experiments/single_population/kermack_mckendrick.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Kermack–McKendrick SIR model\n",
    "\n",
    "The spread of an infection in a population can be modelled by a simple Kermack–McKendrick SIR Model. The population is split into three compartments: susceptible (S), infected (I), and recovered (R). The ODE of a simple SIR model looks like:\n",
    "\n",
    "$\\frac{dS}{dt} = - \\frac{\\beta S I}{A N}$\n",
    "\n",
    "$\\frac{dI}{dt} = \\frac{\\beta S I}{A N} - \\gamma I $\n",
    "\n",
    "$\\frac{dR}{dt} = \\gamma I $\n",
    "\n",
    "The $\\beta$ is the interaction rate between infected (*I*) and susceptible (*S*) individuals for a given area (*A*), following the law of mass action. The area is added to make easier comparisons with explicity spatial IEBMs. The total population of the system (*S*+*I*+*R*) is *N*. The $\\gamma$ is the recovery rate of those infected. \n",
    "\n",
    "The dynamics of the model depend on a ratio called the basic reproduction number,\n",
    "\n",
    "$ R_0 = \\frac{\\beta}{A \\gamma} $\n",
    "\n",
    "and the size of the susceptible compartment.\n",
    "\n",
    "To start, this simple SIR is integrated in Python to visualize the dynamics of a parameter set. The second part of this notebook recreates the simple SIR as an IEBM. The only difference is that the SIR population "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style type='text/css'>\n",
       ".datatable table.frame { margin-bottom: 0; }\n",
       ".datatable table.frame thead { border-bottom: none; }\n",
       ".datatable table.frame tr.coltypes td {  color: #FFFFFF;  line-height: 6px;  padding: 0 0.5em;}\n",
       ".datatable .boolean { background: #DDDD99; }\n",
       ".datatable .object  { background: #565656; }\n",
       ".datatable .integer { background: #5D9E5D; }\n",
       ".datatable .float   { background: #4040CC; }\n",
       ".datatable .string  { background: #CC4040; }\n",
       ".datatable .row_index {  background: var(--jp-border-color3);  border-right: 1px solid var(--jp-border-color0);  color: var(--jp-ui-font-color3);  font-size: 9px;}\n",
       ".datatable .frame tr.coltypes .row_index {  background: var(--jp-border-color0);}\n",
       ".datatable th:nth-child(2) { padding-left: 12px; }\n",
       ".datatable .hellipsis {  color: var(--jp-cell-editor-border-color);}\n",
       ".datatable .vellipsis {  background: var(--jp-layout-color0);  color: var(--jp-cell-editor-border-color);}\n",
       ".datatable .na {  color: var(--jp-cell-editor-border-color);  font-size: 80%;}\n",
       ".datatable .footer { font-size: 9px; }\n",
       ".datatable .frame_dimensions {  background: var(--jp-border-color3);  border-top: 1px solid var(--jp-border-color0);  color: var(--jp-ui-font-color3);  display: inline-block;  opacity: 0.6;  padding: 1px 10px 1px 5px;}\n",
       "</style>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# import necessary modules\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import integrate\n",
    "from multiprocessing import Pool\n",
    "from tqdm.auto import tqdm\n",
    "\n",
    "# import datatime to set threads to 1\n",
    "# allows for better multiprocessing\n",
    "import datatable as dt\n",
    "dt.options.nthreads = 1\n",
    "\n",
    "# set nice plotting style\n",
    "plt.style.use('bmh')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parameters\n",
    "Set parameters that are used in both the ODE and IEBM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "b = 1000 # interaction rate\n",
    "d = 0.001 # recovery rate\n",
    "# size of environmnet\n",
    "xdim = 500\n",
    "ydim = 500\n",
    "A = xdim * ydim\n",
    "# simulation times\n",
    "max_time = 10000\n",
    "ode_times=  np.linspace(0, max_time, 100)\n",
    "# population size\n",
    "pop_size = 1000\n",
    "init_size = [900,100,0]\n",
    "# for the IEBM\n",
    "pred_radius = 1\n",
    "init_frac = [0.9, 0.1, 0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## ODE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dN_dt(N, t=0):\n",
    "    return np.array([-(b*N[0]*N[1])/(pop_size*A),\n",
    "                     (b*N[0]*N[1])/(pop_size*A) - d*N[1],\n",
    "                     d*N[1]])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = integrate.odeint(dN_dt, init_size, ode_times)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAgkAAAEeCAYAAAAAWYZGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+j8jraAAAgAElEQVR4nOzdd3xb1f3/8ddHy5L3jEd2yHDiDDIIe4YRShlllQ7Gr6GDhrYUWlo6aEtLB+TbFr5QWiiloXxpWWWV0YQQ0tCElU2ms5zhveQlW5Z0fn9INooj25It2ZbueT7QQ9JdOm/fYB/de4YopdA0TdM0TevJNNwF0DRN0zRtZNKVBE3TNE3TQtKVBE3TNE3TQtKVBE3TNE3TQtKVBE3TNE3TQtKVBE3TNE3TQtKVBE3TNE3TQtKVBE0bZiKSLyL/KyIHRcQtIjUi8ryInBi0zU0iogIPn4g0icg2EXlYRKb3ON45Qdv2fFw99Ak1TYtXupKgacNIRMYCHwGnAbcAk4FLgE7gPRFZHLS5FygEioB5wI8C228WkatCHH5eYPvgx6uxSaJpWiISPeKipg0fEXkFWAhMVUo19Vj3Ov4/9BOBzwJ/VkpZQhzjOeB8YIJSyiki5wCrgbFKqSMxjqBpWgLTVxI0bZiISBb+qwYP9awgBPwKyAcu6OdQvwEyw9hO0zQtIrqSoGnDZwr+/we397K+a/m0fo7zceB5Uo/lu0WkpcejaIBl1TTNgI67dKlp2pCRftaHey+w6zg9t78IqOyxrCrMY2qapulKgqYNo1LAB8wEXgyxfmbgeTeQ3cdxurbb12P5Qd0mQdO0wdC3GzRtmCil6oE3gKUikh5ikx/g/+a/sp9DfQ+oD2M7TdO0iOgrCZo2vJYC64C3ReRH+NshFADfBs4FrlBKuUT8dxREpCCwXwpQEtj/HOCzSqnmHsfOExFPj2VNSqm2WATRNC3x6EqCpg0jpVSZiCzAP+bBn/CPZdAErAFOVUptCtrcDFTgb3vQCpQFtvuWUmpXiMNvDLHsu8Cy6CXQNC2R6XESNE3TNE0LSbdJ0DRN0zQtJF1J0DRN0zQtJF1J0DRN0zQtJF1J0DRN0zQtJF1J0DRN0zQtJN0FshfvvPOOSkpKGu5iaJqmxZW2trbaRYsW5Q3mGBs2bDDZ7fY7LRbLdPSX2VjyeTyene3t7ffNnz/fF2oDXUnoRVJSEsXFxQPat6ysjPHjx0e5RCObzmwMOrMxDCbzxo0bywb7+Xa7/c6cnJxrk5KSQv7h0qKno6NjVl1dHcCvQ62PmxqaiPxFRKpF5OOgZdkislJESgPPWUHr7hKRvSKyW0QuClo+X0S2BdY9KF1D2UWR1WqN9iFHPJ3ZGHRmYxjuzBaLZbquIAyNpKQkX+CKTUhxU0kA/gos7rHs+8AqpdQUYFXgPSIyA7gO/7C1i4E/iIg5sM8jwFfwT9M7JcQxBy0jIyPahxzxdGZj0JmNYQRkjqe/TYmg15933JwIpdR/8E9iE+xyYHng9XLgiqDl/1BKdSilDgB7gYUiUgikK6XWK/9Qk08G7RM1tbW10T7kiKczG4PObAxGzDwSffDBB44XX3yxu8b23HPPZdxzzz0FADfccMOE//u//8vquc+///3vtEsvvXRytMoQ720S8pVSFQBKqQoRGRVYPhp4L2i7I4FlnYHXPZdH1QiohQ85ndkYdGZjMGLmkWjTpk3JmzdvTvnMZz7jBLjmmmucgHMoyxDvlYTehGpnoPpYfpzq6mqWLFmCxWLB6/Vy5ZVXsnTpUiorK0lJScFsNtPU1EReXh719fUopcjLy6Oqqgqv14vX66WlpYX8/HxqamoQEbKzs6mpqSE9PR2v10traysFBQVUVlZitVrJyMigtraWjIwM3G43Lpere73NZiMtLY26ujqysrJwuVy0t7d3r7fb7TgcDhoaGsjJyaG5uRm329293uFwYLPZcDqd5Obm4nQ66ezs7F7fX6bU1FSAXjP5fD48Hk9CZervPCmlEi5Tf+cJoKOjI6Ey9XeeRASXy5VQmfo7TyaTiba2tgFlSgTNzc2mz3/+85OqqqpsXq9XvvWtb5X/+te/HrN69eqd+fn5nnXr1iX/+Mc/Hrtq1ardK1asSP3Rj340DkBEWLFixa6MjAzfL37xi/yXXnopx2QycdZZZzmXLVt2dNeuXUm33377uIaGBovdbvc9+OCDZbNmzWq/4YYbJiQlJfn27t3rqK+vt959992HP/3pTzf97ne/K+ro6DAtXLgw9dZbb61wuVymzZs3pzzyyCOHAN555520P//5z6O69rnqqqucPXN84xvfGLdnzx6H1+uVO+64o/zaa69tjORnEVcTPInIBOBfSqmZgfe7gXMCVxEKgXeUUtNE5C4ApdSvAtv9G/gpcBBYrZQqDiz/XGD/r/b8rPXr1yvduyF8OrMx6MzGMMjeDRsWLVq0YDCfv3v37r+NGjVqOsCFf940fzDH6s2Km+du6G3d008/nblq1aqMxx9/vAygvr7efMYZZ8wIVUm47LLLJt92220V5513XmtTU5PJ4XD4XnvttfTf/e53Ra+99tqe1NRUX01NjTkvL8974YUXTv39739fNmPGjI61a9em3HPPPaNXrly554YbbphQW1trffXVV0t3796d9JnPfGbapk2btv3tb3/LDq4U/OlPf8rpet/bPmvXrk196KGH8l999dW9d9555+hp06a5lixZUl9XV2c+77zzpr/77rs70tLSjmkUWl1dvXPatGnXh/pZxPuVhFeAG/F33bgReDlo+dMi8lugCH8DxQ+UUl4RaRaRU4D3gRuA/412oQoKCqJ9yBFPZzYGI2RWSqHUJ8+5OXm4Ozzdy7q38XVt07Wsx3oFKFB0vQ48B7aFT953bdd1XVMFNur+Cqc+WRb0dOwxjskQtO0xK4JfquOWdRFTch8/ocQ3Z84c17333jv2jjvuGH3xxRc7zz///Jbetl2wYEHL3XffPXbjxo31V199dcOECRN8q1evTr/mmmtqU1NTfQB5eXnepqYm09atW1NvuummE7r27ezs7L66femll9abzWZmzJjRMXr06I6PP/7Y3l85+9vn3XffTV+1alXmn/70pwKAjo4OOXDggG327Nnt4f4s4qaSICJ/B84BckXkCPAT/JWDZ0VkCXAIuAZAKbVdRJ4FdgAeYKlSyhs41C34e0o4gDcCj6iqrKw03DcPndkYwsns8/rweHx0ur14PF463T68Hi8ejw9Ppw+Px4vX48Pr8eHx+vB2+vB6Aw+PD69X4fX68Hl9eD0Kn88XeK/wev3vfT6Fz6v8zz5f92vl61rmX658+J8V3euVCmyrFD4foBS+roqBL36urMZS9ig7X7rtnOEuBtD3N/5YKSkp6XjnnXd2vPLKKxm/+MUvRq9Zs6bJbDYrr9f/Z8TlcnU3+r/77rsrL7nkEufrr7+ecdFFF01//vnn9yil6Nm73uv1kpqa6vnggw92hPrMntuH0zu/v32UUixfvnzvzJkzO/o9WC/ippKglPpcL6sW9bL9vcC9IZZ/BMyMYtGOY7PZYnn4EUlnjm8+n6KjvZN2VycdLo//ud2Du8NDR/snrxsbmtm6rgG320tnh8f/7PbQ6fb6H51efN74/0MrEviF6/8PMZm6lwU/IxJYH3hPj/1Ejnnvf5bu1lFdv9T9x+qxjk+O/8mCHvtw7LKeGbp26vXvTfdnffK5APaUqA8fE1cOHTpkzc3N9SxZsqQ+NTXV949//COnqKjI/cEHHyRfccUVTS+99FJ3r4Jdu3YlzZ8/3zV//nzXxo0bU3bs2GFftGhR029/+9uiG2+8sT74dsPo0aPdTz31VNYXv/jFBp/Px4YNGxwnnXSSC+Bf//pX1pe//OW60tLSpKNHjyaVlJS0l5aWJrW2tvbaCzHUPmvXru1uHHLmmWc2Pfzww/kPP/zwIZPJxPvvv+84+eSTXZH8LOKmkhBP0tLShrsIQ05nHlmUT9HW6qa1uYPWlg5aW9y0tXTQ1urG1eqmrbUTV6ub9rZOXG1uOto90ftwAavVjMVqxmI1+V9bTFisZswWE2aLCavlk9cWiwmz2YTJIljMJkxm/3KzWfyvTYLJYsJsMmEyCyaTYDabEJNgNgtiEkzi39Zk7nrt/+NsMgXWm4LeiyAmPnktXceg+3WwlpaWhGqUF46Wll6vrhvC5s2bHT//+c/HiAgWi0UtW7asrK2tzXTHHXdMeOCBBzrnzJnT2rXtgw8+OOr9999PN5vNatKkSa7LLrvM6XA41JYtW5LPOuus6RaLRZ1zzjnO++677+hjjz22/7bbbhv/4IMPFno8HrnkkkvquyoJEydO7Dj//POn1dfXW3/5y1+WJScnqwsuuKD5oYceKly4cOGMW2+9taJnOUPtE7z+Jz/5Sfltt902buHChTOUUlJUVNTx6quv7o3kZxFXDReHkm64GBmdeegopXC1duJsaKOpsZ2mRhfNje00N7XT7GynpamdthY3vggvnSfZLdgdVuwOK0l2C0l2K0kOC7Yk/yPJbqGlxUlB0ShsSRasNjM2m/+5+xGoCMRgINNho/9tRybaDReN4IYbbphw0UUXOb/whS80DMfnJ3LDxREpK+u48S0Sns4cfW0tbupqWmiobaWhro3G2jYa6/2PTre33/0dyVZS0pNISU0iOdVGcmoSySm27ocjxYo92YYj2UqS3YrJ1P8f9qamJtLT06MRL27of9uakelKQgy4XC7D/SLVmQfO3eGhuqKZ2spmaqqaqatqoa66BVdbZ6/7JNktZGQ5SM/0P9Iy7aRl+B+p6UmkpNmxWKI/oKo+z8ZgxMzD6cknnzw43GXoja4kxEB7e9i9SxKGzhyeTreXqvImKo80UnHYSXV5Ew31bSG7odmSzGTnpZKdl0JWTjJZOSlk5iSTmZOM3TE8E/Do82wMRsyshaYrCTFghL7kPenMobW2dHDkQANHy/yP6orm47rZmcxCbn4aeQWpgec0ckalkpqeNOLu7evzbAxGzKyFpisJMaD7zxtDqMzuDg+H9tdTVlrLof311FUf20pcBEYVplEwJsP/GJ1BzqhUzDG4NRAL+jwbgxEza6HpSkIM2O39DpSVcIycub62lX07q9m3q5ryssZjehVYrCZGj8/qfhSOzcCWFL//2xn5PBuJETNrocXvb6sRzOFwDHcRhpyRMiulqKloZtuGal4r3UN9bXeXaUSgaFwmE6bkMu6EHArHZMTNVYJwGOk8d9GZjenss88uXrNmza6+tnnrrbdS77zzzvEWi0WtXr16Z0pKStj9jp955pnMadOmtZ944okRNQApKiqaW15evimSfQZDVxJioKGhwXAtg42QuaGulR2bytm5pYLGurbu5Ul2C5OK8ziheBQTpuQOW6PCoWCE89yTzmxM/VUQAJ555pnsr3zlK5Vf+9rX6iI9/muvvZbp8XickVYShpquJMRATk7OcBdhyCVqZneHh11bK/h4w1HKD30yw6ojxcbEqdmUzB3LmIlZmM2Jc7WgL4l6nvuiMxtT1zf2f//732n33XdfUVZWVufevXsdM2bMaHvqqacOPPLII7krVqzIXrduXcZ//vOf9KeffvrAvffem//aa69ld3Z2ygUXXND4y1/+shzgsccey3n00UfzRYSpU6e6br755uo1a9ZkbtiwIe2BBx4ofPLJJ/cBhJpGes+ePbabb755ksfjkbPOOsvZd6mjT1cSYqC5udlww7gmWuaaymY2v3eInVvKcXf4By6y2sxMKclnxolFjJuUTVV1FYWFxvplmmjnORw68/B6s+C0mEwVvbhyXdgTR+3Zs8exdu3a/WPHju0899xzi1evXp26dOnS2vfffz+1a6TEV199Nf3AgQP2d999d6dSiiuuuGLyypUrU3Nzcz0PPfRQ4YoVK3bl5+d7uuZxOPvssxuDR1nsOY307bffPm7lypV7vvvd7467/vrra7785S/X/e53v8uLxc+iL7qSEANut3u4izDkEiGz8in276lhw7sHObS/vnv56PGZzD5pLFNm5mOzffK/TCJkjpTObAxGzNyXkpKS1gkTJnQCFBcXtx08ePC42d1WrVqVvm7duvRTTjllBvhniiwtLbVv3brVdNFFFzXk5+d7wD9tdM99+5pGesuWLanPPffcPoCbbrqp7v777x8Tm5Sh6UpCDOTn5xNqqtBEFs/9qr1eH7u2VPD+mv3U1/gbIVptZkrmjWbOwrHkFYSeyCmeMw+UzmwMIylzJN/4Y8VqtXY3SDSbzXg8nuN+uSuluOWWWyq+8Y1v1AYvX7Zs2SgR6bNBYxjTSA/bJEvGuJE6hP61s5avvriHvXURzcYZ9yorK4e7CBHzen1s/fAwj/92LW88v436mlbSMuycffE0vvq9czj/shm9VhAgPjMPls5sDEbMPFjnn39+0zPPPJPb1NRkAigrK7OWl5dbFi1a1PTmm29mV1dXmwFqamrMAKmpqd7m5mYTQFZWlq9rGmkAn8/Hhx9+6ACYM2dOy5NPPpkN8OSTTw75/U19JSHKDjW2U9HqZcWeeqbkJg93cYZMPHWZUj7F7m2VvPtWaXcvhazcZE4+exLTTywKuxFiPGWOFp3ZGIyYebAuvfTSpl27dtnPO++8YoDk5GTfo48+emDu3LntS5curbj44ouLzWazKi4ubnvyyScPXn311fXf+c53JjzxxBP5y5cv39fbNNL333//oZtvvnnS448/nr948eIhnyVSTxXdi4FOFb2vro1bXtxNWpKZv39+JjaDtHpvbGwkMzNzuIvRryMH6ln92i6qypsAyMpJ5rTzJzNtVmFYsyAGi5fM0aQzG8NgMuupouOPnip6CJ2Qk8yYVDNHWry8f6iJMyca45eL0+kc0b9ImxpdrHljN7u3+S+jpqYncdqiyZTMGz3g7osjPXMs6MzGYMTMWmi6khADF07N5i8ba1ixp84wlYTc3NzhLkJIPq+PDevK+O9bpXg6fVisJhaeNYmTzpyI1WYe1LFHauZY0pmNwYiZtdB0JSEGTswCs8CHR5qoa+skJzlxR+Dr4nQ6SUlJGe5iHKPyiJMVL35MdUUzANNmFXD2xdNIz4zO/daRmDnWdGZjMGJmLTRdSYgBh8nLKeMy+G+Zk1V767l2dv5wFynmOjs7h7sI3bweH+vf3sv7a/ajFKRnObjg8hlMnBrdcUhGUuahojMbgxEza6HpSkIMFBQUcCHt/LfMyco99Vwza1TCj5kwUvpV11a18MZzW/0NEwXmnzGB08+ffMwgSNEyUjIPJZ3ZGIyYWQvNGE3vh1hlZSUnjU0n026hrLGd3TVt/e8U54a7X7VSiq0fHuaph9dRVd5EepaDz968kHM/VRyTCgIMf+bhoDMbgxEza6HpSkIMpKSkYDEJiyZnAbB635B3bR1yw3n/0t3h4Y3ntrHixe14PD5K5o3mxm+cztiJ2TH9XCPes9WZjcGImRNJUVHR3GgdS1cSYsBs9reaP3Oiv5KwrsxJoo9H0ZV5qNXXtPDUH9azY3M5FquZT10zm4uvnkWSPfZ30oYr83DSmY3BiJn74vP58