{
 "metadata": {
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.6-final"
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  "orig_nbformat": 2,
  "kernelspec": {
   "name": "python3",
   "display_name": "Python 3",
   "language": "python"
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 "nbformat": 4,
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 "cells": [
  {
   "source": [
    "# SEIR model"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "import epistochmodels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "pop = 1000\n",
    "beta = 0.7\n",
    "gamma = 0.2\n",
    "e = 0.3\n",
    "model = epistochmodels.SEIR(pop, beta, gamma, e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "inits = 990,10,0,0\n",
    "model.initialize(*inits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "CPU times: user 221 ms, sys: 75.3 ms, total: 296 ms\nWall time: 299 ms\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "res = model.run(0,1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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156.017814 186.003967 \nL 156.243262 185.604628 \nL 156.263989 185.404959 \nL 156.405434 185.804298 \nL 156.527335 186.403306 \nL 156.654137 186.203636 \nL 156.710276 186.403306 \nL 156.736678 186.203636 \nL 156.739201 186.003967 \nL 156.899525 186.003967 \nL 156.988257 185.804298 \nL 156.992882 186.003967 \nL 157.030056 186.203636 \nL 157.036031 185.804298 \nL 157.127027 185.804298 \nL 157.215691 185.404959 \nL 157.248606 185.604628 \nL 157.447284 186.203636 \nL 157.458308 186.003967 \nL 157.543333 185.604628 \nL 157.608229 185.604628 \nL 157.765632 184.80595 \nL 157.859503 185.00562 \nL 157.886655 185.00562 \nL 157.914155 185.604628 \nL 157.944952 185.404959 \nL 158.019809 185.604628 \nL 158.214623 185.00562 \nL 158.260425 185.205289 \nL 158.41475 185.604628 \nL 158.459618 185.404959 \nL 158.554642 185.604628 \nL 158.888216 185.205289 \nL 158.9779 185.804298 \nL 159.015872 185.604628 \nL 159.134201 184.80595 \nL 159.214241 184.80595 \nL 159.345322 184.206942 \nL 159.38322 184.206942 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181.61124 \nL 162.742708 181.41157 \nL 162.769168 181.61124 \nL 162.802151 181.211901 \nL 162.814386 181.41157 \nL 162.900447 181.61124 \nL 162.962814 181.41157 \nL 162.984514 181.61124 \nL 163.047481 181.810909 \nL 163.051905 181.61124 \nL 163.110519 181.61124 \nL 163.175139 181.41157 \nL 163.195016 181.61124 \nL 163.212751 181.810909 \nL 163.296369 181.61124 \nL 163.308448 181.61124 \nL 163.381534 181.41157 \nL 163.38346 181.61124 \nL 163.417243 182.210248 \nL 163.522788 182.409917 \nL 163.686386 182.210248 \nL 163.917782 183.008926 \nL 164.054741 182.609587 \nL 164.088654 182.809256 \nL 164.104911 182.609587 \nL 164.246531 182.010579 \nL 164.288149 182.210248 \nL 164.563568 183.008926 \nL 164.688287 182.409917 \nL 164.847487 182.809256 \nL 164.906998 182.609587 \nL 164.926848 182.809256 \nL 165.046388 183.408264 \nL 165.157613 183.208595 \nL 165.200628 183.408264 \nL 165.207942 183.008926 \nL 165.312064 182.609587 \nL 165.323486 182.409917 \nL 165.370748 182.809256 \nL 165.418836 183.208595 \nL 165.428423 182.809256 \nL 165.527178 182.609587 \nL 165.564669 182.809256 \nL 165.609359 182.409917 \nL 165.624298 182.409917 \nL 165.686965 181.810909 \nL 165.75555 182.010579 \nL 165.836875 182.010579 \nL 165.943846 181.41157 \nL 166.028633 181.61124 \nL 166.063527 182.210248 \nL 166.129485 182.010579 \nL 166.183447 182.210248 \nL 166.199746 182.010579 \nL 166.236372 