GitHub

COVID-19 Composition Model

using StockFlow

using Catlab
using Catlab.CategoricalAlgebra
using LabelledArrays
using OrdinaryDiffEq
using Plots

using Catlab.Graphics
using Catlab.Programs
using Catlab.WiringDiagrams

display_uwd(ex) = to_graphviz(ex, box_labels=:name, junction_labels=:variable, edge_attrs=Dict(:len=>"1"));

Define functions ϕ of flows in the SEIRH model

fNewIncidence(u,p,t)=p.β*u.S*u.I/p.N
fNewInfectious(u,p,t)=u.E*p.ri
fNewRecovery(u,p,t)=u.I/p.tr * (1.0-p.fH )
fWaningImmunityR(u,p,t)=u.R/p.tw
fHICUAdmission(u,p,t) = u.I/p.tr * p.fH * p.fICU
fHNICUAdmission(u,p,t) = u.I/p.tr * p.fH * (1.0-p.fICU)
fOutICU(u,p,t) = u.HICU/p.tICU
fRecoveryH(u,p,t)= u.HNICU/p.tH
fRecoveryH (generic function with 1 method)

StockAndFlowp(stocks, (flow=>function, upstream=>downstream) => stocks linked)

seirh = StockAndFlowp((:S, :E, :I, :R, :HICU, :HNICU),
   ((:NewIncidence=>fNewIncidence, :S=>:E) => (:S, :I),
    (:NewInfectious=>fNewInfectious, :E=>:I) => :E,
    (:NewRecovery=>fNewRecovery, :I=>:R) => :I,
    (:WaningImmunityR=>fWaningImmunityR, :R=>:S) => :R,
    (:HICUAdmission=>fHICUAdmission, :I=>:HICU) => :I,
    (:HNICUAdmission=>fHNICUAdmission, :I=>:HNICU) => :I,
    (:OutICU=>fOutICU, :HICU=>:HNICU) => :HICU,
    (:RecoveryH=>fRecoveryH, :HNICU=>:R) => :HNICU))
StockAndFlowp {Flow:8, Stock:6, Link:9, Name:0, FuncFlow:0}
Flow u d fname ϕf
1 1 2 NewIncidence fNewIncidence
2 2 3 NewInfectious fNewInfectious
3 3 4 NewRecovery fNewRecovery
4 4 1 WaningImmunityR fWaningImmunityR
5 3 5 HICUAdmission fHICUAdmission
6 3 6 HNICUAdmission fHNICUAdmission
7 5 6 OutICU fOutICU
8 6 4 RecoveryH fRecoveryH
Stock sname
1 S
2 E
3 I
4 R
5 HICU
6 HNICU
Link s t
1 1 1
2 3 1
3 2 2
4 3 3
5 4 4
6 3 5
7 3 6
8 5 7
9 6 8

Graph(primitive stock-flow model, direction of the diagram - the default value is "LR" from left to right; users could also use "TB" from top to bottom) Graph(seirh)

Define functions ϕ of flows in the Vaccine model

fFirstdoseVaccine(u,p,t) = u.S * p.rv
fSeconddoseVaccine(u,p,t) = u.VP * p.rv
fWaningImmunityVP(u,p,t) = u.VP / p.tw
fWaningImmunityVF(u,p,t) = u.VF / p.tw
fNewIncidenceVP(u,p,t) = p.β*u.VP*u.I*(1.0-p.eP)/p.N
fNewIncidenceVF(u,p,t) = p.β*u.VF*u.I*(1.0-p.eF)/p.N
fNewIncidenceVF (generic function with 1 method)

Stock and flow diagram of Vaccine model

v = StockAndFlowp((:S, :E, :I, :VP, :VF),
   ((:FirstdoseVaccine=>fFirstdoseVaccine, :S=>:VP) => :S,
    (:SeconddoseVaccine=>fSeconddoseVaccine, :VP=>:VF) => :VP,
    (:WaningImmunityVP=>fWaningImmunityVP, :VP=>:S) => :VP,
    (:WaningImmunityVF=>fWaningImmunityVF, :VF=>:VP) => :VF,
    (:NewIncidenceVP=>fNewIncidenceVP, :VP=>:E) => (:VP, :I),
    (:NewIncidenceVF=>fNewIncidenceVF, :VF=>:E) => (:VF, :I)))
StockAndFlowp {Flow:6, Stock:5, Link:8, Name:0, FuncFlow:0}
Flow u d fname ϕf
1 1 4 FirstdoseVaccine fFirstdoseVaccine
2 4 5 SeconddoseVaccine fSeconddoseVaccine
3 4 1 WaningImmunityVP fWaningImmunityVP
4 5 4 WaningImmunityVF fWaningImmunityVF
5 4 2 NewIncidenceVP fNewIncidenceVP
6 5 2 NewIncidenceVF fNewIncidenceVF
Stock sname
1 S
2 E
3 I
4 VP
5 VF
Link s t
1 1 1
2 4 2
3 4 3
4 5 4
5 4 5
6 3 5
7 5 6
8 3 6