HqPm3JhSA1XOxHdJiEGmpqayMrKonhUMlkOC1Utbg7UtzMpJ3FHMevKPJQOltby6t8309HuIWdUKpd+7kRy84du5rrhyDzcdGZjMGLmnkpLS23XXnvtlIULFzZv3rw59YILLmh4++23M/ubBvqpp546sHfvXtvXv/71CQ0NDZasrCzPH//4x4OZmZneM844Y8a2bdu2mc1mWlpaTPPnz5+5bdu2bfv377eFmib6hhtumJCZmenZsWNHcklJSdstt9xSM9TTSetKQgzk5flb0ZtEOGVcBm/srmNdWWNCVxK6Mg8FpRQb15Xxzuu7UAqmzMjn4mtmYUsa2n/OQ5l5pNCZjWEkZV72gzdjMlX0d365uN+Jow4dOmR/4IEHDn76059ufPnll7PCmQYa4Pbbbx939dVX133lK1+pe+SRR3LuuOOOsS+++OK+qVOntq1cuTJt8eLFzf/85z8zTj/9dKfNZlPf/OY3x4eaJhrgwIED9jfffHOPxWIZlumkdSUhBurr60lO9s/bcNr4rkqCky/OKxzmksVOcOZY8vkUq1/byab1hwA45dwTOH3RZCTCIZWjYagyjyQ6szEYMXMoBQUF7rPOOqv1tttuGxPJNNDbtm1Lef755/cBLFmypP6+++4bA3D55Zc3vPDCC1mLFy9ufumll7K/9KUv1fQ1TTTApZde2mCxWIZtOmldSYiB4PYHc4vSsFtM7K1zUd3iZlTqcdOQJ4ShaHPh8fh4/dmt7Pm4ErNZWHz1LKbPKYr55/Ym0duZhKIzG8NIyhzON/5YsdvtPhjcNNDBrrrqqsb77rtvdE1NjXnHjh3Jixcvbmpubjb1NU10SkqKD4ZvOmndcDEGgi/V2SwmFoxJB/wNGBNVrC9PdrR7+OdfP2LPx5XYksxcddOCYa0gwMi6JDtUdGZjMGLmvkQ6DfTs2bNbn3zyySyAJ554Invu3LktAOnp6b6ZM2e2fvvb3x539tlnOy0WS5/TRAcbrumkdSUhBqqqqo55f9r4DADWlzUOR3GGRM/M0dTu6uT5Jz7k0P56UtKSuO7LJzPuhCGfVv04scw8UunMxmDEzH259NJLmy6//PL68847r3jBggUzrr/++hOamprMwdNAL1y4cMYdd9wxFmDZsmWHnnnmmdyTTjppxgsvvJCzbNmyw13HuuKKKxpef/317Kuuuqq+a9ljjz22/+mnn85duHDhjAULFpS88sorISf96W27+++//9Dy5ctHnXbaadOdTmdUu6boqaJ7MdCpogHq6urIyfnkj1hTu4dr/28bAM99cRZpQ9zAbij0zBwt7a5OnvvLh1Qd9Q+QdO2Sk8jMHhn3SmOVeSTTmY1hMJn1VNHxp6+pohPiSoKIfFtEtovIxyLydxGxi0i2iKwUkdLAc1bQ9neJyF4R2S0iF8W6fOl2C7MLU/Ep+OBwU6w/LmG42tw897i/gpARGEFxpFQQNE3TjCDuKwkiMhr4JrBAKTUTMAPXAd8HVimlpgCrAu8RkRmB9SXAYuAPIhLVyzMtLS3HLTt1nP+WQ6JWEkJlHgx3h4cX/rqBqvImMrOT+eyXF5KRNbK6kEY7czzQmY3BiJm10OK+khBgARwiYgGSgXLgcmB5YP1y4IrA68uBfyilOpRSB4C9wMJoFiY///hZH+cHGi9uOto8oloOR0uozAPl6fTy0t82UnnE6Z+D4csLoza9czRFM3O80JmNwYiZtdDi/ua4UuqoiCwDDgEuYIVSaoWI5CulKgLbVIjIqMAuo4H3gg5xJLDsGNXV1SxZsgSLxYLX6+XKK69k6dKlVFZWkpKSgtlspqmpiby8POrr61FKkZeXR1VVFe3t7eTm5tLS0kJ+fj41NTUIkO2wUO/ysLWsmtGpZlpbWykoKKCyshKr1UpGRga1tbVkZGTgdrtxuVzd6202G2lpadTV1ZGVlYXL5aK9vb17vd1ux+Fw0NDQQE5ODs3Nzbjd7u71DocDm82G0+kkNzcXp9NJZ2dn9/r+MqWm+kcyPCaTCNnZ2dTU1NDR0UF2dvagM7W1udi0tpZD++uxJ1u4+Npi6hurEPPQZ0pPT8fr9faaye12k5GREVfnqb9M/Z0nt9tNenp6QmXq7zx1dnaSkpKSUJn6O08ejweHwzGgTFHii+bBtH71+vOO+4aLgbYGLwCfBRqB54DngYeUUplB2zUopbJE5GFgvVLqqcDyx4HXlVIvBB93MA0Xjxw5wpgxx49lcd+aMt4qreerJ4/mqlmjQuwZv3rLHAmlFCtf2s7WD4+QZLdw3ZdPJq8wLUoljL5oZI43OrMxDCZzNBoubt++/fs5OTnXJiUl6cpCjHV0dJjq6uqeLSkp+XWo9XF/JQE4HziglKoBEJF/AqcBVSJSGLiKUAhUB7Y/AowN2n8M/tsTUZOdHXr2wXlFabxVWs+m8uaEqyT0ljkSH717kK0fHsFiMXHljfNHdAUBopM53ujMxjDcmdvb2++rq6vDYrFMJ3Fui49EPo/Hs7O9vf2+3jZIhErCIeAUEUnGf7thEfAR0ArcCPw68PxyYPtXgKdF5LdAETAF+CCaBaqpqWH8+PHHLZ9b5P+jt7WihU6vD6s5cf7t95Y5XKXbq1jz5m4ALr5mNqPHj/zJZQabOR7pzMYw3Jnnz5/vw/+7WxtmcV9JUEq9LyLPAxsBD7AJeBRIBZ4VkSX4KxLXBLbfLiLPAjsC2y9VSkV1DtD09PSQy3NSrIzPtFPW2M6umjZmFQzdjIWx1lvmcFQecfLas1tAwZkXTWXarIIolix2BpM5XunMxmDEzFpocV9JAFBK/QT4SY/FHfivKoTa/l7g3liVp695x+eOTqOssZ1NR5sTqpIw0LnWW1s6eOmpjXg6fcycP5qFZ02McsliZ7jnlx8OOrMxGDGzFlriXO8eQVpbW3td13XLYVN581AVZ0j0lbk3Pq+Pf/19Cy1NHRSNy+SCy0sQGfrZHAdqIJnjnc5sDEbMrIWmKwkxUFDQ++Xy2YWpmAR2VrfS6k6c2npfmXuzdkUphw/452O47PMnYrbE1z/HgWSOdzqzMRgxsxZafP1WjhOVlZW9rkuxmSnOS8GnYFtl4oxq1lfmUHZvq+TDtQcQk3DpdXNITbfHqGSxE2nmRKAzG4MRM2uh6UpCDFit1j7Xzx0duOVwNHFuOfSXOVhjfRv//ufHAJxz8TTGTIzPLmaRZE4UOrMxGDGzFpquJMRARkZGn+vnFPobLCbSlYT+MnfxeX28/uxW3B0eJs8YxbzT4rdrWbiZE4nObAxGzKyFFnYlITCz4tUi8j0RyQwsO0FE4vNrYAzV1tb2uX5aXjJmgf31roRpl9Bf5i7r3t5H+aFGUtOTuOjKmXHVULGncDMnEp3ZGIyYWQstrEqCiEwGdgJ/xN91sKticAvQ60hNRtVfLdxhNTM5Nxmf8jdgTAThfPM4fKCe99/ZBwKfunY2jmTbEJQsdoz4bUtnNgYjZtZCC/dKwu+BlUA+/lENu7wCnBvtQsU7t9vd7zZdYyRsr0qMSlP8nO4AACAASURBVEJ/mTvaPbz+3FaUglPOnsS4STlDVLLYCec8Jxqd2RiMmFkLLdxKwmnAshAjEx7CP7SxFsTlcvW7TUl+CgAfJ0i7hP4yr3ljF82N7eSPTufURZOHqFSxFc55TjQ6szEYMbMWWiQNF0M1dx0HOKNUloQRTh/jrkrCrupWPL74nokT+s5ctreWrR8ewWwWFl81C3OCzFlhxL7kOrMxGDGzFlq4v61XALcHvVcikg78DHgt6qWKc+H0Mc50WBmTkUSHV7G3tm0IShVbvWV2d3h4M9Dd8dRFk8krGNkzO0bCiH3JdWZjMGJmLbRwKwm3A2eIyG7ADjwDHAQKgO/Hpmjxy2YLr0HezHx/u4SPE6BdQm+Z17yxu/s2w8Iz42dehnCEe54Tic5sDEbMrIUWViVBKVUOnAj8BvgT/qmY7wTmKaVqYle8+JSWFt635ZkF/lsO2xOgXUKozEfLGtjywWFMgdsMpgS5zdAl3POcSHRmYzBiZi20sGeBVEq5gL8EHlof6urqSE3tf4bHmQWfXElQSsX1mAE9M3u9Pla+vB2AhWdOTKjbDF3CPc+JRGc2BiNm1kILd5wEr4i83TWIUtDyfBFJjNGAoigrKyus7QrTbGQ7LDjbPRxxdsS4VLHVM/PGdWXUVraQkeXg5HNPGKZSxVa45zmR6MzGYMTMWmjhXv8VIA34QESmhlinBQm3+5CIUFKQGO0SgjM3NbpYt2ovAIsum4HVah6uYsWUEbuJ6czGYMTMWmjhVhIUcDnwFvCeiJzfY50WpL29PextZ+YnRruE4MyrX9tFp9vLlJJ8Jk3LG8ZSxVYk5zlR6MzGYMTMWmiRXEnwKKW+DvwYeFVEvh67YsW3SPoYlwR6OOyI8+GZuzKX7a2jdHsVVpuZ8z49fZhLFVtG7EuuMxuDETNroUVyJcH/QqmHgU8DPwceiEWh4l0kfYwnZtuxmoUjzg6aOzwxLFVsVVZW4vMpVr++E4BTzplEWoZ9mEsVW0bsS64zG4MRM2uhRXIloZtSahVwCjAn6iVKAHZ7+H8crWYTU3KSAdhdE7+DKtntdrZ9dITayhbSM+3MP33CcBcp5iI5z4lCZzYGI2bWQgt3nASTUqq6x7JSYC4wKRYFi2cOhyOi7aeP8lcS4nlGSLPJyn9XlgJw1uJpWBK0sWKwSM9zItCZjcGImbXQBjW6jVKqXSlVFq3CJIqGhoaIti8e1TWPQ/xeSVi/eh9trW5Gj89k2ixj3M+M9DwnAp3ZGIyYWQut18GURKQJmKSUqhWRZvroxaCUSo9F4eJVTk5k0yBP76ok1MTnoErOBhel2+oBOOeS6XFX/oGK9DwnAp3ZGIyYWQutrxEXvwE0B17fOgRlSRjNzc0RjVaWl2IlO9lCfZuHo00djImzBn/r396Lz6sonl1I4ZiM4S7OkIn0PCcCndkYjJhZC63XSoJSanmo11r/3G53RNuLCMV5Kawrc7Krui2uKgl11S1s33gUMcEZF0wZ7uIMqUjPcyLQmY3BiJm10CJukyAidhG5QUS+LiKTY1GoeDeQPsZdtxzirfHiuytLUQpK5haRGeilYRRG7EuuMxuDETNrofVZSRCRe0RkWdB7C/Bf4K/AQ8AmETklpiWMQwPpY1ycF389HCqPOCndXoXFYmLCdGNVEMCYfcl1ZmMwYmYttP6uJFwOrA96/zlgOnAGkAusAX4Qm6LFr4F0H5qal4xJ4EC9i3aPLwalir61K/YAMPfU8WTnGq/tqhG7ienMxmDEzFpo/VUSxgPbg95fCLyglFqnlKoHfgHMj1Xh4pXNZot4H4fVzIQsB14Fe2tHflfIIwfqKdtbhy3JwsKzJw4oc7zTmY1BZ9aMrL9KghkIbsFyMrAu6H05kB3tQsU7p9M5oP2K42hQpfWr9wEw//TxOJJtA84cz3RmY9CZNSPrr5JQCpwHICITgRPw32LoMgaojU3R4ldubu6A9vuk8eLIvpJQfqghcBXB3D388kAzxzOd2Rh0Zs3I+qsk/AF4QESeBN4A3lNK7Qhafx6wKVaFC5eIZIrI8yKyS0R2isipIpItIitFpDTwnBW0/V0isldEdovIRdEuz4CvJOR1zeEwsq8krH/bfxVh7qnjsTusgDG/eejMxqAza0bWZyVBKfVn/IMqpQGrgat6bFIE/CU2RYvIA8CbSqli/JNO7QS+D6xSSk0BVgXeIyIzgOuAEmAx8AcRiepEA52dnQPab0yGnWSriZrWTuraBnaMWKs44uTAnlqsNvMxkzgNNHM805mNQWfWjKzfcRKUUn9RSn1GKXWLUqqyx7qvK6Veil3x+ici6cBZwOOBMrmVUo34e2Z0DQK1HLgi8Ppy4B9KqQ6l1AFgL7AwmmUaaB9js0mYkuu/mrBnhM4I+V6gLcKJp4wjOeWTxk1G7FetMxuDzqwZ2aAmeBohJgE1wBMisklE/iwiKUC+UqoCIPA8KrD9aOBw0P5HAsuiZjB9jLtuOewagbccqiua2LezGovVxIIzJhyzzoj9qnVmY9CZNSPra+6GeGEB5gHfUEq9LyIPELi10ItQsw8dN3lVdXU1S5YswWKx4PV6ufLKK1m6dCmVlZWkpKRgNptpamoiLy+P+vp6lFLk5eVRVVWFz+ejrq6OlpYW8vPzqampQUTIzs6mpqaG9PR0vF4vra2tFBQUUFlZidVqJSMjg2z8VxC2HW2kLK+ze73NZiMtLY26ujqysrJwuVy0t7d3r7fb7TgcDhoaGsjJyaG5uRm329293uFwYLP5eyHk5ubidDrp7Pzk+P1lSk1N5d23/FcRZswtpL6hmobGTzIppaitrQ2Zqba2loyMDNxuNy6Xa0RlAgZ0nmpra7v/nSRSpv7Ok4hQVVWVUJn6O09ms5mKioqEytTfeTKbzZSXlw8ok5ZYRKleJ3eMCyJSgL9B5YTA+zPxVxImA+copSpEpBB4Ryk1TUTuAlBK/Sqw/b+BnyqlggeNYv369aq4uHhAZWpoaCArK6v/DUOoaXXzhb9vJ9Vm5oXrZ42YGRWbGl08tuw/ANx8x1lkZB072MpgMscrndkYdObIbNy4ccOiRYsWRLlI2jCJ+9sNgXYSh0VkWmDRImAH8ApwY2DZjcDLgdevANeJSFKgW+cU4INolqmpqWnA++Ym+2eEbHF7KW/qiGKpBmfDfw+ifIppMwuOqyDA4DLHK53ZGHRmzcgS4XYD+Htg/J+I2ID9wP/DXwF6VkSWAIeAawCUUttF5Fn8FQkPsFQp5Y1mYfLy8ga8r4gwLS+F9WVOdtW0MXoEzAjZ7upk64dHADjprIkhtxlM5nilMxuDzqwZWdiVBBH5LP5v6aPocQVCKXVZlMsVEaXUZiDU5a1FvWx/L3BvrMpTX19PcvLAJzwqzktmfZmT3TVtLJo8/ANabnn/EJ1uL+Mn55BfFHqOhsFmjkc6szHozJqRhVVJEJH7gdvwj5VQToiGftonBtvOY9oIGlTJ4/Gxcf0hAE46M/RVBBh85nikMxuDzqwZWbhXEm4APqeUej6WhUkUg71UNzUwVsLeOhedXh9W8/A1Hdm5pZzW5g7yCtMYPzmn1+2MeHlSZzYGnVkzsnD/+piAzbEsSCKpqqoa1P6pSRbGZCTR6VUcaGiPUqkip5Ri07oyABacPqHPnhaDzRyPdGZj0Jk1Iwu3kvAo8MVYFiSRRKO/cPcth2GcEfLowQaqK5pJTrExbXZhn9sasY+0zmwMOrNmZOHebsgEPi8iFwBbgWMG9lZKfTPaBTO6aXkprNrbwO6aNi4dpjJsXO+/ijB74VgslrjvLatpmqZFKNzf/DPw325wA8XArKDHzNgULX61tLQM+hjTuodnHp45HJoaXZTuqMZkEk48eWy/20cjc7zRmY1BZ9aMLKwrCUqpc2NdkESSn58/6GOckO3AYhION7bT6vaSYovqRJX92vzeIf/gSbMLSU3vf6yGaGSONzqzMejMmpFFdA1ZROwiMlNESkRk+Ef5GaFqamoGfQybxcQJOQ4UsKd2aK8mdLq93YMnzTttfFj7RCNzvNGZjUFn1owsrEqCiFgDYyU0AFuAbUCDiNwnItZYFjAeRWu+he5bDkPceHHX1graXZ0UjMmgaFxmWPuMlDkmhpLObAw6s2Zk4V5J+A3+3g1fA6bin+/gFuB64FexKVr8ys6OziiJxXkpAOwe4nYJm9/3D5504injwt4nWpnjic5sDDqzZmThVhI+DyxRSi1XSu0LPP4K3Ax8IWali1PRulRXPKqr8WLrkI2AVnnESdXRJuwOK9NmFYS9nxEvT+rMxqAza0YWbiUhA9gXYvk+/N0jtSDp6aHnN4hUUXoSqTYz9W0ealo7+98hCrZ8cBiAknlFWK3hN5aMVuZ4ojMbg86sGVm4lYQtQKixEL6FHonxOF5vdCaVNIkEzeMQ+1sOHe2d7NxSAcCchf13ewwWrczxRGc2Bp1ZM7JwKwl3AjeKyB4RWS4ifxWR3fjbKXw3dsWLT62t0WtoWDzK3y5hKBov7thUjqfTy9hJ2WTnRTbiWjQzxwud2Rh0Zs3IwqokKKX+g7/B4nNAKpAeeD1NKfVu7IoXnwoKwr+X35+hupKglOq+1RDpVQSIbuZ4oTMbg86sGVnY4yQopcqVUj9USl2llLpSKfUjpVR5LAsXryorK6N2rK5Kwp7aNry+2DVeLD/USG1VC8kpNqbMiHwglWhmjhc6szHozJqR9TrioojMAzYrpXyB171SSm2MesnimNUavaEjshxW8lNtVLW4KWtoZ1KOI2rHDtZ1FWHmgtGYBzBPQzQzxwud2Rh0Zs3I+hqW+SOgAKgOvFZAqBE2FDC0YwaPcBkZGVE9XvGoZKpa3OyuaY1JJaGjvZM9H/u/OcxeEPmtBoh+5nigMxuDzqwZWV9fGScCNUGvJwWeez4mxbKA8ai2tjaqx+saVClWkz3t2lKBp9PH2InZZOYkD+gY0c4cD3RmY9CZNSPr9UqCUqos+C1wWIUY0UdEwh+WzyCifiUhxsMzb9twFIBZC8YM+BhG/OahMxuDzqwZWbg3nw8AeT0XikhOYJ0WxO12R/V4k3OTMQuUBWaEjKaaymYqjzhJsluYMnPgM79FO3M80JmNQWfWjCzcSoLgv5rQUyrQHr3iJAaXyxXV4yVZTEzOTcanYHdNdK8mbPvIP9tj8ZzCiEZY7CnameOBzmwMOrNmZH01XEREHgy8VMCvRCT4prgZWIgecfE4sehjPGNUCrtr2thR3ca80dEZMtXj8bFjk78X62BuNYAx+1XrzMagM2tG1t+VhFmBhwDTg97PAiYDG4GbYli+uBSLPsYz8v2NF3dUtUTtmHt3VNHu6iSvMI38osFVPIzYr1pnNgadWTOyPq8kKKXOBRCRJ4BvKaWahqRUcc5ms0X9mF2VhJ3VbfiUwhSF+d63bww0WJw/etDzx8ci80inMxuDzqwZWbjDMv8/XUEIX1paWtSPmZdiIy/FSqvby6HGwTcDaWlq52BpLSazUDynaNDHi0XmkU5nNgadWTOysIfWE5FzReRREXlTRN4OfsSygPGorq4uJsf95JbD4Bsv7txSgVIwaVoeySmD/9YQq8wjmc5sDDqzZmRhVRJE5CbgDSANOAf/IEtZwDxgR4zKFreysrJictwZo8KvJCifD19H6G5MSqnuWw0l80ZHpWyxyjyS6czGoDNrRtZnm4Qg3wFuVUr9WUSagbuUUvtF5CEgei3pEoTL5SI9PTo9EIKV5Punb97Ry6BKDR9speLFlTRtL6V5+158HR1kLZxD3vmnkXfh6aROHg9AdXkTtVUtOJKtTJp63PAXAxKrzCOZzmwMOrNmZOFWEiYBbwVed+AfHwHgIeAd4PvRLVZ8a2+PzdARk3IcJJmFI84OnO0eMuz+0+fzeNj3P0+w7/d/heBBMUWoX7eR+nUb2X3PQ4z70tVM/eEtbN/o7/ZYPKdwQJM5hRKrzCOZzmwMOrNmZOFWEurw32oAOArMBLYCOUBspiWMY7HqY2wxCVPzUthW2cLO6lZOGZdBe0UNW275CQ3vbQYRxn/1s+SdewppJVMwWS3UvvMBNW/9l4qX3uLQX56n+p0P2HHhl4Do3WoAY/ar1pmNQWfWjCzcr5FrgQsDr58FHgx0i/w7sDIWBYuUiJhFZJOI/CvwPltEVopIaeA5K2jbu0Rkr4jsFpGLol2WWPYxDm686G5o4v3LvkbDe5tJGpXDSc89wPSffYvcc04mKS8ba2Y6hVecz+yHfsKpbz5O6vQTqPbYaXf7SE/yDXpshGBG7FetMxuDzqwZWbiVhFvxVwgAfgXcj/8qwrPAzTEo10B8C9gZ9P77wCql1BRgVeA9IjIDuA4oARYDfxCRqE51bbfbo3m4Y3Q3XqxsYdu3foHrcAXps4s5bdVycs5Y0Ot+6TOnctqbj9N54acBcLz7Nof+8kLUyhXLzCOVzmwMOrNmZGHdblBK1Qe99gG/iVmJBkBExgCXAPcCtwcWX46/JwbAcvxtJ74XWP4PpVQHcEBE9uIfXnp9tMrjcMTuDkzXlQT7i69Ss+JdLBlpnPjne0nKy+53X7dPqJY0wEfmvm3s/OE6fG43E2/5/KDLFcvMI5XObAw6s2ZkvV5JCFyuD+sxlAXuxe+BOwFf0LJ8pVQFQOB5VGD5aOBw0HZHAsuipqGhIZqHO0aG3cKJDUc59c0XAZj1wA9JHlcY1r57Pq7E61WMOyGXOT/5GgC7f/YQZY8/P+hyxTLzSKUzG4POrBlZX1cSagk982Owrtkho3q5PhIi8mmgWim1QUTOCWeXEMuOy1ldXc2SJUuwWCx4vV6uvPJKli5dSmVlJSkpKZjNZpqamsjLy6O+vh6lFHl5eVRVVWGxWKirq6OlpYX8/HxqamoQEbKzs6mpqSE9PR2v10traysFBQVUVlZitVrJyMigtraWjIwM3G43Lpere73NZiMtLY2a8grOePJRzD4fzk9dSOa5J1NWVobdbsfhcNDQ0EBOTg7Nzc243e7u/R0OB1s/PATACdNzsEwYTYHzy1T+8jF2/vh3eLLTyD5nYa+ZUlP9HVp6y2S1WqmtrR1Qprq6OrKysnC5XLS3t3evDyeTzWbD6XSSm5uL0+mks7Oze31/56m/TP2dJ5vNRnV1dUJl6u882e12qqqqEipTf+fJ4XBQUVGRUJn6O0/JycmUl5cPKJOWWESp0PUAETk73IMopdZErUQREpFfAdcDHsAOpAP/BE4CzlFKVYhIIfCOUmqaiNwVKPOvAvv/G/ipUuqY2w3r169XxcXFAypTRUUFhYXhfbuP1MFHn2HX3Q9Qk1/Ezl/8gl9eGl4ZnQ0uHrt/DRaLiVt+cB5Jge6Tpb95jH2/ewJzajKnvPon0qafMKByxTLzSKUzG4POHJmNGzduWLRoUe8NpLS40uuVhOH8wx8JpdRdwF0AgSsJ31FKfVFE7gduBH4deH45sMsrwNMi8lugCJgCfBDNMrndoUc6HCxPSyv7fr8cgHcvvJzyug48PoXF1P/kTLu2+MdGOGH6qO4KAsDkO2+mdf8hKl9exYYvfodT33w8rPYNPcUq80imMxuDzqwZWbjDMo/0Ngmh/Bq4QERKgQsC71FKbcffK2MH8CawVCnljeYHx6qP8cFHn6WzvpHMk2bhOWkeHR4fe2ra+t1PKcX2Tf5Kwoy5x07mJCLM+v2PyJhfQvvRKjZ/5cf4PJ6Iy2bEftU6szHozJqRhdsFshb/fA29PUYEpdQ7SqlPB17XKaUWKaWmBJ6De2jcq5Q6QSk1TSn1RrTLEYs+xu56JwcfeRqAqT/4GrOL/GNbba1s7nff6opm6mtacSRbmTAl97j1ZkcS8574NUmjcmhYv4m99/054vIZsV+1zmwMOrNmZOFWEs4Fzgt6XIR/3IEy/O0BtCCx6D504KGn8DS3knvuyWSfOpfZhYFKQkX/U2fs2Oy/ijBtdiFmc+hTnjQqh9mP/AxMJvY/+CQ1b62LqHxG7DKlMxuDzqwZWViVBKXUmh6Pt5RS9wPfRVcSjmOzDX7q5WDuukbK/vIcAFO+/1UAZhf6WxJ/XNmKx9d7JxSfT7FrSwUAM07suyFSzunzmPL9rwCw9Rv34DpcEXYZo505HujMxqAza0Y22Nl9NgNnRaMgicTpdEb1eEeefgVfu5u8RaeSMcffmyEn2cqYjCTaPT5Ka3tvl3B4fz2tzR1kZDsoHJvZ72dNuvWL5C06lc6GJrbc8pOw2ydEO3M80JmNQWfWjGzAlQQRSQVu49iBiTQgN/f4+/4DpbxeDv3VP3DSuCXXHLOu62pCX7ccdgZ6NUyfU4RI/70gxGRi1v/eTVJhHo0ffcy+3/41rHJGM3O80JmNQWfWjCzc3g3NItIU9GgGnPi7Fn43piWMQ9GshVev/C/tR6