000072
reaction: metaid_0000062
reaction: metaid_0000052
parameter: metaid_0000022
parameter: metaid_0000012
is: MODEL1003290000
parameter: metaid_0000016
parameter: metaid_0000006
rule: metaid_0000049
rule: metaid_0000041
parameter: metaid_0000019
parameter: metaid_0000009
rule: metaid_0000039
parameter: metaid_0000020
species: metaid_0000030
rule: metaid_0000043
species: metaid_0000028
reaction: metaid_0000055
type: SBMLModel
occurs in: http://identifiers.org/taxonomy/520
parameter: metaid_0000021
parameter: metaid_0000011
species: metaid_0000032
parameter: metaid_0000015
parameter: metaid_0000005
is version of: DOID:1116
volume units: 845199
reaction: metaid_0000068
reaction: metaid_0000058
reaction: metaid_0000061
reaction: metaid_0000051
reaction: metaid_0000053
rule: metaid_0000037
species: metaid_0000029
reaction: metaid_0000064
rule: metaid_0000042
rule: metaid_0000044
parameter: metaid_0000018
parameter: metaid_0000008
occurs in: http://identifiers.org/taxonomy/9606
rule: metaid_0000045
species: metaid_0000034
is described by: http://identifiers.org/pubmed/16615206
species: metaid_0000031
reaction: metaid_0000054
reaction: metaid_0000067
reaction: metaid_0000065
reaction: metaid_0000057
species: metaid_0000033
units def: metaid_0000073
units def: metaid_0000074
reaction: metaid_0000070
reaction: metaid_0000060
parameter: metaid_0000010
parameter: metaid_0000014
parameter: metaid_0000004
has version: A37
curated: true
time units: metaid_0000072
length unit: length
parameter: metaid_0000023
parameter: metaid_0000013
parameter: metaid_0000017
parameter: metaid_0000007
rule: metaid_0000050
rule: metaid_0000046
rule: metaid_0000040
substance units: metaid_0000071
rule: metaid_0000038
area units: metaid_0000005
compartment: metaid_0000027
reaction: metaid_0000063
rule: metaid_0000047
species: metaid_0000035
notes: This is the model described in the article: Integrating life history and cross-immunity into the evolutionary dynamics of pathogens. Restif O, Grenfell BT. Proc Biol Sci. 2006 Feb 22;273(1585):409-16. PMID: 16615206 , doi: 10.1098/rspb.2005.3335 ; Abstract: Models for the diversity and evolution of pathogens have branched into two main directions: the adaptive dynamics of quantitative life-history traits (notably virulence) and the maintenance and invasion of multiple, antigenically diverse strains that interact with the host's immune memory. In a first attempt to reconcile these two approaches, we developed a simple modelling framework where two strains of pathogens, defined by a pair of life-history traits (infectious period and infectivity), interfere through a given level of cross-immunity. We used whooping cough as a potential example, but the framework proposed here could be applied to other acute infectious diseases. Specifically, we analysed the effects of these parameters on the invasion dynamics of one strain into a population, where the second strain is endemic. Whereas the deterministic version of the model converges towards stable coexistence of the two strains in most cases, stochastic simulations showed that transient epidemic dynamics can cause the extinction of either strain. Thus ecological dynamics, modulated by the immune parameters, eventually determine the adaptive value of different pathogen genotypes. We advocate an integrative view of pathogen dynamics at the crossroads of immunology, epidemiology and evolution, as a way towards efficient control of infectious diseases. 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 reproduces the deterministic time courses. Stochastic interpretation with Copasi UI gave results similar to the article, but was not extensively test…
species: metaid_0000036
parameter: metaid_0000003
name: Restif2006_Whooping_Cough
reaction: metaid_0000066

943925
stoichiometry: 1.0
species: metaid_0000031
type: SpeciesReference

943407
stoichiometry: 1.0
species: metaid_0000029
type: SpeciesReference

metaid_0000058
kinetic law: 943563
reactant: 943551
is version of: GO:0016265
is: SBO:0000375
fast: false
reversible: false
name: Death in I_2p
type: Reaction

943321
exponent: 1.0
scale: 0
multipler: 1.0
kind: ITEM
type: SBMLUnit

944107
stoichiometry: 1.0
species: metaid_0000036
type: SpeciesReference

metaid_0000022
constant: false
units: dimensionless
value: NaN
type: Parameter

metaid_0000060
modifier: 943648
modifier: 943624
is: SBO:0000375
fast: false
modifier: 943636
kinetic law: 943660
reactant: 943599
reversible: false
type: Reaction
name: Primary Infection with strain 1
product: 943611

