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   "source": [
    "# A General CTMC solver\n",
    "EpiStochModels also provides a class to simulate any CTMC model you want, as long as you provide it with a transition matrix and propensity functions. So far this class is available for D programs, because of the impossibility of passing the propensity functions from Python into D. Nevertheless, We will demonstrate here how to use it:\n",
    "\n",
    "Let's use the SIRD model as an example. The corresponding ODE model is:\n",
    "\n",
    "\\begin{align}\n",
    "\\frac{dS}{dt} &= -\\beta S \\frac{I}{N}\\\\\n",
    "\\frac{dI}{dt} &= \\beta S \\frac{I}{N} -\\gamma I -\\mu I\\\\\n",
    "\\frac{dR}{dt} &= \\gamma I\\\\\n",
    "\\frac{dD}{dt} &= \\mu I\n",
    "\\end{align}\n",
    "\n",
    "For this model, the following events are possible:\n",
    "\n",
    "\n",
    "1. **Infection** propensity: $\\beta S \\frac{I}{N}$\n",
    "1. **Recovery** propensity: $\\gamma I$\n",
    "1. **Death** propensity: $\\mu I$\n",
    "\n",
    "The following transition matrix describe the changes in the state of the system when these events happen:\n",
    "\n",
    "TM = \\begin{bmatrix}\n",
    "-1 & 1 & 0 & 0\\\\\n",
    "0 & -1 & 1 & 0\\\\\n",
    "0 & -1 & 0 & 1\n",
    "\\end{bmatrix}.\n",
    "\n",
    "The D code required to implement this model is:\n",
    "\n",
    "```D\n",
    "int[][] tmat = [[-1,1,0,0],\n",
    "                    [0,-1,1,0], \n",
    "                    [0,-1,0,1]];\n",
    "double[string] pars = [\n",
    "    \"beta\": 0.3,\n",
    "    \"gam\": 0.05,\n",
    "    \"mu\": 0.01\n",
    "];\n",
    "alias double delegate(int[], double[string]) dy;\n",
    "dy[] props = [\n",
    "    (v,p)=> p[\"beta\"]*v[0]*v[1]/sum(v[0..$-1]), // infection\n",
    "    (v,p)=> p[\"gam\"]*v[1], // recovery\n",
    "    (v,p)=> p[\"mu\"]*v[1] // death\n",
    "    ];\n",
    "CTMC model = new CTMC(tmat, props,[\"S\", \"I\", \"R\", \"D\"], [\"beta\", \"gamma\", \"mu\"]);\n",
    "model.initialize([995,5,0,0],pars);\n",
    "auto res = model.run(0, 1000);\n",
    "```"
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   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Locally registered package pyd 0.13.1+commit.5.g93d8235 was not found. Please run 'dub remove-local \"/home/fccoelho/Downloads/pyd/\"'.\n",
      "Locally registered package epistochmodels ~master was not found. Please run 'dub remove-local \"/home/fccoelho/Documentos/Software_projects/EpiStochModels/epistochmodels/\"'.\n",
      "Performing \"release\" build using ldc2 for x86_64.\n",
      "mir-core 1.0.3: target for configuration \"library\" is up to date.\n",
      "mir-algorithm 3.5.7: target for configuration \"default\" is up to date.\n",
      "mir-random 2.2.15: target for configuration \"extended\" is up to date.\n",
      "pyd 0.14.0: target for configuration \"python38\" is up to date.\n",
      "epistochmodels 0.3.1: target for configuration \"library\" is up to date.\n",
      "CTMC_example ~master: building configuration \"application\"...\n",
      "Linking...\n",
      "To force a rebuild of up-to-date targets, run again with --force.\n",
      "Running ./CTMC_example \n",
      "Time of the SIR run with N=1000: 1 ms, 350 μs, and 5 hnsecs\n"
     ]
    }
   ],
   "source": [
    "!dub run --build=release --compiler=ldc2 --single CTMC_example.d"
   ]
  },
  {
   "source": [
    "After running the line above, an executable called `CTCM_example`  will be created alongside the source file that you can simply run:"
   ],
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   "metadata": {}
  },
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   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Time of the SIR run with N=1000: 1 ms, 261 μs, and 8 hnsecs\n"
     ]
    }
   ],
   "source": [
    "!./CTMC_example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
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  }
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