Discrete SIR model using the DiffEq integrator interface

pomp_integrator.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "WARNING: Method definition non_autodiff_setup(Any, Any) in module OrdinaryDiffEq at /Applications/JuliaPro-0.6.0.1.app/Contents/Resources/pkgs-0.6.0.1/v0.6/OrdinaryDiffEq/src/misc_utils.jl:49 overwritten in module DiffEqCallbacks at /Applications/JuliaPro-0.6.0.1.app/Contents/Resources/pkgs-0.6.0.1/v0.6/DiffEqCallbacks/src/manifold.jl:32.\n"
     ]
    }
   ],
   "source": [
    "using DifferentialEquations\n",
    "using Distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sir (generic function with 1 method)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function sir(t,u,du,parms)\n",
    "    (S,I,R,Y)=u\n",
    "    (β,γ,α,ι,N,δt)=parms\n",
    "    λ=β*((convert(Float64,I)+ι)^α)/N\n",
    "    ifrac=1.0-exp(-λ*δt)\n",
    "    rfrac=1.0-exp(-γ*δt)\n",
    "    infection=rand(Binomial(S,ifrac))\n",
    "    recovery=rand(Binomial(I,rfrac))\n",
    "    du[1]=S-infection\n",
    "    du[2]=I+infection-recovery\n",
    "    du[3]=R+recovery\n",
    "    du[4]=Y+infection\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "γ=7.0/13.0\n",
    "α=1.0\n",
    "ι=0.5\n",
    "N=403.0\n",
    "M=10\n",
    "R₀=5.0\n",
    "δt=1.0/convert(Float64,M)\n",
    "β=R₀*(1.0-exp(-γ*δt))/δt;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.62110617498984, 0.5384615384615384, 1.0, 0.5, 403.0, 0.1)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "u0=[60,1,342,0]\n",
    "tspan=(0,540)\n",
    "parms=(β,γ,α,ι,N,δt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "DiffEqBase.DiscreteProblem with uType Array{Int64,1} and tType Int64. In-place: true\n",
       "timespan: (0, 540)\n",
       "u0: [60, 1, 342, 0]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f = (t,u,du)->sir(t,u,du,parms)\n",
    "prob=DiscreteProblem(f,u0,tspan)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
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      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n",
      "[47, 0, 356, 13]\n"
     ]
    }
   ],
   "source": [
    "u=copy(u0)\n",
    "du=u\n",
    "for i in 1:tspan[2]\n",
    "    f(i,u,du)\n",
    "    u=du\n",
    "    println(u)\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "  0.205316 seconds (631.00 k allocations: 17.975 MiB, 3.42% gc time)\n"
     ]
    }
   ],
   "source": [
    "@time begin\n",
    "for j in 1:1000\n",
    "    u=copy(u0)\n",
    "    du=u\n",
    "    for i in 1:tspan[2]\n",
    "        f(i,u,du)\n",
    "        u=du\n",
    "    end\n",
    "end\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "ename": "LoadError",
     "evalue": "\u001b[91mInexactError()\u001b[39m",
     "output_type": "error",
     "traceback": [
      "\u001b[91mInexactError()\u001b[39m",
      "",
      "Stacktrace:",
      " [1] \u001b[1mconvert\u001b[22m\u001b[22m at \u001b[1m./rational.jl:85\u001b[22m\u001b[22m [inlined]",
      " [2] \u001b[1mInt64\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::Rational{Int64}\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m./sysimg.jl:24\u001b[22m\u001b[22m",
      " [3] \u001b[1m(::DiffEqBase.#kw##init)\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::Array{Any,1}, ::DiffEqBase.#init, ::DiffEqBase.DiscreteProblem{Array{Int64,1},Int64,true,##1#2,Void}, ::OrdinaryDiffEq.Discrete{true,false}, ::Array{Array{Int64,1},1}, ::Array{Int64,1}, ::Array{Any,1}, ::Type{Val{true}}\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m./<missing>:0\u001b[22m\u001b[22m (repeats 2 times)",
      " [4] \u001b[1minclude_string\u001b[22m\u001b[22m\u001b[1m(\u001b[22m\u001b[22m::String, ::String\u001b[1m)\u001b[22m\u001b[22m at \u001b[1m./loading.jl:515\u001b[22m\u001b[22m"
     ]
    }
   ],
   "source": [
    "integrator=init(prob,FunctionMap(scale_by_time=false);dt=δt)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Julia 0.6.0",
   "language": "julia",
   "name": "julia-0.6"
  },
  "language_info": {
   "file_extension": ".jl",
   "mimetype": "application/julia",
   "name": "julia",
   "version": "0.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}

@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!