943551
stoichiometry: 1.0
species: metaid_0000035
type: SpeciesReference

944069
stoichiometry: 1.0
species: metaid_0000033
type: SpeciesReference

metaid_0000017
constant: false
units: dimensionless
value: NaN
type: Parameter

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

metaid_0000036
is version of: http://identifiers.org/taxonomy/9606
is: SBO:0000240
constant: false
boundary condition: false
has only substance units: true
initial concentration: 0.0
initial amount: NaN
in compartment: metaid_0000027
type: Species

metaid_0000070
kinetic law: 944131
product: 944119
reactant: 944107
is: SBO:0000375
fast: false
reversible: false
name: Loss of Immunity (R_p)
type: Reaction

metaid_0000069
kinetic law: 944094
product: 944081
reactant: 944069
is: SBO:0000375
fast: false
reversible: false
name: Loss of Immunity (R_2)
type: Reaction

943455
stoichiometry: 1.0
species: metaid_0000031
type: SpeciesReference

943369
stoichiometry: 1.0
species: metaid_0000029
type: SpeciesReference

943888
stoichiometry: 1.0
species: metaid_0000030
type: SpeciesReference

metaid_0000059
kinetic law: 943587
reactant: 943575
is version of: GO:0016265
is: SBO:0000375
fast: false
reversible: false
name: Death in R_p
type: Reaction

metaid_0000014
constant: true
units: metaid_0000072
value: 20.0
name: immune period
type: Parameter

943611
stoichiometry: 1.0
species: metaid_0000030
type: SpeciesReference

metaid_0000035
constant: false
has version: http://identifiers.org/taxonomy/520
is: SBO:0000240
has version: http://identifiers.org/taxonomy/9606
initial amount: NaN
boundary condition: false
initial concentration: 0.0
has only substance units: true
type: Species
in compartment: metaid_0000027

944033
stoichiometry: 1.0
species: metaid_0000032
type: SpeciesReference

943744
stoichiometry: 1.0
species: metaid_0000033
type: SpeciesReference

metaid_0000071
unit: 943321
name: individuals
type: SBMLUnitsDef

943599
stoichiometry: 1.0
species: metaid_0000029
type: SpeciesReference

metaid_0000066
kinetic law: 943985
product: 943973
reactant: 943961
is: SBO:0000375
fast: false
reversible: false
name: Recovery (I_1p)
type: Reaction

943997
stoichiometry: 1.0
species: metaid_0000035
type: SpeciesReference

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

metaid_0000051
kinetic law: 943394
modifier: 943382
product: 943369
is version of: GO:0007567
is: SBO:0000375
fast: false
reversible: false
name: Birth
type: Reaction

943333
exponent: 1.0
scale: 0
multipler: 3.1536E7
kind: SECOND
type: SBMLUnit

943937
stoichiometry: 1.0
species: metaid_0000033
type: SpeciesReference

944009
stoichiometry: 1.0
species: metaid_0000036
type: SpeciesReference

metaid_0000015
notes: force of infection strain 1
constant: false
units: metaid_0000074
value: NaN
type: Parameter

944119
stoichiometry: 1.0
species: metaid_0000029
type: SpeciesReference

metaid_0000034
type: Species
is: SBO:0000240
has version: http://identifiers.org/taxonomy/9606
in compartment: metaid_0000027
boundary condition: false
constant: false
initial concentration: 0.0
has version: http://identifiers.org/taxonomy/520
has only substance units: true
initial amount: NaN

943527
stoichiometry: 1.0
species: metaid_0000034
type: SpeciesReference

metaid_0000005
notes: transmission rate pathogen 1
constant: false
units: metaid_0000074
value: NaN
type: Parameter

metaid_0000072
unit: 943333
name: years
type: SBMLUnitsDef

metaid_0000067
kinetic law: 944021
product: 944009
reactant: 943997
is: SBO:0000375
fast: false
reversible: false
name: Recovery (I_2p)
type: Reaction

metaid_0000052
kinetic law: 943419
reactant: 943407
is version of: GO:0016265
is: SBO:0000375
fast: false
reversible: false
name: Death in S
type: Reaction

W3 CDTF: Tue May 15 22:58:47 BST 2012

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

given: Lukas
family: Endler

orgname: EMBL-EBI