tInjiG3HMWHrNuTqCSsKUidONFT6eX0u1VAEyfE36fZ1t2BrP/924QYd/v/0r9e5v73ceI3zx0ZmPQmTUjC3eq6Ft7vPfh79XwvlJKj9/ZQ2dnZ9SOdegJ/yRM4266EjEdW6ebXeBvvLi9qjXkeAn7d9fQ0e5hVFE6OaMiGw0t54z5TPrG9ex/8Em2Lv0Zp69ajjWz91kjo5k5XujMxqAza0YW7gRPy2NdkEQSrT7GLaUHqVvzIWaHndGf/dRx63NS/O0Sjjg72FXdysyCYysCOwMNFiO5ihBs8ndvpm7tRzg37WD7d+9jzqM/7/WWhRH7VevMxqAza0YWdpsEEbGLyJdEZFng8SUR0f1kQohWH+NDf/0nAIVXXdjrt/iTxviXf3i46ZjlHe2d7N9dAwLFswdWSTBZLcx55KeYU5KpfPVtyp/tfUgJI/ar1pmNQWfWjCzcNgnzgAPA/+CfVnkhsAzYH1inBUlJSRn0MTytbd1/lMf9v6t63e6ksYFKwpFjKwl7tlfh9fgYOyGbtIyBzw2fPGEM039xGwA7fvBb2sqOhtwuGpnjjc5sDDqzZmThXkl4FFgLjFFKnaWUOgsYC/wnsE4LYjYPflLMqn+9g6e5lcyTZpFeMqXX7WYVpGIzC3vrXDS0fXIfsWtshOn9jI0QjtHXXUL+JefgbW1j6633hOwWGY3M8UZnNgadWTOycCsJJfhnSmztWhB4fU9gnRakqamp/436cfTZ1wFCtkUIlmQxMScw+uJHR/2f29LUzqF9dZjNwtSZg7+3KCKU3P89kgpyafxwG/sf/Ntx20Qjc7zRmY1BZ9aMLNxKwi78Myb2VAjsiV5xEkNeXt6g9ncdrqD+vxsx2W0UXLao3+0XjAlUEo74u0Lu3laJUjBxWh52h3VQZeliy85g1oM/BmDf//yFxo3bj1k/2MzxSGc2Bp1ZM7JwKwk/Ah4UketEZELgcR3we+CHcTAj5JCqr6/vf6M+lL/wbwBGLT4La3r/XRcXBtolfHSkCa9PBfVqCFWvG7jcs05iwtc+h/J62fr1n+Jp6b6wNOjM8UhnNgadWTOycCsJrwLFwNPAvsDjaWAG8DL+MRO6Zoo0PKV6n0shnH2PBhosjr7m4rD2KUpPojDNRnOHl02ldVQecWK1mZlUHP1vA1Pv+ippJVNoO3iUnT/6/THlNhqd2Rh0Zs3Iwh1M6dyYliLBDOZSXeOGj2nbf5ikUTnknH1SWPuICCeNTeeVHbV8+IF/lOwpJflYrdFvfGRKsjH74Z+wfvGXOPqP18hbdCoFl55nyMuTOrMx6MyakQ10FsheH7EucDyoqqoa8L5d3R4Lr7oIkyXcOhwsGJMOStF4wH+ZcKADKIUjrXgS037sH4Tz4+/8BteRykFljlc6szHozJqRRTKYUr6I3CMiz4vIcyLyUxHJj2Xh4lVqamRDIHfxtndQ8fIqAEZfG96thi5zClPJ6vRibe/EkWJj/Ak5AypDuMZ96Sryzj8Nj7OZrbf+jBQDzj8/0PMcz3RmYzBiZi20cAdTOh3YC3wecAHtwBeBUhE5NXbFM5aat9bhcTaTNnMKadNPiGhfh9XMTOX1vx6bick82FnA+yYizPr9D0kalUPDe1so/9OzMf08TdM0beiF+5dkGfB3YKpS6nql1PXAVOAf+Edh1IK0tPQ+dXNfKl5cCUDRVRdFvK/Pp0ir9/c2OGiPTrfH/thys5j98E9AhPJH/k7D+1uG5HNHioGe53imMxuDETNroYVbSTgR+B+llK9rQeD1b4G5sShYPMvPj/wuTKezmZq31oEIhVdcEPH+h/fX4XF10mYx82FTJ03tx4+KGAs5Zy5g4tIvgE+x5es/xV1vnClmB3Ke453ObAxGzKyFFm4lwQlMDLF8ItAYveIkhpqayHuCVr2+Bl+Hm+zT5mIvjLxl8Y7N5f4XRel4EdYfGro/1lO+9xUcMyfTfrSKbd/8Ocrn63+nBDCQ8xzvdGZjMGJmLbRwKwn/AB4XkS+IyMTAYEpfBB7DfxtCC9LbdMp9qfjnCgAKr7ww4n073V5Kt/tbI8+cNxqA/+wfurqbyWph7K++jTUzjZq31nHwEWP8kxjIeY53OrMxGDGzFlq4lYQ7geeBv+BvwLgP+DPwHPD92BQtfmVnRzbwZHtVLXXvbkBsVgouOSfiz9u3qxp3h5eCMRmcNysfk8Cm8maaO4bmlgNAQcm07mGb9/zyjzR8uG3IPnu4RHqeE4HObAxGzKyFFu44CW6l1LeALPztE+YC2Uqpbyul3LEsYDyK9FJd5curQCnyFp2KNTM94s/rutUw48QiMh1WZhem4vEp1pcN3S2HmpoaRl14BhNu+TzK62XzV35ER01iD+1qxEuyOrMxGDGzFlqflQQRSRaRh0XkqIhU4796UKGU2qqUahuaIsaf9PTI/tB33Woo+kzktxraWt0c3FOLmIRps/0zPp41MQuAtQeG7pZDV+apP/gamSfNoqOihi1fvTvktNKJItLznAh0ZmMwYmYttP6uJPwMuAl4DX+7ZlyzCwAAIABJREFUhAuAR2Jcprjn9XrD3rZ1/2Gcm3diTk0m74LTI/6s3dsq8fkUEybnkJKaBMDp4zMwCWw82kzLEN1y6Mpsslo48bFfkDQqh/p1G9lz7x+H5POHQyTnOVHozMZgxMxaaP1VEq4EliilvqKU+iZwCXCFiER/UoAE0tra2v9GAV0zPuZffDZmR1LEn7Uz6FZDl6xkK7MKUun0KdYM0dWE4Mz2gjzmPPpzxGLm4CNPd48imWgiOc+JQmc2BiNm1kLrr5IwFljb9UYp9QHgAaI7B3GCKSgoCGs7pRQVgUpC0TWLI/6c+tpWyg81YrWZOWHGqGPWXTTVPyzzG7vqIj7uQPTMnH3KiUz76TcA+Pjbv6Rpe+mQlGMohXueE4nObAxGzKyF1l8lwQz0bJjoIfzZIw2psrIyrO2cG7fTdvAoSfm55Jw+L+LP2bHxKABTZxZgsx17Ss6cmEmqzcye2jb21cW++UiozOOXXEPR1YvxtrnYeMOdCdeQMdzznEh0ZmMwYmYttP4qCQI8JSKvdD0AO/BYj2VaEKs1vGGRy5/3X0Uo/MwFiDmyOzjKp9i+yX+roWtshGBJFhOLJvu7Mb2xO/ZXE0JlFhFKln2PjPkltB+tYtOX7sLXkTidYcI9z4lEZzYGI2bWQuuvkrAcKAfqgh5PAYd7LNOCZGRk9LuNz91JxctvAVB0deRzNRzaX0+zs530LAdjJmSF3OZTxf5bDqv2NtDuie0oiL1lNtuTmPfEr7GPzqfxw218/J3foJSKaVmGSjjnOdHozMZgxMxaaH3eNlBK/b+hKkgiqa2tJSUlpe9t3nmfznonqdMmklYyJeLP2L7Jf6uhZG4RYgo9OtrEbAfFecnsqmlj7YEGLpgSu+mj+8qcNCqHect/w/uXfo3y594gecJoJt/xpZiVZaiEc54Tjc5sDEbMrIUW2/mEh4CIjBWR1SKyU0S2i8i3AsuzRWSliJQGnrOC9rlLRPaKyG4RifxrfD/CqYV33WoouvqiiIdAdXd42POxfxjmkrnH32oIdnFxLhD7Boz9ZU6fOZU5f7oHTCb23v9njvz9XzEtz1Aw4rctndkYjJhZCy3uKwn4G1LeoZSaDpwCLBWRGfiHi16llJoCrAq8J7DuOqAEWAz8IdpdOt3uvu+7dza1UL3C32mk8MrI6yi7P67E0+llzIQsMnOS+9z2nEmZOKwmPq5qpazBFfFnhau/zACjLjyDGb+6A4Dt3/kNNW+/F7PyDIVwMicandkYjJhZCy3uKwlKqQql1MbA62ZgJzAauBx/mwoCz1cEXl8O/EMp1aGUOoB/LoqF0SyTy9X3H+Oqf63G1+4m69S5OEZHPiXr9kCvhpIQDRZ7cljNLDrB34Dx+W3VEX9WuPrL3GXcjZ9h0jdv8A/dfPMPady4PWZlirVwMycSndkYjJhZCy2hujKKyAT880q8D+QrpSrAX5EQka6BBEYDwV9hjwSWHaO6upolS5ZgsVjwer1ceeWVLF26lMrKSlJSUjCbzTQ1NZGXl0d9fT1KKfLy8qiqqsJut1NXV0dLSwv5+fnU1NQgImRnZ1NTU8Ph5S8CYL/gZDo6OqisrMRqtZKRkUFtbS0ZGRm43W5cLhcFBQVUVlZis9lIS0vj4P4KjhxowGwRHBnu7v3tdjsOh4OGhgZycnJobm7G7XZTUFDAqTmdvAa8VVrPuaO8TBubj9PppLOzs/v4/WVKTU0F6DWTw+GgtraW1tbW7mP2lmnc7TdRV3oA5xtr+ehztzP2Dz+i8KQ5uFwu2tvbu/fvK1NlZSUOhwObzYbT6SQ3NzfqmdLT0/F6vb1mSk5Oprq6OuR5qqurIysrK+4y9fVvr66ujpSUFKqqqhIqU3/nKS0tjYqKioTK1N95Sk9Pp7y8fECZtMQiidLSXERSgTXAvUqpf4pIo1IqM2h9g1IqS0QeBtYrpZ4KLH8ceF0p9ULw8davX6+Ki4sHVJaysjLGjx8fcl3zrv3895wvYk5N5twtr2JJcUR07DVv7ubD/xygZN5oLr56Vtj7/Wr1QVbva+CKkjy+fuqYiD4zHH1lDsXX6WHzl39I9ZtrseVlc/LLj5AyaWzUyxVLkWZOBDqzMQwm88aNGzcsWrRoQZSLpA2TuL/dACAiVuAF/n979x0lR3nme/z7VOfpyTPSzEgaJRAKIERQMsGABQZkFkxaYxwwxscBOWDvnj329b1evPf6GO/Zy9p318denMBeGwwYkwwYLMC2BFYEoYgSkmY0OfXk6fTeP7o0akk90oTumZ6u53NOn65+q6vm/albmkdvvVUFvzbGPGU3N4pIlb2+Cjg21l5L4kqSx8wgcZpn2ni93iHX1T76HADTbvngiAuEWDTOzi2JQw1Llo/sF/0dSxKHNV7c00J7X2RE2w7H6TKnYnncLPnxv1B2+VLCzW1suv3L9B6pT3u/MmmkmXOBZnYGJ2ZWqU36IkESpwb8DNhtjHkwadWzwF328l3AM0ntd4iIT0TmAPOAjensU0FBQcr2+ECYuideAmDGnX834v0e2NNEb0+Ysqn5VFUXn3mDJHNKA6ycWchAzPD0jvTfBnaozKfj8vu48OEHKF56Hv1HG9l4yxp6D6e1Xsuo0WSe7DSzMzgxs0pt0hcJwKXAJ4APiMjb9mM18ABwjYjsI3H3ygcAjDE7gceBXcBLwBpjTFpvedbamvp0w6Y/riPSFqJg0dkULhn5oYx3NtUAiVGEkZ42CfDRCxLXY39mVzM94fTe5W2ozGfiDuZx8W8eTFyVsbbBLhSOprVvmTLazJOZZnYGJ2ZWqU36IsEYs84YI8aY840xF9iPF4wxrcaYVcaYefZzW9I23zHGnGWMmW+MeTHdfSopSX0FxJrfJK5gPePOvxvxL/mOtl4O7W/F5bZYeMHo7q+1cGqQJVX59EbiPL6tcVT7GMpQmYfDU5jPsse+T/GyxYkRhZvX0HPgSBp7lxljyTxZaWZncGJmldqkLxKyUarTh/pq6mn98yYsn5eqW0d+bYQdm2vBwPzzKgnkjf544d1LEwXGkzuaqO8cGPV+TjbWU6bcBUGWPvogJSuW0F/XxIYbP09o25409S4znHiamGZ2BidmVqlpkZAB/f39p7TV/OoZMIaK1VfgLSkc0f5isTg77GsjLF42tjMTFlUEWXV2CZGY4aEN6RvWT5V5pNz5QS7+zYOUX7WScGsHG2/9Iq3rtqShd5mRjsyTjWZ2BidmVqlpkZABJ9+LPdbbT82vngZg5qdvG/H+9u1spLtzgNIpwSFv5jQSn1k2Hb/bYv3hEG8d7Rrz/iB99593BwNc9Mj3qLr5GmLdvWy+82vUP/2ntOw73dKVeTLRzM7gxMwqNS0SMuDke7EffeJFIu2dFF10LsVLzxvx/ra+cRiAi943a1QTFk9WFvTw0QsSp0T+6