Graph(v,"TB")

Define functions ϕ of flows in the Persist Asymptomaticity model

fNewPersistentAsymptomaticity(u,p,t) = u.E * p.ria
fNewRecoveryIA(u,p,t) = u.IA / p.tr
fNewRecoveryIA (generic function with 1 method)

Stock and flow diagram of Persistent Asymptomaticity Model

ia = StockAndFlowp((:E, :IA, :R),
   ((:NewPersistentAsymptomaticity=>fNewPersistentAsymptomaticity, :E=>:IA) => :E,
    (:NewRecoveryIA=>fNewRecoveryIA, :IA=>:R) => :IA))
StockAndFlowp {Flow:2, Stock:3, Link:2, Name:0, FuncFlow:0}
Flow u d fname ϕf
1 1 2 NewPersistentAsymptomaticity fNewPersistentAsymptomaticity
2 2 3 NewRecoveryIA fNewRecoveryIA
Stock sname
1 E
2 IA
3 R
Link s t
1 1 1
2 2 2

Graph(ia)

covid = @relation (S, E, I, R) begin
    modelA(S,E,I,R)
    modelB(S,E,I)
    modelC(E,R)
end;
display_uwd(covid)

Open three Stock and Flow Diagrams

openseirh = Open(seirh, [:S], [:E], [:I], [:R])
openv = Open(v, [:S], [:E], [:I])
openia = Open(ia, [:E], [:R])
Catlab.CategoricalAlgebra.StructuredCospans.StructuredCospan{Catlab.CategoricalAlgebra.StructuredCospans.DiscreteACSet{ACSets.DenseACSets.AnonACSet{ACSets.Schemas.TypeLevelBasicSchema{Symbol, Tuple{:Stock}, Tuple{}, Tuple{:Name, :FuncFlow}, Tuple{(:sname, :Stock, :Name)}, Tuple{}}, Tuple{Symbol, Function}, @NamedTuple{Stock::ACSets.DenseACSets.IntParts, Name::ACSets.DenseACSets.IntParts, FuncFlow::ACSets.DenseACSets.IntParts}, @NamedTuple{sname::ACSets.ColumnImplementations.DenseColumn{Union{ACSets.ColumnImplementations.AttrVar, Symbol}, Vector{Union{ACSets.ColumnImplementations.AttrVar, Symbol}}}}, ACSets.DenseACSets.IntParts}, StockAndFlowp}, Catlab.CategoricalAlgebra.FreeDiagrams.Multicospan{StockAndFlowp, Catlab.CategoricalAlgebra.CSets.StructTightACSetTransformation{ACSets.Schemas.TypeLevelBasicSchema{Symbol, Tuple{:Flow, :Stock, :Link}, Tuple{(:u, :Flow, :Stock), (:d, :Flow, :Stock), (:s, :Link, :Stock), (:t, :Link, :Flow)}, Tuple{:Name, :FuncFlow}, Tuple{(:sname, :Stock, :Name), (:fname, :Flow, :Name), (:ϕf, :Flow, :FuncFlow)}, Tuple{}}, @NamedTuple{Flow::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Stock::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Link::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Name::Catlab.CategoricalAlgebra.FinSets.VarFunction{Symbol}, FuncFlow::Catlab.CategoricalAlgebra.FinSets.VarFunction{Function}}, StockAndFlowp, StockAndFlowp}, StaticArraysCore.SVector{2, Catlab.CategoricalAlgebra.CSets.StructTightACSetTransformation{ACSets.Schemas.TypeLevelBasicSchema{Symbol, Tuple{:Flow, :Stock, :Link}, Tuple{(:u, :Flow, :Stock), (:d, :Flow, :Stock), (:s, :Link, :Stock), (:t, :Link, :Flow)}, Tuple{:Name, :FuncFlow}, Tuple{(:sname, :Stock, :Name), (:fname, :Flow, :Name), (:ϕf, :Flow, :FuncFlow)}, Tuple{}}, @NamedTuple{Flow::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Stock::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Link::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Name::Catlab.CategoricalAlgebra.FinSets.VarFunction{Symbol}, FuncFlow::Catlab.CategoricalAlgebra.FinSets.VarFunction{Function}}, StockAndFlowp, StockAndFlowp}}}, StaticArraysCore