{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.rcParams[\"animation.html\"] = \"jshtml\"\n",
    "import matplotlib.animation\n",
    "import numpy as np\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Compartmental models\n",
    "\n",
    "Comparmental models are a category of infectious diseases in which a population is divided into compartments, with the assumption that all elements in the same compartment present the same characteristics"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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YS4+wKMlUDArRiq5dFeVq2dGjVHfePPL/6CMKxSrdN3CNPIAl653mzalxqVJJjQrh3lrXo4eiXO2LjKTnli+nwlOnku+kSUq7VzFRYSuWSlVxX82AssTK1cJDh6jSrFmUC5Mc/r/48GGlnJWQSrCwqrQc44xBnAtb1IpjjPbEZW1gGWJL27cYt0pG5NH2PQCWq+l79lBlTIB8YbnytaZPMNJvRSws+Axys3I19+BBqoD7njGqALnnQykcCutfZpBhC5Y6uHLl/Gj4cL72SxAHXp869YB+/fUWXGRXlfior7664jB2KT0Cvv12GRznJILVExSXHRMr5E2b5qKePUtSvXrJM+Zz5ywrm6pWRdbTNFBEhKV+z54nU63NgfV6pLr/7PeVLm0xCV+8qK8I2tdPz29XHNNZudMzXg+oy7byaDA/idiEyuYW5kXWctYCPgG72nqGLjOOduKB/tt77P200PldO+mnYcPolf/9j0rD4pQeajh6NPni4Xt4yRJa07tXUtPYixdozyfTKQFBjazg1B8+nM7t2K7sb/zGm+QHFwe76Ba3aEbW9FXKvttod2TpNwq7ghqMHElemAWewox9bb++SV3eDDtNa/r0VpS8cs88Qw1GjaIfBw5w6pDsEmT6ddxYuAYtE7gH0bfp1Ib1CgulCwFWphqC2WTDb3zm4eAXwWxFZh/VEjDfn4+V9NI18ICWHztG/4Y1SksjGzakAFh3l0DR6b8m2XV+CffJTCgacVByWDkaVr8+7ba6/F5v3JiC4OJj914rTArMicnvlkuwkH0L5YhZpRENGlAOTBzWY9I0aO3apPJwuMUH4JisqD2DCcBI1BuKiQ5TNFz6q//+m7rBEvZqrVo0xW7cvWC9YsVsNdyXXFclI/IkNcbGF3Ddva0z+TDSL8udE3LzGEfgflcpAnKznEWgqHbExCqjyWkFSztAVngqVvRTuEqV3DRmzFnasCEqXQoWK2l6VL68H61bV4O2bo1G8Hg0HTt2m06fTsAKwYfg0/Txx6HIHB+o1/SRZZprNNW6jsbmqJHGIuuoisvL03PMjJLboFDPoh1r6u5MyU+T5FGyZs/cDcwzbLZy7QWz+YetXG5NhxYtSjG+yN1sMIBQ6TSjs3LCtA+zRD06vnKFomCVxEtCpfJwXTBtgWVLq1zptXe2LLRFC6WLXR9/rNsVK5ssQ+iTT+ruT0/hJcyaQxD70WvLVjry3/8ihmw7Xd6/lxIyWsj0DNJSl1futAN7p79pprXgGBD7VRVsnFAnOTyxmQjmYKdFYHYjZn7+EBxUj85HR9OkbdtslCGux4oN02xYbvVoFeKfWMFqjPgpldrD0sw0YcuWFP3p9dECbkamqYir1KMpmNjwOJ601lPrsJuQFSx2E9orWH2gdDHZuweNyKMdE8dG6ZGRflsiCTITx5jp0VTIneUULK0gjRpZTItXrqTUmFgJYGXl3r1EBJ572ch/6ZLeO8xSxdfXi9q2DVSY6fbtBFq48ApchlE0d+6FJAWrVClvJDtNoL/+up8iFYMe2CEhXnTuXCKC0qtQqVL8pZT0UXj4QyVdhD1xOVNwsK2M9vWM/HbFMZ2V28i4HbQJRbknTOtVZYsVLVYYmTc6kNktiv85m9J7E/PAct16a+JC0jLY/NaHWv/frYHiVm3fpGr91v+qdYf7zG99sF+yKnVpOY7ROv4lLPr7tWO2rhq1v6gjlqD+AGs9o8fhdmwFfHnjRiqMl1Rrq0LHwf5nN2+m3dOnU8TW35zp3pVtJ6OzPq7s8DH0xYYCjuNg5g9MdwfXfAzjSIp98kYcVXVYRD9u04Y4lmo93HrV5szBKvVkPbE0gtuZ9lhzy7HGyKTeL+rvwppYq1Brm32XLF4caxOH/0r4W+KgT1y7plvneJRlHVAJO1fg1vBwOgfFkI/XAvf1trNnlfZPwjXIZZxAVS1TOzYij3ZQYbAu6ZGRfjkejemkA7lPItg9M8ilFiztgI8etcQrFS6sXibJezkQnhWvv/66R/Xr2wbCr12rD7IeGAEB3oj/KqooWKq7i+s1bx4EBSuKvvjiHBSvyuSN+IfUqFmzglCwotDPZXr33dDUquruW7z4IhQsDs2xpUWLLioF/F1GLaWmYNr34eh3eo+p14+zcuv1abAsAu16gvWD2Qx2mgHNXkWfVVLp9z728erFw+C3wPpT01Q6yOxdKac/xkegBo6b8HJJjdTP66RWJ6vvu3r0CM0sFUKVunSl0q1aUQm4eVjZKo94F7barUKQ8l+w6LkBsYLFCXkz7F3gAhl54jISbHlrpuyQrVX8wuGXx3fgZJ93yrqZUpIA994hKEEdEIt4YOBAqoxVca9hFd9/NPGEatC59yPcDuzqehy0EFas92HN7YvYKFWZYosWE8dz2ZOz8miVT23fzvZrP07+bU6vO0qvkzSUGb6punQ5guSbQVhV548UBL5KegYec1RUrOLG40/pMLVuXSjFMOrVC6Aff4xGCoOz9N57ZRWX4vXrscTK1ddfW5a02jfq2fMoPftsUSXWKjjYV0nmeelSHGK9IpWqJUokX4Q9exZG6oRrSIkQi5QOx5HDKgQJQ/PgQ9QmHIfTNNzHqkdOvVBVafvqq4Xx+xqtWXOLbt6MoZdeKk7lyuVCIlNvfMDaTOfPx6AN586KoqVLq9sPjbZtu0+TJ0coaRqKFfOhy5djoaxdUVYQ8r3TvXtyACE3LlnSC30mQt5rSHFRiPz80n8DpfeYKQbtArn1+nSibKkTbTOrqd5Mn12CvIqB7dvsmmBbvCv1lsySzenjRCMuhFMszK5YMc2rD/+JiKCCWM1UvHHTpFQMTg/EQQd3EBQciMDdglWrI11CSpdJoeoWo8dt1NNSIpYYs1Lo4+tDsTFIjqehwNJlHBwNPi28ZI99963CTLkC/KnZ+AnUGCksWuA7aG6iYLEJc7pDIdxjB/ueR+kMhYPbmBeA51u3dao9vqI4XDuv//wzbezZk0Yj5uoTxFYlWK1Y7DrkFAuVENQdfsMSp/eokbLliJW1+lgNZ5+KQa9t5J07VBZJTiuizd4LF1JUqYxgcKZInRWOi6FEvQu3+gu4P0cixQRb1jphOxEv+iU6CpYReVIMSKfASL+8YrMcUrBwsPs+HbkrWeXWOZxLiwwrWOHhCRQebvmgs6MR1aiRkwYPLppid58+JWjjxmjF6tSnj+0y8B49CtGyZSnNmcePx9Px4xaLUIoOUTB8eKmkYv4m4pw55ZE49DTyZMXRyJFn9JoklRUsmJO+/LIcEpOGKUrR9u1hqda339m1a5CSC0tNVaHdP25cSSpb1hLsrpa3bl2QFiyIomnTLimsUnq+P5jeY9qPmX87K7denx5cxhGRFpu+5VM8/ETkJ9Zn4JVgx75tDwZFKxoHj3PepyZjx9K6Af3TJDW3YQXrKawaWvJkC+UbR4+ihJgY4tQPegpPam0jEAfDClbTt96i5c8/l6KquvIvYutWm313kJMoH1Y0lmjSjM5u4awDyVSrj57OnaJrpeDh7Tu0Y9IHioLFH8oWSjMCrFyprg7OdcDMqRtmgP9Ocy+PqeJmfIvwAKxZnCKgd82a9DXi85g48JxzU72JHFhD1q1L0+i4DStYH2ABShssJtEGuet1sA0TGFawxiIesDNWHNoT54hi2op69hQJBXAzXIO8YrB7jRrKijxOIcHfVuR99mREHvs+9H4b6XcLxs0K1hjEe770HRs1bYnxyAxKv+nEOqpVqyrTsGHF8R1CPyX3FVtqmIOCTNS4sR+9/34IlIgqiLFK6S4IDcXKiSWVqEkTP+VzNGyNqlTJG9asEHrjDX0v0bJlFenllwtThQrecPkhIhPMMUQdO2Lp8/JKiL9S332WAdaokQcxVVWRZLSI0jcfh8dXtKgJObD8Yb0qb4NvtWp5kXy0uiJTtWo5Sc0Jx/85WemgQUWIZdajceNClIztfBweF6erqFcvF5S8crpZ3DmHWJ8+hRVL1iOsw3qHU8rSe0xHHTkjt6M+PbR8DuTiQDvWvt8H1wBz0pb/grO9cgUMkKjzP/QAM/Ha/fpR97XriHNi+SNQnh8yvnn8qHidulDAxtDA/cnBrLy6kNuUwnL0Prt2U/l27SlX3jxKm4DgklS9x8vUe+s27j6J2FLG9MTgobiv0z5H5ESnnEi1AlIldJw7jwqULYfVUKT8f27+14rrjq1VXE9LEdY8RJw/i5OU5szhTYFlylLLSZNJVcpsGuDHgH37qcGIkXALVlfqe+NAQRUqUtuZ/F1xaAh2VjL79vI7CQF2MzwJZrMi57foAubZ9GCw2ytXGKNC06zB1rwKUI2x+gRlN5C6pB/cbt8j1xvneiqCmCl2tefFBKIWFLKRUMD2wMWo0mewgHGb5kjdsBXK/dMIevdn6xLacPqEl/DNw197906qz8lK47GaiQO6P8d1Hwqlg+vy/y+RD4qD5uOwn+vpkRrIzq5BdhUysetQj4zIo9ePfZmRfnnhAMvFeb5mwi0fCiVTlZtxyIwAd5aDlVJzlSo58I2/lK4ve0Hlty0CrsjI7umY3ruXgESwSlAxR/W2zKLy8n3CwbPs60kZfGBMqAloNrEbeq5krH2aWjnKQu6oXO3U0X5H5Wq7EvUbKElDH7UCUZu3Skk0iiXj2uB3e+G09Vv9+0ObHF1qXW0dR+OsN2SokmhUb2bD1oANQ4bQwa/m2RyeFaOBWOGkTZ6qVtg7Y4aS1oFJ7/j2cvBvM1yHq/BCPb6KDZ8ZR/+Do9rqCG2Fo2zJuCNlaM+8wpFn3Wx+ueuiI8Xwp0By4ly7irTZyPX6ZKXqb+Sc428SvgCLipqhvQ4WVHDS0GKaxLx67bWJQznR6Gq00Qa/27fR1h+InE+caJQfYvbE7r6hGzbQAqtVzX4/B+tH4qsHnP2diZW7YCzS4BgzPTIiz6Ow4+MY6Zflnm1dpWw/1jn79yflwtJiZV/P0G9M4uKQawy007AFy9CBpZEgkDUR4JiqcWBXKVdZE4U0jDpy3176vHJF2jJ+PEViVvwQMSOsUPB/TiS6DckD5+AzG1q6+PsemlOtCm1HIsArmB3HIm6ELUlsqTq6dCktsqZXUNtsnTCedk6ZQjfDwpTcWumh/V/MoQVIpnoCSuA9rKBiixb//xsf4V0At4G9csV93zh1khbCwhaGVYExiO3ghKk8znWw1P382mjdw3OS1d+R+PEqchzF4Vt0zDdPn1YSms5DhumMVq50B5U1C3kVLqfWd5Vy9VhQ4KDqT2F9YnpDk6bkICyZNZDcdjzSLuzF9j9YaZqAuvyfE4l+ALc2rz7U0n582qY6yiYh9Qd/quYO7gG21nCs0lIk/nxy0SKb+vOgTDRHwlvOCRV1755i0eL/PyDXVTOUO1KuuBNWpL7R5NXiZKmOlCuub0Qem8E6+GGkX5b7mW++IXYX3gVG9/FM4U8Qceb60T/95OBIri0WC5YTeIoF69HgeYgF69GCpr9Gpliw0j8saeEpCHiIBSsjTofLLVgZMUjpM4siIBasLHriZNiCgCAgCAgCgoAgkCUQEBdhljhNMkhBQBAQBAQBQUAQyEoIpH0JTlaSKpPGmp60Cpk0JDmMICAICAKCgCAgCLgBAmLBcoOTIEMQBAQBQUAQEAQEAc9CQBQszzqfIo0gIAgIAoKAICAIuAEComC5wUmQIQgCgoAgIAgIAoKAZyEgCpZnnU+RRhAQBAQBQUAQEATcAAFRsNzgJMgQBAFBQBAQBAQBQcCzEBAFy7POp0gjCAgCgoAgIAgIAm6AgChYbnASZAiCgCAgCAgCgoAg4FkIiILlWedTpBEEBAFBQBAQBAQBN0BAFCw3OAkyBEFAEBAEBAFBQBDwLAREwfKs8ynSCAKCgCAgCAgCgoAbIMAKVkJiotkNhiJD8EQEEhOTpErwRPmckCme28qd5wSC0jRVBJJvPVKuNaEkBBLJLHeeXA8ZhEDySy+BFaxL4eEJ5vh4ze2YQceVbrMfAufOPVCFjsx+0qd9KCtFAAAByElEQVQq8SXee0Oe86mCJDuNI3Ajuance7YwRtK1a2aKF73T+NUlLR0hkHgj6c67yArWxthYMq1efdNRfSkXBAwjsHjxZbXtRsOdeGbDXyFWwu8wYsV4pnwi1WNE4CqOfcpiIMU/OvMYh+KOh94IC5Yp/sABdxybjCmLI5C4a5cqwc/e2PoL3H/Xrts5g4JymipWzEVeXqYsLqIM/3EjcOdOAk2bdpE2bIjmofwJfg0s9prkE3MHmwVjiRqcx0YIbrncj/ukyfE9AoGzkGKpmcywz/CDfAj4uEcI5johjqGr/hQW5kO5c5u8ihUDUvLOcx282bMnc0wMJfzyC5kPHWIA+BoboV5V7fBjJTiPjw+Zy5bNIVdb9rxGXCJ1fLwZz64EM8Ic+DoKA7cBR7ikc8/qxBfi8H3XkcUKAnOBkCBgFIFbaGh1yvNk5n3wRKN9eXi71pBvNTgveXubqUgReed5+AnPUPE47urqVUxrzHwdhYP5ncf/k6gMtuaD2afDN6ewYGD0GojD9XMS/D7YHyzkGAF20/cG7wE/BBvFXNoJdnwN3AavB7cAC6WOQGnsngfmeEi5fwQDZ64BDuhjdzxPaALUy+7/AWUS+CmJqoVxAAAAAElFTkSuQmCC"
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SIR model\n",