G+1xOJjv1ZGOu8/b3k9nP/Df2bmp2/DhCNs+/y3OPDvv8i6u0emM/NkoZmdwYmZVWpaJGSA3+8fXDbxOIce+i0Asz/7kRH/kq+vDVF3pAOf382ii0Y3YTGVW8+bSlWBl0Pt/Ty1Y+yXa07OnA5iWSz8zldZ8O0vgwj7vvcTtn/pfxMfyJ5ryqc782SgmZ3BiZlValokZEAgcPwiSc1/epPeA0fwT6+g4oYrR7yvrW8cAhJzEbze9F1F2+u2WHNJYn7Dw5vrOdDaO6b9JWdOFxFh9ufu4KKHH8AV8FP35EtsuHkN/XWZuwfFSGQic7bTzM7gxMwqNS0SMqC9vX1w+dBDjwEw657bsdwj+yXf3dnPu9sbEIELV6b/srDLq4u4YWE5kbjhu68dpj8aH/W+kjOn29RrL2fFsz/CP72C0NadvHHNp7JiQmMmM2crzewMTsysUtMiIQPKysoA6Nyxl7Z1W3AF85jxsZFfYfHtDTXEY4azF1VQVJKZyv6zK6ZTXeTjSEc/P904+rMdjmXOlMLF87nk5V9Q9v5lhFs72PyR+zj4H7/ExEdf2IxVpjNnI83sDE7MrFLTIiEDuroSZwwc+H7iTtUzPvohPEUju8xpNBJj28bEFRYvviRzN5fxuy2+cdVs3Jbw7K4W1h/qGNV+jmXOJG9ZMUsffZA5X/oEJhZj73d+zOaP3Ed/Y0vGf3Yq45E522hmZ3BiZpWaFgkZEA6HCW3bQ+Pzr2H5vcxZ8/ER72P75lr6esJUTCtkehpOezyds8vz+PTSKgAeeP0we5tHPj8hHB6fCYXicjH/m1/g4v/+N7xlxbT+dTPrr/okjS/9ZVx+frLxypxNNLMzODGzSk2LhAyorKxk73d/DMDMu2/DXzVlRNvHonE2/uU9AFZcOTctpz2eya2Lp3LNvFIGonH+18sHaOga2dUYx/u86ilXX8Ilr/6SsvcvI9LWwVuf+jrvfPHbhNs7x60PTjyXXDM7gxMzq9S0SMiAA394ldbXN+LKz2Pulz4x4u13vnWUrlA/5RX5zFtUkYEenkpEuO+yai6clk97X5RvvnSAroHosLefiPOq/RXlLH3s31nwL1/BCvioe/KPrL/iYzS+8OdxuaaCE88l18zO4MTMKjUtEtLMGEPrfz0OwJwv3Im3tGhE28dicf72+kEAVl55FmJlfhThGI/L4ltXz2V2iZ+a0ABff3E/of7hFQoTdcqUWBazP/sRLl37S4qXn89AUytvffobbP3kP9F7pD6jP9uJp4lpZmdwYmaVmhYJadb8ynp6tr2Lt6yY2Z/7yIi33/12HZ3tfZSWBzln8fgP+QW9Lv7PtWcxrdDLvpY+/uH5fTT3nPn4pNc7+ptOpUNwbjUrfv9DFn7na7gLgjS/sp51V9zJge8/TKwvfTeySjbRmSeCZnYGJ2ZWqWmRkGaHf/4kAHO/chfu/OCIto3HDRvsUYQVV87FGsdRhGRT87383xvOYXaJnyMd/XztuX0cDZ3+hi+hUGicejc0cbmYdc9tXLbuUSo/fDXxvgH2PfAQf73sDup+/3LaD0FkQ+bxppmdwYmZVWqu+++/f6L7kJVqa2vvLy8vH/F2lauvhII8Zt9964gvnrR9cy07t9ZRVBrggx8+d1wPNZwsz+PiirklvFPfzeGOfv60v53qIh8zi1NfrtXj8WTN/z7c+XlU3nAVJSuX0LVzP70HjtD4h9dpWfsmgRmVBGZNT8tk0GzKPF40szOMJXN9fX393LlzH0pzl9QE0ZGENHPl+cm/ZRUuv29E2w30R1n38j4ALr/mHCzXxH80hX4331t9NpfOKqInHOPbf3qPhzYcJZrihlDZ+D+PssuWcsnLP+e8B/8HvqllhN7ezeY7vsrGm++l7Y23xjyykI2ZM00zO4MTM6vUJv43UQ6KRCIj3mbDnw/Q2xNm2sxi5p+fPacfBTwuvnX1HD67YjqWwJPbm7jv2b2n3OthNJnHg7hczLjzBt7/tyc453/ei6ekkPa/bWPjLWvYcOPnaXpl/aiLhWzNnEma2RmcmFmlpocbhjDaww2QmBnsHsGhhlB7Ly88vh0TN9x45wUUFGXXzGIRYVFFkAunFbD1aBc1oQFefLeV3kicRRVBPC5rxJnHm+VxU7L8fKo/+WFcPi9du/bTe7CG+t+/QuMfXsfyegiePRvLM/wM2Z45EzSzM4wlsx5uyC06kpABIz3H+C8v7SUWjbPwgiqqqosz1KuxO7cyn5/cupCbz01cHOrJ7U3c/cQunt3VTG1dZk83TBdPYT5n/+M9XLH5Keb/8xfxVZTTvecgO772XV6/+Gb2fvfHwz510onnkmtmZ3BiZpWajiQMYSwjCdFolLy8vGG998iBVv7y0l7cHosPf/wifH7PqH7mePG4LJZVF7K8uoj9rX3UhgbYWNPJhoYIfq+LmcV+3BM44XK4LK+XkmWLmfXpW8mbW03/0Ub6Dh2lfcM2Dv/0CTq27MDy+8ibNR1xu1LuYySfc67QzM4wlsw6kpBbnDWGNk5crtS/VE4WHojy0lM7AFhxxVwKi7PrMMPpnDMlj/+46RzWHwrxyJZ6Dnf084N1Nfx8Ux2r55dxw8IpVBRk/4xwy+dl+t9fz7Tbr6Nj4zvU/OppGp57jZbXNtDy2gY8xQVU3ng1026/juKLz0Ws44Nvw/2cc4lmdgYnZlap6UjCEMYyktDU1ERx8ZkPG6x9bhdHDrRRMa2Q625bPGHXRRgtEWFmiZ8PLSgnEOmix3io6wyzs7GH3+9s5u26bmJxQ2WBF587u49siQiBGZVUrL6S6rtuxldRzkBTG3019XRu28PRR5/n6KPP01fXiLsgiL9yCk3NzcP6nHPJcL/buUQzj4yOJOQWGY9r3E9Gb775plmwYMGotu3t7T3jUN17e5v53cNbcLmEj6+5hCmVI7uVdLY5lnl3Uw/P7Gxm3aEOwrHEd8slcF5lPitnFrFiZiHTC33jctOqdOjafYC6J16i/pk/0X+0cbDdO6WU0qtWULX6CsouX4o76Izh6OF8t3ONZh6ZrVu3blm1atXSNHdJTRAtEoYwliKhtraWGTNmDLm+vy/Cwz9YR3fnAJdfew4rrpg72m5mjZMz94RjrD/Uwdr97Wyr7yL50grleR6WTMvn/Mp8FkwNMrPYjyvLR1FMPE7H1p00PPcqjX/4M/21xyd2icdNybLzKb9qOWWXLaVg8TkjvpDWZHGm73Yu0swjo0VCbsnNf8km2OkKr3gszvOPbaO7c4Cq6iKWXTZ7/DqWQSdnDnpdfPCcMj54ThldA1E213bytyOdbD3aRUtvhLX721m7vx2API/FvPI85pYFOKs0wNzSADOK/fiz6BCFWBYlSxdTsnQxC+7/Mt17DrLv8ecZ2LiD0Fu7aXtjK21vbAXAXRCkZOUFlKxYQsny8ylasgDLl/3zM4bDif+p0MzKyXQkYQhjGUno7+/H7099+eLX/rCbLesPE8jz8LF730dxaW4MY54uc7K4MRxu7+ftui52Nvawp7mHpu5TL9wiJO4hUV3sY1qhj6qCxPPUfA9Tgl4KfK4JP2RxLHO4vZO2v26m5c8baFu/ld5DR094n+XzUnDePIovXETRhYsoPH8+wbnVyCScHDbczzmXaOaR0ZGE3KIjCRnQ2NjIrFmzTmnfvrmWLesPY7mEGz92Yc4UCDB05pNZIswpDTCnNMDN5yXa2noj7G3p5WBrHwfb+nivrY+6zgEau8M0doeBrlP243dblAc9lOV5KM3zUBJwUxJIPBf53RT6E88FPhdBrwsrAwXFsczekkIqb/wAlTd+AIC+o420vbGVjk3bad/4Dt17DhLaspPQlp2D27ryAhScezYFi+zHwrPInz8HT1F2z00Z7uecSzSzcjItEjIgPz//lLbD+1t45ZnEL4lrbjqX6jml492tjEqVebhK8zysnFnEyplFg23RuKG+c4CaUD91nWEaugao7wzT1BOmqTtMXyRObWiA2tCZbwMtQL5dLAS9LoKexHOe1yLP4yLPY+H3uAh4LPxuC5/71Gefy8LrFrwuC68r8RwMpr7LZ2B6BdNvv57pt18PQCTURWjbHkJbdxJ6axed2/fSX9dEx6btdGzafsK2vopygvNmETxrJsG51eTNrSZvzgzyqquy4pDFWD7nyUozKyfTImEcHNjTxLO/eZt4zHDxpbNYvNRZk6BGw20J1cV+qlPcddIYQ084RmtvhNbeCC09ETr6o3T0RWnvixDqj9I1EKOjL0p3OEZPOEbXQOKRbh6rFrdL8FhiP1t4XILbOvHhsopxz78M98LLcVmCr7uL/MOHCNbWEqipwX+kBt/Roww0tjDQ2ELbui0nZhYhXl5GvGIqpmIKpnIqZuoUmDIFppYhU8qR/Dwsy8KSRGEkIollAUEQwV4ndlviPQKQtA4Y3C6xSgaXu7r6KOrvTLzv2D7sPh4frJGkbY+vJ2n/yQM7wok/64QVpy6euDzEAFHyfoY7iDTU+0KdEbqtvtP+jJNWjEg6x7jSNWDW0xulrCw9+1KTmxYJGdDd3U2Z/Tds385GnnssUSAsWVHNldePbp5DtkvOnGkiQr7PTb7PzaySM1+AKhY3g8VCdzhGz0CMnkiMvkiM3nCcvmiMvkic/kicvkicgVhiuT8aYyBqCMfi9EfjRGKJ5YFonEjcEImZxHPccOqvkGHInwkLZsKxr0Q8TmFHG2XNDRS3NlHSkngUt7VQEGrD1dyCq7kFdqTeXcTjpauwiJ6CInryC+jNL6Qnv5C+YAG9wXx68wvoywvSnxek358H1mgnhjaPcrvJbHJcdjxd5hS5+K/qionuhsoCji0SROQ64AeAC/ipMeaBdO27oqICYwzbNtSw9vndmLjh4stmc+X18yd8sl2mVFRk7z8oLksosucopFNfXx8ur49IzBCNGyKxRPEQjSUKiKgxxOxiImYvR+1H/NizgZg53hYzM4nFDXFjr4sbIkBLOII0NiFNzVgNTbiamnE1N+NqbcfV0oK7tQ3PwAAlrc2UtJ75l7gRIRYMEk1+5AWJ5uURDQSI5uUR8QeIBQJE/f7Ew+cn4vUSzwsQ9fqJ+XzEXYk/02PTnw1m8IUBkudFG3uFOf6WwdfJ6zlpuxP6nWK7k9ec+DNTL592xyc1GxNH5MSCaqgJ3xM5DTydc9Criib+0JbKDo4sEkTEBfwQuAaoBTaJyLPGmF3p2H/d0QZ2buzg3e2Jc+lXXnUWl159ds4WCADNzc1UV1dPdDfGVUtLC9XV1XjH7SSFof98jTHEunvpb2hOHLJobiPc3M5AUyvh1g7CLe2EW9qJtIcIt4WIdnbj7k48xkI8blx5AVwBH66AH8vvw+X3DT67Aj4snxfL78PyerD8Xlw+e9nnwfJ6sbwexOvB8niwvG7E48HyuBGPG8vjxvJ4EI8bcbkS7W434nYNvsZlYblciTa3C3G5EZeFuCywrDH/vaupqXHcd7umpmaiu6CyhCOLBGA5sN8YcxBARB4DbgLGXCQ01XfyypMH6QqF8XhdXHvzeSxYUjXW3Wa9XC6AhpJNmUUEd0GQ/IIg+fNmn/H98UiUaKiLSKiLcHuIaKibSGcX0Y4uot09RDp7iHZ2E+3uIdrVS7Srh1hPH/2hTmQgTKy3n1hvH8beTzR06hko2UJcLrCLBhErqYBwJZYtCyxBrJOWXRaIRTQW5bDXe8I6EMSSxCEbsb8LxwoSAeT4slgWSZNA7O+N2MvY65JeQ9IkDTn+PUvVdqw9abtT3g8nzu84/kNOes/x5WhpPtX33zfKP3GVS5xaJEwHkkvlWmBF8huampq45557cLvdxGIxbrnlFtasWUNDQwPBYBCXy0VnZydTpkyhra0NYwxTpkzhj7/fRlcoTMmUACs+UMXs+SXU1NQgIpSWltLc3ExhYSGxWIyenh4qKytpaGjA4/FQVFRES0sLRUVFhMNh+vr6Btd7vV4KCgpobW2lpKSEvr4++vv7B9f7/X4CgQDt7e2UlZXR1dVFOBweXB8IBPB6vYRCIcrLywmFQkQikcH1p8vU2Ng4ONu5u7ubiooKmpubT8jk8/loaWnJqUxn+pz8fj9NTU2TOlNLTyeeaWUULZw7rM8pEAhgjBnMVF9Ti8eA1wjtjU0U+gJ0t7UT7umhKBCkrbEJD4IVjdET6iLP46E31EWsf4A8r5eu9g7cCERjDPT04nO7GejpJR6O4LEsBnr6sOIGE4sRDYdxI0QGBiAWR+KGWDiCmDgmGiMeiyPxOPFoFGKJbTD2cyw2pkMBZz6HJrcEz59PXV3dqL57Krc48mJKInI7cK0x5jP2608Ay40xXzr2ntFeTKkr1M+rL7zD6tsuxuOZfBfLGa3Dhw877rxqzZz9TDyOicUxsRgmFgdjv46bROEQjw++h3ii3cSPLSfa6+rqmFZVdbzoiJvEekNif3FjT7SwtzX2nAWTtByP220cf+/g5Iyk15A8SePENvv9J/ybneiEvZg02eOU93D8Pfa+U7bbOmJhzvvYzaP6M9eLKeUWp44k1HLiAd4ZQF06dlxQ5Of9181zVIEAUFhYONFdGHeaOfsNHkLwjP6fuqkVJRSUlKSxV9kv2N4+0V1QWSJ7Lo4/vjYB80Rkjoh4gTuAZ9O181gs/efjZzvN7Aya2RmcmFml5sgiwRgTBb4I/BHYDTxujNl5+q2Gr6enJ127mjQ0szNoZmdwYmaVmlMPN2CMeQF4IRP7rqyszMRus5pmdgbN7AxOzKxSc+RIQqY1NDRMdBfGnWZ2Bs3sDE7MrFLTIiEDnn766YnuwrjTzM6gmZ3BiZlValokZMBTTz010V0Yd5rZGTSzMzgxs0pNi4QMiEajE92FcaeZnUEzO4MTM6vUHHkxpeFYu3ZtM3B4NNu2tbWVl5aWtqS5S1lNMzuDZnaGMWaetWrVqilp7ZCaMFokKKWUUiolPdyglFJKqZS0SFBKKaVUSlokpJmIXCci74rIfhH5+kT3Z7REpFpEXhOR3SKyU0S+YreXisgrIrLPfi5J2uYbdu53ReTapPaLRWS7ve7/STbdYzkFEXGJyFsi8rz9Oqczi0ixiDwpInvsz/t9Dsj8Vft7vUNEHhURf65lFpGfi0iTiOxIaktbRhHxichv7fYNIjJ7PPOpcWLsu4/pY+wPwAUcAOYCXmAbsGii+zXKLFXARfZyAbAXWAT8K/B1u/3rwPfs5UV2Xh8wx/5zcNnrNgLvI3FX+xeB6yc63xmyfw34DfC8/TqnMwOPAJ+xl71AcS5nJnGr+PeAgP36ceBTuZYZeD9wEbAjqS1tGYF7gR/by3cAv53ozPpI/0NHEtJrObDfGHPQGBMGHgNumuA+jYoxpt4Ys9Ve7iJxj4vpJPI8Yr/tEeDD9vJNwGPGmAFjzHvAfmC5iFQBhcaYN03iX5NfJm2TdURkBvAh4KdJzTmbWUQKSfwy+RmAMSZsjOkghzPb3EBARNxAHom7wOZUZmPMX4C2k5rTmTF5X08Cq7JpJEWlhxYJ6TUdqEl6XWuFtdGiAAAEWklEQVS3TWr2MOKFwAagwhhTD4lCAphqv22o7NPt5ZPbs9X3gX8C4kltuZx5LtAM/MI+xPJTEQmSw5mNMUeBfwOOAPVAyBjzMjmcOUk6Mw5uYxI3zQsBZRnruZoQWiSkV6oqelKfYyoi+cDvgPuMMZ2ne2uKNnOa9qwjIjcATcaYLcPdJEXbpMpM4n/UFwE/MsZcCPSQGIYeyqTPbB+Hv4nEsPo0ICgiHz/dJinaJlXmYRhNxlzKr4agRUJ61QLVSa9nkBjGnJRExEOiQPi1MebYdVob7SFI7Ocmu32o7LX28snt2ehS4EYROUTiUNEHROS/ye3MtUCtMWaD/fpJEkVDLme+GnjPGNNsjIkATwGXkNuZj0lnxsFt7MM2RZx6eENNclokpNcmYJ6IzBERL4nJPM9OcJ9GxT62+DNgtzHmwaRVzwJ32ct3Ac8ktd9hz3ieA8wDNtpDml0istLe5yeTtskqxphvGGNmGGNmk/jsXjXGfJzcztwA1IjIfLtpFbCLHM5M4jDDShHJs/u6isScm1zOfEw6Mybv6zYSf190JCHXTPTMyVx7AKtJnAlwAPjmRPdnDDkuIzF0+A7wtv1YTeKY41pgn/1cmrTNN+3c75I0yxtYCuyw1/0n9pU+s/kBXMnxsxtyOjNwAbDZ/qyfBkockPnbwB67v78iMas/pzIDj5KYcxEh8b/+e9KZEfADT5CY5LgRmDvRmfWR/odellkppZRSKenhBqWUUkqlpEWCUkoppVLSIkEppZRSKWmRoJRSSqmUtEhQSimlVEpaJCillFIqJS0SlFJKKZWSFglKKaWUSkmLBKWUUkqlpEWCUkoppVLSIkEppZRSKWmRoFSWEZFPiUj3RPdDKaX0Bk9KjSMROdNfuEeALwAFxpimceiSUkoNyT3RHVDKYaqSlm8AfnJSW58xpg/oG9deKaVUCnq4QalxZIxpOPYAOk5uM8aETj7cICL3i8gOEblLRA6JSLeI/EJEvCJyr4jUiEiriDwoIlbSdl4R+Z6I1IpIj4hsEpFrJyC2UmqS0pEEpSaH2cBNJEYfpgO/AyqBBuCDwALgcWC9vQ7gF8BZwJ1ALbAaeE5Elhljto1n55VSk5MWCUpNDi7gbmNMCNghIi8BVwDTjTFhYLeIrAeuAn4nImcBHwVmG2OO2Pv4TxG5GvgccO/4R1BKTTZaJCg1ORyxC4RjGoG9doGQ3DbVXr4IEGCXiCTvxwe8msmOKqVyhxYJSk0OkZNemyHaXPayZb9eluJ9OilSKTUsWiQolZveIjGSUGmMeW2iO6OUmpy0SFAqBxlj9orIr4GHReQfgK1AKXAlcNAY89RE9k8pNTlokaBU7rob+Cbwr8AMoA3YCOjIglJqWPSKi0oppZRKSS+mpJRSSqmUtEhQSimlVEpaJCillFIqJS0SlFJKKZWSFglKKaWUSkmLBKWUUkqlpEWCUkoppVLSIkEppZRSKWmRoJRSSqmU/j+3IDGAtLx3uwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()\n",
    "ax.plot(ode_times, X[:,0], label='susceptible')\n",
    "ax.plot(ode_times, X[:,1], label='infected')\n",
    "ax.plot(ode_times, X[:,2], label='recovered')\n",
    "#ax.set_ylim(0, pop_size)\n",
    "ax.set_title('ODE')\n",
    "ax.set_ylabel('Population Size', labelpad=20, fontsize=14)\n",
    "ax.set_xlabel('Time', labelpad=10, fontsize=14)\n",
    "plt.legend(bbox_to_anchor=(1.05,1), loc='upper left', borderaxespad=0)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## IEBM\n",
    "\n",
    "The SIR model can be recreated as an IEBM following these steps"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# point path to IEBM files\n",
    "import sys\n",
    "sys.path.append('../../')\n",
    "# model population in 2-dimensions\n",
    "from iebm.populations.population2D import Population2D\n",
    "# import Trait classes to set up Events\n",
    "from iebm.traits.static_trait import StaticTrait\n",
    "from iebm.traits.linked_trait import LinkedTrait\n",
    "from iebm.traits.categorical_trait import CategoricalTrait\n",
    "# movement is simulated by time to boundary (wall) events\n",
    "from iebm.events.wall import WallEvent\n",
    "# import 2D interaction for 2D populations\n",
    "from iebm.events.interact2d import Interact2DEvent\n",
    "# import event to handle infections\n",
    "from iebm.events.infection import InfectionSIREvent\n",
    "# import class to simulate model\n",
    "from iebm.simulation import Simulation\n",
    "\n",
    "# we need to update the model\n",
    "import datatable as dt\n",
    "import heapq"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# start with a blank population\n",
    "pop = Population2D(name='pop', init_size=pop_size, xdim=xdim, ydim=ydim)\n",
    "\n",
    "# the interaction rate (b) can be converted into a speed based on a derivation \n",
    "# in Donalson & D'angelis (1999) from their predator-prey model\n",
    "vel = b * np.pi / (8 * (pred_radius + pred_radius)) / pop_size\n",
    "\n",
    "# the population needs 5 traits\n",
    "# 1. A radius for individual body sizes. The radius is StaticTrait that doesn't \n",
    "#    ever change between individuals\n",
    "# 2. An interact_radius that is the distance between individuals for them to \n",
    "#    interact. The interact_radius is a LinkedTrait that depends on the radius. \n",
    "#    In this case, the interact_radius is the same as the radius, so interactions \n",
    "#    occur at a collision.\n",
    "# 3. A velocity trait is static and uses the derived vel value above\n",
    "# 4. A categorical infection trait. Each individual can be one of the categories\n",
    "#    depending on the given fractions. Exactly how individuals change states \n",
    "#    is determind by the infection event. This trait will also be tracked to \n",