.SVector{2, ACSets.DenseACSets.AnonACSet{ACSets.Schemas.TypeLevelBasicSchema{Symbol, Tuple{:Stock}, Tuple{}, Tuple{:Name, :FuncFlow}, Tuple{(:sname, :Stock, :Name)}, Tuple{}}, Tuple{Symbol, Function}, @NamedTuple{Stock::ACSets.DenseACSets.IntParts, Name::ACSets.DenseACSets.IntParts, FuncFlow::ACSets.DenseACSets.IntParts}, @NamedTuple{sname::ACSets.ColumnImplementations.DenseColumn{Union{ACSets.ColumnImplementations.AttrVar, Symbol}, Vector{Union{ACSets.ColumnImplementations.AttrVar, Symbol}}}}, ACSets.DenseACSets.IntParts}}}(Catlab.CategoricalAlgebra.FreeDiagrams.Multicospan{StockAndFlowp, Catlab.CategoricalAlgebra.CSets.StructTightACSetTransformation{ACSets.Schemas.TypeLevelBasicSchema{Symbol, Tuple{:Flow, :Stock, :Link}, Tuple{(:u, :Flow, :Stock), (:d, :Flow, :Stock), (:s, :Link, :Stock), (:t, :Link, :Flow)}, Tuple{:Name, :FuncFlow}, Tuple{(:sname, :Stock, :Name), (:fname, :Flow, :Name), (:ϕf, :Flow, :FuncFlow)}, Tuple{}}, @NamedTuple{Flow::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Stock::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Link::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Name::Catlab.CategoricalAlgebra.FinSets.VarFunction{Symbol}, FuncFlow::Catlab.CategoricalAlgebra.FinSets.VarFunction{Function}}, StockAndFlowp, StockAndFlowp}, StaticArraysCore.SVector{2, Catlab.CategoricalAlgebra.CSets.StructTightACSetTransformation{ACSets.Schemas.TypeLevelBasicSchema{Symbol, Tuple{:Flow, :Stock, :Link}, Tuple{(:u, :Flow, :Stock), (:d, :Flow, :Stock), (:s, :Link, :Stock), (:t, :Link, :Flow)}, Tuple{:Name, :FuncFlow}, Tuple{(:sname, :Stock, :Name), (:fname, :Flow, :Name), (:ϕf, :Flow, :FuncFlow)}, Tuple{}}, @NamedTuple{Flow::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Stock::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Link::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Name::Catlab.CategoricalAlgebra.FinSets.VarFunction{Symbol}, FuncFlow::Catlab.CategoricalAlgebra.FinSets.VarFunction{Function}}, StockAndFlowp, StockAndFlowp}}}(StockAndFlowp:
  Flow = 1:2
  Stock = 1:3
  Link = 1:2
  Name = 1:0
  FuncFlow = 1:0
  u : Flow → Stock = [1, 2]
  d : Flow → Stock = [2, 3]
  s : Link → Stock = [1, 2]
  t : Link → Flow = [1, 2]
  sname : Stock → Name = [:E, :IA, :R]
  fname : Flow → Name = [:NewPersistentAsymptomaticity, :NewRecoveryIA]
  ϕf : Flow → FuncFlow = Function[Main.fNewPersistentAsymptomaticity, Main.fNewRecoveryIA], Catlab.CategoricalAlgebra.CSets.StructTightACSetTransformation{ACSets.Schemas.TypeLevelBasicSchema{Symbol, Tuple{:Flow, :Stock, :Link}, Tuple{(:u, :Flow, :Stock), (:d, :Flow, :Stock), (:s, :Link, :Stock), (:t, :Link, :Flow)}, Tuple{:Name, :FuncFlow}, Tuple{(:sname, :Stock, :Name), (:fname, :Flow, :Name), (:ϕf, :Flow, :FuncFlow)}, Tuple{}}, @NamedTuple{Flow::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Stock::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Link::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Name::Catlab.CategoricalAlgebra.FinSets.VarFunction{Symbol}, FuncFlow::Catlab.CategoricalAlgebra.FinSets.VarFunction{Function}}, StockAndFlowp, StockAndFlowp}[ACSetTransformation((Flow = FinFunction(Int64[], 0, 2), Stock = FinFunction([1], 1, 3), Link = FinFunction(Int64[], 0, 2), Name = Catlab.CategoricalAlgebra.FinSets.VarFunction{Symbol}(FinDomFunction(Union{ACSets.ColumnImplementations.AttrVar, Symbol}[], FinSet(0), TypeSet(Union{ACSets.ColumnImplementations.AttrVar, Symbol})), FinSet(0)), FuncFlow = Catlab.CategoricalAlgebra.FinSets.VarFunction{Function}(FinDomFunction(Union{ACSets.ColumnImplementations.AttrVar, Function}[], FinSet(0), TypeSet(Union{ACSets.ColumnImplementations.AttrVar, Function})), FinSet(0))), StockAndFlowp {Flow:0, Stock:1, Link:0, Name:0, FuncFlow:0}, StockAndFlowp {Flow:2, Stock:3, Link:2, Name:0, FuncFlow:0}), ACSetTransformation((Flow = FinFunction(Int64[], 0, 2), Stock = FinFunction([3], 1, 3), Link = FinFunction(Int64[], 0, 2), Name = Catlab.CategoricalAlgebra.FinSets.VarFunction{Symbol}(FinDomFunction(Union{ACSets.ColumnImplementations.AttrVar, Symbol}[], FinSet(0), TypeSet(Union{ACSets.ColumnImplementations.AttrVar, Symbol})), FinSet(0)), FuncFlow = Catlab.CategoricalAlgebra.FinSets.VarFunction{Function}(FinDomFunction(Union{ACSets.ColumnImplementations.AttrVar, Function}[], FinSet(0), TypeSet(Union{ACSets.ColumnImplementations.AttrVar, Function})), FinSet(0))), StockAndFlowp {Flow:0, Stock:1, Link:0, Name:0, FuncFlow:0}, StockAndFlowp {Flow:2, Stock:3, Link:2, Name:0, FuncFlow:0})]), ACSets.DenseACSets.AnonACSet{ACSets.Schemas.TypeLevelBasicSchema{Symbol, Tuple{:Stock}, Tuple{}, Tuple{:Name, :FuncFlow}, Tuple{(:sname, :Stock, :Name)}, Tuple{}}, Tuple{Symbol, Function}, @NamedTuple{Stock::ACSets.DenseACSets.IntParts, Name::ACSets.DenseACSets.IntParts, FuncFlow::ACSets.DenseACSets.IntParts}, @NamedTuple{sname::ACSets.ColumnImplementations.DenseColumn{Union{ACSets.ColumnImplementations.AttrVar, Symbol}, Vector{Union{ACSets.ColumnImplementations.AttrVar, Symbol}}}}, ACSets.DenseACSets.IntParts}[ACSets.DenseACSets.AnonACSet{ACSets.Schemas.TypeLevelBasicSchema{Symbol, Tuple{:Stock}, Tuple{}, Tuple{:Name, :FuncFlow}, Tuple{(:sname, :Stock, :Name)}, Tuple{}}, Tuple{Symbol, Function}, @NamedTuple{Stock::ACSets.DenseACSets.IntParts, Name::ACSets.DenseACSets.IntParts, FuncFlow::ACSets.DenseACSets.IntParts}, @NamedTuple{sname::ACSets.ColumnImplementations.DenseColumn{Union{ACSets.ColumnImplementations.AttrVar, Symbol}, Vector{Union{ACSets.ColumnImplementations.AttrVar, Symbol}}}}, ACSets.DenseACSets.IntParts}:
  Stock = 1:1
  Name = 1:0
  FuncFlow = 1:0
  sname : Stock → Name = [:E], ACSets.DenseACSets.AnonACSet{ACSets.Schemas.TypeLevelBasicSchema{Symbol, Tuple{:Stock}, Tuple{}, Tuple{:Name, :FuncFlow}, Tuple{(:sname, :Stock, :Name)}, Tuple{}}, Tuple{Symbol, Function}, @NamedTuple{Stock::ACSets.DenseACSets.IntParts, Name::ACSets.DenseACSets.IntParts, FuncFlow::ACSets.DenseACSets.IntParts}, @NamedTuple{sname::ACSets.ColumnImplementations.DenseColumn{Union{ACSets.ColumnImplementations.AttrVar, Symbol}, Vector{Union{ACSets.ColumnImplementations.AttrVar, Symbol}}}}, ACSets.DenseACSets.IntParts}:
  Stock = 1:1
  Name = 1:0
  FuncFlow = 1:0
  sname : Stock → Name = [:R]])

