Catalyst: the reaction-network view

Start from a lowering — a Gamma(3, 1.5) delay as its chain — the same starting point every backend page uses. See Lowering a distribution to a dynamical system for what lower does.

using LoweredDistributions
using Distributions

d = Gamma(3.0, 1.5)
chain = lower(d)

ErlangChain(3 compartments)

reaction_system threads a from species, through one species per phase, to a to species. This is the form to reach for when the delay is one transition inside a larger model: an Erlang-distributed infectious period in an SIR model, say, where the I -> R transition needs a non-exponential dwell time.

using Catalyst

t = Catalyst.default_t()
@species Infectious(t) Recovered(t)

rs = reaction_system(d, Infectious, Recovered;
    prefix = :Iphase, name = :infectious_period)
Catalyst.reactions(rs)

4-element Vector{Catalyst.Reaction}:
 0.6666666666666666, Infectious --> Iphase1
 0.6666666666666666, Iphase1 --> Iphase2
 0.6666666666666666, Iphase2 --> Iphase3
 0.6666666666666666, Iphase3 --> Recovered

Three phases give three phase species and, with the entry reaction from Infectious, four reactions: Infectious -> Iphase1, two interior hops, and the exit into Recovered.

Catalyst.species(rs)

5-element Vector{SymbolicUtils.BasicSymbolicImpl.var"typeof(BasicSymbolicImpl)"{SymbolicUtils.SymReal}}:
 Infectious(t)
 Iphase1(t)
 Iphase2(t)
 Iphase3(t)
 Recovered(t)