    "#    see how it changes in the population over time\n",
    "# 5. A recovery_rate trait is the population level value of d   \n",
    "traits = [(StaticTrait, {'name' : 'radius', \n",
    "                         'value' : pred_radius}), \n",
    "          (LinkedTrait, {'name' : 'interact_radius', \n",
    "                         'link_trait' : 'radius', \n",
    "                         'link_func' : lambda x: x}),\n",
    "          (StaticTrait, {'name' : 'velocity', \n",
    "                         'value' : vel}),\n",
    "          (CategoricalTrait, {'name' : 'infection', \n",
    "                              'categories' : ['susceptible', \n",
    "                                              'infected', \n",
    "                                              'recovered'],\n",
    "                              'fractions' : init_frac, \n",
    "                              'track' : True}), \n",
    "          (StaticTrait, {'name' : 'recovery_rate', \n",
    "                         'value' : d})]\n",
    "\n",
    "# from these 5 traits, the population needs 3 Events\n",
    "# 1. WallEvent to handle movement based on the velocity trait. This is a primary\n",
    "#    event because the next wall event needs to be pre-calculated and stored \n",
    "# 2. InteractEvent to calculate interactions between individuals of the population \n",
    "#    and trigger secondary events. Also a primary event so value can be pre-\n",
    "#    calculated.\n",
    "# 3. InfectionSIREvent is a secondary event after an interaction that handles \n",
    "#    both the transmission and recovery of the infection\n",
    "events = [(WallEvent, {'name' : 'wall', \n",
    "                       'is_primary' : True, \n",
    "                       'current_time' : 0, \n",
    "                       'bounce' : 'random'}),\n",
    "          (Interact2DEvent, {'name' : 'interact',\n",
    "                             'is_primary' : True,\n",
    "                             'current_time'  : 0}), \n",
    "          (InfectionSIREvent, {'name' : 'infection', \n",
    "                               'is_primary' : False, \n",
    "                               'current_time' : 0})]\n",
    "\n",
    "# lets add these traits and events to the population\n",
    "pop.add_traits(traits)\n",
    "pop.add_events(events)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# next we need to set the secondary triggers\n",
    "\n",
    "# after a wall collision, the direction is changed and new interactions\n",
    "# need to be pre-calculated and stored.\n",
    "pop.event_dict['wall'].triggers = pop.event_dict['interact'].set_next\n",
    "\n",
    "# after an interaction, an infection could be transmitted\n",
    "pop.event_dict['interact'].triggers = pop.event_dict['infection'].handle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# add the pop to a dictionary \n",
    "pop_dict = {str(pop) : pop}\n",
    "# create the simulation with the population dictionary\n",
    "sim = Simulation(pop_dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# before we run the simulation, one more things needs to be set. This is \n",
    "# specific to the SIR model. The trait of some individuals have been set to\n",
    "# \"infected\", but no recovery event is in the sim event_heap. The recovery\n",
    "# event is a secondary event only added to the heap after an infection --- \n",
    "# there is no column in the population dataframe for recovery time and so\n",
    "# no recovery events are in the heap for those initially infected indivuals.\n",
    "# as the simulation runs, new infected will have the recovery event added.\n",
    "\n",
    "# iterate over all infected individuals in the population\n",
    "for i in pop.df[dt.f.infection=='infected', 'id'].to_numpy().reshape(-1):\n",
    "    # explicity create a recovery event for an individual\n",
    "    params = dict(actor_id = i, current_time = 0)\n",
    "    new_event = pop.event_dict['infection'].set_next(params)\n",
    "    # add single new event to the heap\n",
    "    heapq.heappush(sim.event_heap, new_event[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "3b5501e3aa9f44a2a739b32714396f17",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=0.0, max=10000.0), HTML(value='')))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "CPU times: user 1min 15s, sys: 3.24 s, total: 1min 18s\n",
      "Wall time: 1min 14s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "# run simulation\n",
    "sim.run(max_time)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get the tracked trait history for each compartment from the simulation\n",
    "infect_dict = dict(infected = [], recovered = [], susceptible = [])\n",
    "for time, (labels, counts) in zip(sim.time_history, \n",
    "                                  sim.trait_history[('pop', 'infection')]):\n",
    "    for t in ['susceptible', 'infected', 'recovered']:\n",
    "        if t in labels:\n",
    "            infect_dict[t].append(counts[np.where(labels==t)][0])\n",
    "        else:\n",
    "            infect_dict[t].append(0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1,2, figsize=(12,5), sharex=True, sharey=True)\n",
    "\n",
    "ax[0].plot(ode_times, X[:,0], label='susceptible')\n",
    "ax[0].plot(ode_times, X[:,1], label='infected')\n",
    "ax[0].plot(ode_times, X[:,2], label='recovered')\n",
    "ax[0].set_title('ODE')\n",
    "ax[0].set_ylabel('Population Size', labelpad=20, fontsize=14)\n",
    "ax[0].set_xlabel('Time', labelpad=10, fontsize=14)\n",
    "\n",
    "for k in ['susceptible', 'infected', 'recovered']:\n",
    "    ax[1].plot(sim.time_history[:-1], infect_dict[k], label=k)\n",
    "ax[1].set_title('IEBM')\n",
    "ax[1].set_xlabel('Time', labelpad=10, fontsize=14)\n",
    "\n",
    "plt.legend(bbox_to_anchor=(1.05,1), loc='upper left', borderaxespad=0)\n",
    "\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}