Compose those three models according the UWD-algebra

openCOVID19 = oapply(covid, [openseirh, openv, openia])
Catlab.CategoricalAlgebra.StructuredCospans.StructuredMulticospan{Catlab.CategoricalAlgebra.StructuredCospans.DiscreteACSet{ACSets.DenseACSets.AnonACSet{ACSets.Schemas.TypeLevelBasicSchema{Symbol, Tuple{:Stock}, Tuple{}, Tuple{:Name, :FuncFlow}, Tuple{(:sname, :Stock, :Name)}, Tuple{}}, Tuple{Symbol, Function}, @NamedTuple{Stock::ACSets.DenseACSets.IntParts, Name::ACSets.DenseACSets.IntParts, FuncFlow::ACSets.DenseACSets.IntParts}, @NamedTuple{sname::ACSets.ColumnImplementations.DenseColumn{Union{ACSets.ColumnImplementations.AttrVar, Symbol}, Vector{Union{ACSets.ColumnImplementations.AttrVar, Symbol}}}}, ACSets.DenseACSets.IntParts}, StockAndFlowp}, Catlab.CategoricalAlgebra.FreeDiagrams.Multicospan{StockAndFlowp, Catlab.CategoricalAlgebra.CSets.StructTightACSetTransformation{ACSets.Schemas.TypeLevelBasicSchema{Symbol, Tuple{:Flow, :Stock, :Link}, Tuple{(:u, :Flow, :Stock), (:d, :Flow, :Stock), (:s, :Link, :Stock), (:t, :Link, :Flow)}, Tuple{:Name, :FuncFlow}, Tuple{(:sname, :Stock, :Name), (:fname, :Flow, :Name), (:ϕf, :Flow, :FuncFlow)}, Tuple{}}, @NamedTuple{Flow::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Stock::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Link::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Name::Catlab.CategoricalAlgebra.FinSets.VarFunction{Symbol}, FuncFlow::Catlab.CategoricalAlgebra.FinSets.VarFunction{Function}}, StockAndFlowp, StockAndFlowp}, Vector{Catlab.CategoricalAlgebra.CSets.StructTightACSetTransformation{ACSets.Schemas.TypeLevelBasicSchema{Symbol, Tuple{:Flow, :Stock, :Link}, Tuple{(:u, :Flow, :Stock), (:d, :Flow, :Stock), (:s, :Link, :Stock), (:t, :Link, :Flow)}, Tuple{:Name, :FuncFlow}, Tuple{(:sname, :Stock, :Name), (:fname, :Flow, :Name), (:ϕf, :Flow, :FuncFlow)}, Tuple{}}, @NamedTuple{Flow::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Stock::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Link::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Name::Catlab.CategoricalAlgebra.FinSets.VarFunction{Symbol}, FuncFlow::Catlab.CategoricalAlgebra.FinSets.VarFunction{Function}}, StockAndFlowp, StockAndFlowp}}}, Vector{Union{Nothing, ACSets.DenseACSets.AnonACSet{ACSets.Schemas.TypeLevelBasicSchema{Symbol, Tuple{:Stock}, Tuple{}, Tuple{:Name, :FuncFlow}, Tuple{(:sname, :Stock, :Name)}, Tuple{}}, Tuple{Symbol, Function}, @NamedTuple{Stock::ACSets.DenseACSets.IntParts, Name::ACSets.DenseACSets.IntParts, FuncFlow::ACSets.DenseACSets.IntParts}, @NamedTuple{sname::ACSets.ColumnImplementations.DenseColumn{Union{ACSets.ColumnImplementations.AttrVar, Symbol}, Vector{Union{ACSets.ColumnImplementations.AttrVar, Symbol}}}}, ACSets.DenseACSets.IntParts}}}}(Catlab.CategoricalAlgebra.FreeDiagrams.Multicospan{StockAndFlowp, Catlab.CategoricalAlgebra.CSets.StructTightACSetTransformation{ACSets.Schemas.TypeLevelBasicSchema{Symbol, Tuple{:Flow, :Stock, :Link}, Tuple{(:u, :Flow, :Stock), (:d, :Flow, :Stock), (:s, :Link, :Stock), (:t, :Link, :Flow)}, Tuple{:Name, :FuncFlow}, Tuple{(:sname, :Stock, :Name), (:fname, :Flow, :Name), (:ϕf, :Flow, :FuncFlow)}, Tuple{}}, @NamedTuple{Flow::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Stock::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Link::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Name::Catlab.CategoricalAlgebra.FinSets.VarFunction{Symbol}, FuncFlow::Catlab.CategoricalAlgebra.FinSets.VarFunction{Function}}, StockAndFlowp, StockAndFlowp}, Vector{Catlab.CategoricalAlgebra.CSets.StructTightACSetTransformation{ACSets.Schemas.TypeLevelBasicSchema{Symbol, Tuple{:Flow, :Stock, :Link}, Tuple{(:u, :Flow, :Stock), (:d, :Flow, :Stock), (:s, :Link, :Stock), (:t, :Link, :Flow)}, Tuple{:Name, :FuncFlow}, Tuple{(:sname, :Stock, :Name), (:fname, :Flow, :Name), (:ϕf, :Flow, :FuncFlow)}, Tuple{}}, @NamedTuple{Flow::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Stock::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Link::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Name::Catlab.CategoricalAlgebra.FinSets.VarFunction{Symbol}, FuncFlow::Catlab.CategoricalAlgebra.FinSets.VarFunction{Function}}, StockAndFlowp, StockAndFlowp}}}(StockAndFlowp:
  Flow = 1:16
  Stock = 1:9
  Link = 1:19
  Name = 1:0
  FuncFlow = 1:0
  u : Flow → Stock = [1, 2, 3, 4, 3, 3, 5, 6, 1, 7, 7, 8, 7, 8, 2, 9]
  d : Flow → Stock = [2, 3, 4, 1, 5, 6, 6, 4, 7, 8, 1, 7, 2, 2, 9, 4]
  s : Link → Stock = [1, 3, 2, 3, 4, 3, 3, 5, 6, 1, 7, 7, 8, 7, 3, 8, 3, 2, 9]
  t : Link → Flow = [1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 13, 14, 14, 15, 16]
  sname : Stock → Name = [:S, :E, :I, :R, :HICU, :HNICU, :VP, :VF, :IA]
  fname : Flow → Name = [:NewIncidence, :NewInfectious, :NewRecovery, :WaningImmunityR, :HICUAdmission, :HNICUAdmission, :OutICU, :RecoveryH, :FirstdoseVaccine, :SeconddoseVaccine, :WaningImmunityVP, :WaningImmunityVF, :NewIncidenceVP, :NewIncidenceVF, :NewPersistentAsymptomaticity, :NewRecoveryIA]
  ϕf : Flow → FuncFlow = Function[Main.fNewIncidence, Main.fNewInfectious, Main.fNewRecovery, Main.fWaningImmunityR, Main.fHICUAdmission, Main.fHNICUAdmission, Main.fOutICU, Main.fRecoveryH, Main.fFirstdoseVaccine, Main.fSeconddoseVaccine, Main.fWaningImmunityVP, Main.fWaningImmunityVF, Main.fNewIncidenceVP, Main.fNewIncidenceVF, Main.fNewPersistentAsymptomaticity, Main.fNewRecoveryIA], Catlab.CategoricalAlgebra.CSets.StructTightACSetTransformation{ACSets.Schemas.TypeLevelBasicSchema{Symbol, Tuple{:Flow, :Stock, :Link}, Tuple{(:u, :Flow, :Stock), (:d, :Flow, :Stock), (:s, :Link, :Stock), (:t, :Link, :Flow)}, Tuple{:Name, :FuncFlow}, Tuple{(:sname, :Stock, :Name), (:fname, :Flow, :Name), (:ϕf, :Flow, :FuncFlow)}, Tuple{}}, @NamedTuple{Flow::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Stock::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Link::Catlab.CategoricalAlgebra.FinSets.FinDomFunctionVector{Int64, Vector{Int64}, Catlab.CategoricalAlgebra.FinSets.FinSetInt}, Name::Catlab.CategoricalAlgebra.FinSets.VarFunction{Symbol}, FuncFlow::Catlab.CategoricalAlgebra.FinSets.VarFunction{Function}}, StockAndFlowp, StockAndFlowp}[ACSetTransformation((Flow = FinFunction(Int64[], 0, 16), Stock = FinFunction([1], 1, 9), Link = FinFunction(Int64[], 0, 19), Name = Catlab.CategoricalAlgebra.FinSets.VarFunction{Symbol}(FinDomFunction(Union{ACSets.ColumnImplementations.AttrVar, Symbol}[], FinSet(0), TypeSet(Union{ACSets.ColumnImplementations.AttrVar, Symbol})), FinSet(0)), FuncFlow = Catlab.CategoricalAlgebra.FinSets.VarFunction{Function}(FinDomFunction(Union{ACSets.ColumnImplementations.AttrVar, Function}[], FinSet(0), TypeSet(Union{ACSets.ColumnImplementations.AttrVar, Function})), FinSet(0))), StockAndFlowp {Flow:0, Stock:1, Link:0, Name:0, FuncFlow:0}, StockAndFlowp {Flow:16, Stock:9, Link:19, Name:0, FuncFlow:0}), ACSetTransformation((Flow = FinFunction(Int64[], 0, 16), Stock = FinFunction([2], 1, 9), Link = FinFunction(Int64[], 0, 19), Name = Catlab.CategoricalAlgebra.FinSets.VarFunction{Symbol}(FinDomFunction(Union{ACSets.ColumnImplementations.AttrVar, Symbol}[], FinSet(0), TypeSet(Union{ACSets.ColumnImplementations.AttrVar, Symbol})), FinSet(0)), FuncFlow = Catlab.CategoricalAlgebra.FinSets.VarFunction{Function}(FinDomFunction(Union{ACSets.ColumnImplementations.AttrVar, Function}[], FinSet(0), TypeSet(Union{ACSets.ColumnImplementations.AttrVar, Function})), FinSet(0))), StockAndFlowp {Flow:0, Stock:1, Link:0, Name:0, FuncFlow:0}, StockAndFlowp {Flow:16, Stock:9, Link:19, Name:0, FuncFlow:0}), ACSetTransformation((Flow = FinFunction(Int64[], 0, 16), Stock = FinFunction([3], 1, 9), Link = FinFunction(Int64[], 0, 19), Name = Catlab.CategoricalAlgebra.FinSets.VarFunction{Symbol}(FinDomFunction(Union{ACSets.ColumnImplementations.AttrVar, Symbol}[], FinSet(0), TypeSet(Union{ACSets.ColumnImplementations.AttrVar, Symbol})), FinSet(0)), FuncFlow = Catlab.CategoricalAlgebra.FinSets.VarFunction{Function}(FinDomFunction(Union{ACSets.ColumnImplementations.AttrVar, Function}[], FinSet(0), TypeSet(Union{ACSets.ColumnImplementations.AttrVar, Function})), FinSet(0))), StockAndFlowp {Flow:0, Stock:1, Link:0, Name:0, FuncFlow:0}, StockAndFlowp {Flow:16, Stock:9, Link:19, Name:0, FuncFlow:0}), ACSetTransformation((Flow = FinFunction(Int64[], 0, 16), Stock = FinFunction([4], 1, 9), Link = FinFunction(Int64[], 0, 19), Name = Catlab.CategoricalAlgebra.FinSets.VarFunction{Symbol}(FinDomFunction(Union{ACSets.ColumnImplementations.AttrVar, Symbol}[], FinSet(0), TypeSet(Union{ACSets.ColumnImplementations.AttrVar, Symbol})), FinSet(0)), FuncFlow = Catlab.CategoricalAlgebra.FinSets.VarFunction{Function}(FinDomFunction(Union{ACSets.ColumnImplementations.AttrVar, Function}[], FinSet(0), TypeSet(Union{ACSets.ColumnImplementations.AttrVar, Function})), FinSet(0))), StockAndFlowp {Flow:0, Stock:1, Link:0, Name:0, FuncFlow:0}, StockAndFlowp {Flow:16, Stock:9, Link:19, Name:0, FuncFlow:0})]), Union{Nothing, ACSets.DenseACSets.AnonACSet{ACSets.Schemas.TypeLevelBasicSchema{Symbol, Tuple{:Stock}, Tuple{}, Tuple{:Name, :FuncFlow}, Tuple{(:sname, :Stock, :Name)}, Tuple{}}, Tuple{Symbol, Function}, @NamedTuple{Stock::ACSets.DenseACSets.IntParts, Name::ACSets.DenseACSets.IntParts, FuncFlow::ACSets.DenseACSets.IntParts}, @NamedTuple{sname::ACSets.ColumnImplementations.DenseColumn{Union{ACSets.ColumnImplementations.AttrVar, Symbol}, Vector{Union{ACSets.ColumnImplementations.AttrVar, Symbol}}}}, ACSets.DenseACSets.IntParts}}[ACSets.DenseACSets.AnonACSet{ACSets.Schemas.TypeLevelBasicSchema{Symbol, Tuple{:Stock}, Tuple{}, Tuple{:Name, :FuncFlow}, Tuple{(:sname, :Stock, :Name)}, Tuple{}}, Tuple{Symbol, Function}, @NamedTuple{Stock::ACSets.DenseACSets.IntParts, Name::ACSets.DenseACSets.IntParts, FuncFlow::ACSets.DenseACSets.IntParts}, @NamedTuple{sname::ACSets.ColumnImplementations.DenseColumn{Union{ACSets.ColumnImplementations.AttrVar, Symbol}, Vector{Union{ACSets.ColumnImplementations.AttrVar, Symbol}}}}, ACSets.DenseACSets.IntParts}:
  Stock = 1:1
  Name = 1:0
  FuncFlow = 1:0
  sname : Stock → Name = [:S], ACSets.DenseACSets.AnonACSet{ACSets.Schemas.TypeLevelBasicSchema{Symbol, Tuple{:Stock}, Tuple{}, Tuple{:Name, :FuncFlow}, Tuple{(:sname, :Stock, :Name)}, Tuple{}}, Tuple{Symbol, Function}, @NamedTuple{Stock::ACSets.DenseACSets.IntParts, Name::ACSets.DenseACSets.IntParts, FuncFlow::ACSets.DenseACSets.IntParts}, @NamedTuple{sname::ACSets.ColumnImplementations.DenseColumn{Union{ACSets.ColumnImplementations.AttrVar, Symbol}, Vector{Union{ACSets.ColumnImplementations.AttrVar, Symbol}}}}, ACSets.DenseACSets.IntParts}:
  Stock = 1:1
  Name = 1:0
  FuncFlow = 1:0
  sname : Stock → Name = [:E], ACSets.DenseACSets.AnonACSet{ACSets.Schemas.TypeLevelBasicSchema{Symbol, Tuple{:Stock}, Tuple{}, Tuple{:Name, :FuncFlow}, Tuple{(:sname, :Stock, :Name)}, Tuple{}}, Tuple{Symbol, Function}, @NamedTuple{Stock::ACSets.DenseACSets.IntParts, Name::ACSets.DenseACSets.IntParts, FuncFlow::ACSets.DenseACSets.IntParts}, @NamedTuple{sname::ACSets.ColumnImplementations.DenseColumn{Union{ACSets.ColumnImplementations.AttrVar, Symbol}, Vector{Union{ACSets.ColumnImplementations.AttrVar, Symbol}}}}, ACSets.DenseACSets.IntParts}:
  Stock = 1:1
  Name = 1:0
  FuncFlow = 1:0
  sname : Stock → Name = [:I], ACSets.DenseACSets.AnonACSet{ACSets.Schemas.TypeLevelBasicSchema{Symbol, Tuple{:Stock}, Tuple{}, Tuple{:Name, :FuncFlow}, Tuple{(:sname, :Stock, :Name)}, Tuple{}}, Tuple{Symbol, Function}, @NamedTuple{Stock::ACSets.DenseACSets.IntParts, Name::ACSets.DenseACSets.IntParts, FuncFlow::ACSets.DenseACSets.IntParts}, @NamedTuple{sname::ACSets.ColumnImplementations.DenseColumn{Union{ACSets.ColumnImplementations.AttrVar, Symbol}, Vector{Union{ACSets.ColumnImplementations.AttrVar, Symbol}}}}, ACSets.DenseACSets.IntParts}:
  Stock = 1:1
  Name = 1:0
  FuncFlow = 1:0
  sname : Stock → Name = [:R]])