181.810909 \nL 166.375414 181.810909 \nL 166.500519 182.010579 \nL 166.560625 182.010579 \nL 166.698581 182.409917 \nL 166.76871 182.809256 \nL 166.771159 182.609587 \nL 167.025861 183.208595 \nL 167.070061 182.409917 \nL 167.095309 182.809256 \nL 167.183609 182.809256 \nL 167.378559 182.210248 \nL 167.474511 182.210248 \nL 167.534498 182.809256 \nL 167.588516 182.609587 \nL 167.72927 181.61124 \nL 167.747127 182.010579 \nL 167.789451 182.210248 \nL 167.798562 181.61124 \nL 167.828288 181.61124 \nL 168.01423 182.010579 \nL 168.202779 181.012231 \nL 168.20718 181.211901 \nL 168.570613 180.812562 \nL 168.634886 181.012231 \nL 168.815793 181.012231 \nL 168.844761 181.211901 \nL 169.210597 180.213554 \nL 169.233666 180.413223 \nL 169.253683 180.612893 \nL 169.254114 180.413223 \nL 169.53343 179.614545 \nL 169.558062 179.814215 \nL 169.902201 180.812562 \nL 169.907336 180.612893 \nL 170.008409 181.012231 \nL 170.04214 180.812562 \nL 170.220537 180.213554 \nL 170.244533 180.013884 \nL 170.316971 180.213554 \nL 170.379298 180.413223 \nL 170.802934 178.815868 \nL 171.045367 178.616198 \nL 171.15906 178.815868 \nL 171.222207 178.416529 \nL 171.287097 178.616198 \nL 171.293727 178.616198 \nL 171.461582 180.013884 \nL 171.539069 180.413223 \nL 171.57212 180.013884 \nL 171.719352 179.614545 \nL 171.839375 180.213554 \nL 171.948039 179.814215 \nL 171.970698 180.013884 \nL 172.061006 180.013884 \nL 172.169524 180.213554 \nL 172.271879 179.814215 \nL 172.379126 180.013884 \nL 172.39963 180.013884 \nL 172.514391 180.213554 \nL 172.53716 180.013884 \nL 172.557589 180.213554 \nL 172.83765 181.211901 \nL 173.057057 180.812562 \nL 173.152876 181.211901 \nL 173.238494 181.012231 \nL 173.345696 181.211901 \nL 173.500848 181.41157 \nL 173.571175 181.810909 \nL 173.601009 181.61124 \nL 173.65501 181.810909 \nL 173.662012 181.61124 \nL 173.758129 181.61124 \nL 173.970939 182.210248 \nL 174.065121 181.810909 \nL 174.874577 180.213554 \nL 174.88596 180.413223 \nL 174.963034 181.012231 \nL 174.991007 180.812562 \nL 175.100657 180.812562 \nL 175.379398 182.609587 \nL 175.383703 182.409917 \nL 175.405268 182.409917 \nL 175.428116 182.609587 \nL 175.503467 182.409917 \nL 175.555388 182.409917 \nL 175.651547 182.609587 \nL 175.70563 182.409917 \nL 175.830913 182.609587 \nL 176.0217 183.008926 \nL 176.023359 183.208595 \nL 176.082939 182.809256 \nL 176.099123 183.008926 \nL 176.176797 182.809256 \nL 176.416864 183.208595 \nL 176.55703 183.807603 \nL 176.647115 184.007273 \nL 176.835647 183.408264 \nL 176.852567 183.607934 \nL 176.904099 183.408264 \nL 176.957848 183.408264 \nL 176.963832 183.607934 \nL 176.98496 183.208595 \nL 177.066439 183.408264 \nL 177.139887 183.807603 \nL 177.155878 183.607934 \nL 177.320315 183.408264 \nL 177.325547 183.208595 \nL 177.427794 183.408264 \nL 177.66021 183.008926 \nL 177.714062 183.208595 \nL 177.697754 182.809256 \nL 177.741417 182.809256 \nL 177.782182 183.008926 \nL 177.811684 182.809256 \nL 177.980481 182.809256 \nL 177.997314 182.609587 \nL 178.07382 182.809256 \nL 178.143304 182.809256 \nL 178.160021 183.008926 \nL 178.231638 182.809256 \nL 178.315872 182.809256 \nL 178.462401 183.208595 \nL 178.509042 183.208595 \nL 178.735057 183.607934 \nL 178.740769 183.408264 \nL 178.770084 183.607934 \nL 178.968978 184.007273 \nL 179.230614 183.208595 \nL 179.2843 183.208595 \nL 179.376212 183.008926 \nL 179.48133 183.408264 \nL 179.544908 183.408264 \nL 179.641762 183.208595 \nL 179.684239 182.809256 \nL 179.752273 183.408264 \nL 179.796964 183.408264 \nL 179.958375 182.809256 \nL 179.992152 183.008926 \nL 180.147884 183.408264 \nL 180.149132 183.208595 \nL 180.223267 183.607934 \nL 180.287261 184.007273 \nL 180.306837 183.607934 \nL 180.363247 183.408264 \nL 180.376168 183.607934 \nL 180.597121 183.208595 \nL 180.696071 183.408264 \nL 180.813706 183.408264 \nL 180.885364 183.807603 \nL 181.14256 183.807603 \nL 181.318493 183.408264 \nL 181.353561 183.408264 \nL 181.383424 183.607934 \nL 181.4119 183.208595 \nL 181.474341 183.408264 \nL 181.650622 183.408264 \nL 181.698079 182.809256 \nL 181.829594 183.008926 \nL 181.840552 182.609587 \nL 181.934134 183.208595 \nL 182.033665 183.408264 \nL 182.085904 183.008926 \nL 182.121175 183.408264 \nL 182.149717 183.408264 \nL 182.26441 183.807603 \nL 182.279289 183.807603 \nL 182.339383 183.607934 \nL 182.545848 184.007273 \nL 182.598392 183.807603 \nL 182.818609 183.607934 \nL 182.82442 183.408264 \nL 182.851742 183.607934 \nL 182.948728 183.807603 \nL 182.961251 183.607934 \nL 183.039382 183.607934 \nL 183.15462 183.807603 \nL 183.210224 183.807603 \nL 183.320188 184.206942 \nL 183.389164 184.007273 \nL 183.55762 184.206942 \nL 183.662983 183.807603 \nL 183.694274 184.007273 \nL 183.715829 184.206942 \nL 183.755504 183.807603 \nL 183.836965 183.807603 \nL 183.838738 184.007273 \nL 183.901148 183.807603 \nL 183.953607 183.807603 \nL 184.038859 183.408264 \nL 184.080516 183.607934 \nL 184.190863 183.807603 \nL 184.22661 183.607934 \nL 184.25509 183.807603 \nL 184.308349 184.007273 \nL 184.384973 183.807603 \nL 184.398757 184.007273 \nL 184.668782 184.206942 \nL 184.681209 184.007273 \nL 184.743571 184.406612 \nL 184.835952 184.406612 \nL 184.942555 184.606281 \nL 184.975951 184.606281 \nL 184.987436 184.80595 \nL 185.046319 184.606281 \nL 185.201186 184.206942 \nL 185.254799 184.406612 \nL 185.312494 184.206942 \nL 185.746663 185.00562 \nL 185.763813 185.00562 \nL 185.764611 185.205289 \nL 185.803183 184.80595 \nL 185.874174 185.00562 \nL 185.907526 185.00562 \nL 186.037861 184.80595 \nL 186.147289 185.205289 \nL 186.150953 185.00562 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184.80595 \nL 153.641166 184.606281 \nL 153.826057 184.007273 \nL 153.829223 184.206942 \nL 153.972649 184.206942 \nL 154.07276 184.606281 \nL 154.215519 184.606281 \nL 154.313864 184.406612 \nL 154.46517 184.80595 \nL 154.483524 184.606281 \nL 154.575102 184.606281 \nL 154.673207 185.00562 \nL 154.761487 184.606281 \nL 154.76653 184.406612 \nL 154.840928 184.80595 \nL 154.948175 185.00562 \nL 155.101257 185.00562 \nL 155.286068 184.606281 \nL 155.370591 184.606281 \nL 155.536847 183.607934 \nL 155.590486 184.007273 \nL 155.640199 184.606281 \nL 155.696651 184.206942 \nL 155.740011 184.406612 \nL 155.988558 184.007273 \nL 156.017814 183.807603 \nL 156.263989 183.807603 \nL 156.405434 183.408264 \nL 156.415041 183.208595 \nL 156.446733 183.607934 \nL 156.487001 183.408264 \nL 156.521506 183.408264 \nL 156.623278 183.008926 \nL 156.654137 183.208595 \nL 156.710276 183.008926 \nL 156.739201 183.008926 \nL 156.908614 183.208595 \nL 157.036031 182.609587 \nL 157.104728 182.809256 \nL 157.215691 183.208595 \nL 157.523061 182.010579 \nL 157.543333 182.010579 \nL 157.655142 182.210248 \nL 157.687063 182.010579 \nL 157.694491 182.409917 \nL 157.722193 182.409917 \nL 157.765632 182.409917 \nL 157.90521 182.010579 \nL 158.019809 181.61124 \nL 158.124512 181.61124 \nL 158.302727 181.211901 \nL 158.302932 181.41157 \nL 158.549129 181.012231 \nL 158.55444 181.211901 \nL 158.554642 181.012231 \nL 158.747223 181.012231 \nL 159.134201 180.013884 \nL 159.288043 181.211901 \nL 159.345322 181.211901 \nL 159.453609 181.41157 \nL 159.681183 181.810909 \nL 159.700437 181.61124 \nL 159.872706 181.61124 \nL 159.927749 181.012231 \nL 160.083864 180.413223 \nL 160.197338 180.612893 \nL 160.210172 180.413223 \nL 160.286729 180.812562 \nL 160.38573 180.612893 \nL 160.676813 181.41157 \nL 160.739521 181.211901 \nL 161.01277 181.61124 \nL 161.133912 180.812562 \nL 161.136357 181.012231 \nL 161.410414 180.413223 \nL 161.439399 180.612893 \nL 161.444445 180.612893 \nL 161.48875 181.012231 \nL 161.552839 180.812562 \nL 161.690683 180.413223 \nL 161.928338 181.012231 \nL 161.985001 180.612893 \nL 162.035102 181.012231 \nL 162.129872 181.012231 \nL 162.200789 181.810909 \nL 162.243103 181.61124 \nL 162.266285 181.61124 \nL 162.358401 181.211901 \nL 162.441298 181.41157 \nL 162.526872 181.211901 \nL 162.671759 181.41157 \nL 162.769168 180.612893 \nL 162.802151 180.612893 \nL 162.900447 180.213554 \nL 162.962814 180.213554 \nL 163.051905 179.814215 \nL 163.175139 180.213554 \nL 163.195016 180.013884 \nL 163.245088 179.814215 \nL 163.27416 180.013884 \nL 163.381534 180.612893 \nL 163.384547 180.213554 \nL 163.522788 179.614545 \nL 163.686386 179.614545 \nL 163.878596 178.616198 \nL 163.917782 178.815868 \nL 164.054741 178.815868 \nL 164.147797 178.616198 \nL 164.209971 178.616198 \nL 164.340053 178.01719 \nL 164.421778 178.21686 \nL 164.428613 178.01719 \nL 164.552938 177.218512 \nL 164.570258 177.418182 \nL 164.627896 177.418182 \nL 164.749971 177.018843 \nL 164.750909 177.218512 \nL 164.847487 177.018843 \nL 164.906998 177.018843 \nL 165.059996 176.419835 \nL 165.269219 176.020496 \nL 165.323486 176.220165 \nL 165.361661 176.020496 \nL 165.417535 175.421488 \nL 165.428423 175.820826 \nL 165.527178 175.820826 \nL 165.555065 175.621157 \nL 165.609359 175.820826 \nL 165.686965 176.220165 \nL 165.75555 176.020496 \nL 165.943846 176.220165 \nL 166.039612 175.820826 \nL 166.183447 175.221818 \nL 166.217674 175.221818 \nL 166.375414 175.820826 \nL 166.500519 175.621157 \nL 166.560625 175.820826 \nL 166.656495 175.621157 \nL 166.692769 176.020496 \nL 166.701102 175.621157 \nL 166.991092 174.62281 \nL 167.008638 175.022149 \nL 167.070061 175.221818 \nL 167.095309 174.822479 \nL 167.297256 175.022149 \nL 167.315942 174.822479 \nL 167.378559 175.221818 \nL 167.474511 175.820826 \nL 167.483177 175.421488 \nL 167.583181 175.221818 \nL 167.588516 175.421488 \nL 167.654895 175.421488 \nL 167.72927 176.020496 \nL 167.754633 175.421488 \nL 167.828288 175.820826 \nL 167.917721 175.621157 \nL 168.010542 176.220165 \nL 168.115406 176.020496 \nL 168.20718 175.621157 \nL 168.512949 175.621157 \nL 168.570613 176.020496 \nL 168.634886 175.820826 \nL 168.815793 176.020496 \nL 168.932435 175.820826 \nL 169.005748 175.820826 \nL 169.122503 176.020496 \nL 169.210597 176.020496 \nL 169.345534 175.621157 \nL 169.53343 175.621157 \nL 169.621198 175.221818 \nL 169.639497 175.621157 \nL 169.782703 175.221818 \nL 169.804224 175.621157 \nL 169.827995 175.421488 \nL 170.035939 174.822479 \nL 170.04214 175.022149 \nL 170.244533 175.022149 \nL 170.324151 174.822479 \nL 170.490201 175.221818 \nL 170.587227 175.022149 \nL 170.720468 175.022149 \nL 170.738979 174.822479 \nL 170.802934 175.022149 \nL 170.950861 175.022149 \nL 171.045367 175.221818 \nL 171.059772 175.022149 \nL 171.143377 175.022149 \nL 171.176254 174.822479 \nL 171.222207 175.221818 \nL 171.271355 175.022149 \nL 171.287097 175.221818 \nL 171.293727 175.421488 \nL 171.361555 