Discrete SIR model using the DiffEq integrator interface

pomp_integrator.ipynb

@ChrisRackauckas any idea what's going wrong here?

using OrdinaryDiffEq
using Distributions

function sir(t,u,du,parms)
    (S,I,R,Y)=u
    (β,γ,α,ι,N,δt)=parms
    λ=β*((convert(Float64,I)+ι)^α)/N
    ifrac=1.0-exp(-λ*δt)
    rfrac=1.0-exp(-γ*δt)
    infection=rand(Binomial(S,ifrac))
    recovery=rand(Binomial(I,rfrac))
    du[1]=S-infection
    du[2]=I+infection-recovery
    du[3]=R+recovery
    du[4]=Y+infection
end

γ=7.0/13.0
α=1.0
ι=0.5
N=403.0
M=10
R₀=5.0
δt=1.0/convert(Float64,M)
β=R₀*(1.0-exp(-γ*δt))/δt;

u0=[60,1,342,0]
tspan=(0,540.0)
parms=(β,γ,α,ι,N,δt)

f = (t,u,du)->sir(t,u,du,parms)
prob=DiscreteProblem(f,u0,tspan)
@time solve(prob,FunctionMap(scale_by_time=false);dt=δt)

The issue was tspan=(0,540) meant time was integers when you should've been using Float64 (or Rationals to be exact). I think this is the kind of "quick" problem where you'll measure our keyword argument + startup time though,

0.001946 seconds (10.97 k allocations: 1.105 MiB)

is definitely too much and mostly due to kwarg + splat penalty for the big type. Hopefully that's fixed in 1.0 though!