Generate the composed model (Stock and Flow Diagram)

COVID19 = apex(openCOVID19)
StockAndFlowp {Flow:16, Stock:9, Link:19, Name:0, FuncFlow:0}
Flow u d fname ϕf
1 1 2 NewIncidence fNewIncidence
2 2 3 NewInfectious fNewInfectious
3 3 4 NewRecovery fNewRecovery
4 4 1 WaningImmunityR fWaningImmunityR
5 3 5 HICUAdmission fHICUAdmission
6 3 6 HNICUAdmission fHNICUAdmission
7 5 6 OutICU fOutICU
8 6 4 RecoveryH fRecoveryH
9 1 7 FirstdoseVaccine fFirstdoseVaccine
10 7 8 SeconddoseVaccine fSeconddoseVaccine
11 7 1 WaningImmunityVP fWaningImmunityVP
12 8 7 WaningImmunityVF fWaningImmunityVF
13 7 2 NewIncidenceVP fNewIncidenceVP
14 8 2 NewIncidenceVF fNewIncidenceVF
15 2 9 NewPersistentAsymptomaticity fNewPersistentAsymptomaticity
16 9 4 NewRecoveryIA fNewRecoveryIA
Stock sname
1 S
2 E
3 I
4 R
5 HICU
6 HNICU
7 VP
8 VF
9 IA
Link s t
1 1 1
2 3 1
3 2 2
4 3 3
5 4 4
6 3 5
7 3 6
8 5 7
9 6 8
10 1 9
11 7 10
12 7 11
13 8 12
14 7 13
15 3 13
16 8 14
17 3 14
18 2 15
19 9 16

Graph(COVID19)

Define constant parameters

p_COVID19 = LVector(
    β=0.8, N=38010001.0, tr=12.22, tw=2*365.0,
    fH=0.002, fICU=0.23, tICU=6.0, tH = 12.0,
    rv=0.01, eP=0.6, eF=0.85, ri=0.207, ria=0.138
)
13-element LabelledArrays.LArray{Float64, 1, Vector{Float64}, (:β, :N, :tr, :tw, :fH, :fICU, :tICU, :tH, :rv, :eP, :eF, :ri, :ria)}:
    :β => 0.8
    :N => 3.8010001e7
   :tr => 12.22
   :tw => 730.0
   :fH => 0.002
 :fICU => 0.23
       ⋮
   :rv => 0.01
   :eP => 0.6
   :eF => 0.85
   :ri => 0.207
  :ria => 0.138

Define initial values for stocks

u0_COVID19 = LVector(
    S=38010000.0, E=0.0, I=1.0, IA=0.0, R=0.0, HICU=0.0, HNICU=0.0, VP=0.0, VF=0.0
)
9-element LabelledArrays.LArray{Float64, 1, Vector{Float64}, (:S, :E, :I, :IA, :R, :HICU, :HNICU, :VP, :VF)}:
     :S => 3.801e7
     :E => 0.0
     :I => 1.0
    :IA => 0.0
     :R => 0.0
  :HICU => 0.0
 :HNICU => 0.0
    :VP => 0.0
    :VF => 0.0

Check the dependencies of links of all flows' functions checkfls(COVID19, u0COVID19, pCOVID19)

Solve the ODEs

prob_COVID19 = ODEProblem(vectorfield(COVID19),u0_COVID19,(0.0,300.0),p_COVID19);
sol_COVID19 = solve(prob_COVID19,Tsit5(),abstol=1e-8);
plot(sol_COVID19)
Example block output

Flow of FirstdoseVaccine

ϕFirstdoseVaccine = map(x->fFirstdoseVaccine(sol_COVID19.u[x],p_COVID19,sol_COVID19.t[x]),collect(1:length(sol_COVID19.t)))
73-element Vector{Float64}:
 380100.0
 380099.9999998586
 380099.9999984444
 380099.9999843023
 380099.99984288134
 380099.9984286719
 380099.98428657756
 380099.84286566736
 380098.4286598555
 380084.28693077463
      ⋮
  24993.702422388375
  25975.606336685047
  26896.203059104606
  27755.494973309615
  28553.8809027126
  29292.127379132937
  29971.341951615042
  30592.94630595571
  30842.079132188224