174.223471 \nL 171.385292 174.62281 \nL 171.455753 174.223471 \nL 171.553396 173.424793 \nL 171.57212 173.624463 \nL 171.59523 173.624463 \nL 171.625045 173.824132 \nL 171.657305 173.624463 \nL 171.719352 173.624463 \nL 171.821065 173.424793 \nL 171.948039 174.023802 \nL 171.970698 173.824132 \nL 172.029741 174.023802 \nL 172.152272 174.223471 \nL 172.162525 174.023802 \nL 172.261336 174.223471 \nL 172.271879 174.223471 \nL 172.379126 174.023802 \nL 172.39963 174.223471 \nL 172.513713 174.023802 \nL 172.514391 174.223471 \nL 172.53716 174.223471 \nL 172.692764 173.424793 \nL 172.761142 173.824132 \nL 172.775912 173.424793 \nL 172.824471 173.424793 \nL 172.896205 173.225124 \nL 172.954067 173.225124 \nL 173.057057 173.624463 \nL 173.058888 173.424793 \nL 173.073334 173.225124 \nL 173.152876 173.624463 \nL 173.210235 173.624463 \nL 173.345696 173.025455 \nL 173.500848 172.825785 \nL 173.601009 172.426446 \nL 173.662012 172.226777 \nL 173.758129 172.426446 \nL 174.065121 171.627769 \nL 174.169294 171.627769 \nL 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169.830744 \nL 178.07382 169.631074 \nL 178.315872 170.230083 \nL 178.34514 170.030413 \nL 178.392468 170.230083 \nL 178.509042 170.629421 \nL 178.659183 170.230083 \nL 178.740769 170.429752 \nL 178.770084 170.230083 \nL 178.918619 170.030413 \nL 179.376212 171.428099 \nL 179.424786 171.02876 \nL 179.48133 171.22843 \nL 179.845212 172.426446 \nL 179.937012 172.226777 \nL 179.958375 172.426446 \nL 179.992152 172.226777 \nL 180.223267 171.428099 \nL 180.472803 170.829091 \nL 180.597121 171.22843 \nL 180.674125 171.02876 \nL 180.696071 170.829091 \nL 180.870265 171.22843 \nL 180.874091 171.428099 \nL 180.885364 171.22843 \nL 181.078807 171.428099 \nL 181.318493 172.626116 \nL 181.353561 172.825785 \nL 181.4119 172.626116 \nL 181.474341 172.426446 \nL 181.635618 172.825785 \nL 181.698079 173.225124 \nL 181.874425 172.825785 \nL 181.958492 172.426446 \nL 182.033665 172.626116 \nL 182.0514 172.626116 \nL 182.085904 172.825785 \nL 182.121175 172.426446 \nL 182.149717 172.626116 \nL 182.2134 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171.627769 \nL 189.889002 171.22843 \nL 189.90578 171.428099 \nL 189.984357 171.428099 \nL 190.150152 171.02876 \nL 190.175909 171.22843 \nL 190.323362 171.02876 \nL 190.406993 171.22843 \nL 190.535841 171.02876 \nL 190.821624 171.428099 \nL 190.972556 171.02876 \nL 191.066689 171.22843 \nL 191.087184 171.02876 \nL 191.105026 170.829091 \nL 191.160709 171.02876 \nL 191.421386 171.827438 \nL 191.476417 171.827438 \nL 191.633829 173.225124 \nL 191.71489 172.825785 \nL 191.802063 172.626116 \nL 191.921388 172.825785 \nL 191.943314 172.426446 \nL 192.042889 172.626116 \nL 192.100679 172.226777 \nL 192.124294 172.426446 \nL 192.375677 173.225124 \nL 192.428737 173.025455 \nL 192.600813 172.426446 \nL 192.776313 172.426446 \nL 192.955092 172.626116 \nL 193.076253 172.226777 \nL 193.192217 172.426446 \nL 193.197076 172.226777 \nL 193.25117 172.226777 \nL 193.303823 172.027107 \nL 193.31415 172.226777 \nL 193.417931 172.426446 \nL 193.540761 172.426446 \nL 193.690783 173.025455 \nL 193.731961 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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plot(res[0],res[1])\n",
    "legend(['S','E','I','R']);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": [
       "inf"
      ]
     },
     "metadata": {},
     "execution_count": 17
    }
   ],
   "source": [
    "res[0][-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ]
}