    "\n",
    "The SIR model is one of the most basic examples of compartmental models. The model consists of three compartments: \n",
    "- Susceptible (S)\n",
    "- Infectious (I)\n",
    "- Recovered (R) (or better not infectious, includes deceased)\n",
    "\n",
    "The assumptions underlying this model require the disease to be able to infect through human to human transmission, and to have the recovered individuals acquire lasting immunity.\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "A full modeling requires the specification of the transition rates. The S->I infection rate depends on the average number of contacts per person per time, the probability of transmission when in contact with an infected individual, and the number of infected instances (or the probability that any individual is infected).\n",
    "The I->R rate depends on the rate of recovery and mortality, and the total number of infected individuals."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### ODE formulation of SIR model\n",
    "\n",
    "Compartmental models can be formulated in a deterministic manner through differential equations. This makes them less realistic than stochastic models, but this formalism is easier to analyse.\n",
    "\n",
    "The ODE SIR model for diseases whose dynamics are faster than the birth and death dynamics of a population (i.e. without vital dynamics) is modeled by the following equations.\n",
    "\n",
    "$$\\begin{aligned}\n",
    "&\\frac{d S}{d t}=-\\frac{\\beta I S}{N}\\\\\n",
    "&\\frac{d I}{d t}=\\frac{\\beta I S}{N}-\\gamma I\\\\\n",
    "&\\frac{d R}{d t}=\\gamma I\n",
    "\\end{aligned}$$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "If we discretize these equations in order to simulate it we obtain:\n",
    "$$\\begin{aligned}\n",
    "&S_{k+1}= S_K (1 -\\frac{\\beta I_k}{N})\\\\\n",
    "&I_{k+1}=I_k (1 +\\frac{\\beta S_k}{N}-\\gamma)\\\\\n",
    "&R_{k+1}= R_k + \\gamma I_k\n",
    "\\end{aligned}$$\n",
    "\n",
    "Where $\\beta$ is a product of number of encounters and infection probability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def SRI_step(s, i, r, beta=0.5, gamma=0.5):\n",
    "    N = int(s+i+r)\n",
    "    s_new = s*(1 - beta*i/N)\n",
    "    r_new = r + gamma * i\n",
    "    #i_new = i*(1 - gamma + beta*s/N)\n",
    "    i_new = N - s_new - r_new\n",
    "    return s_new, i_new, r_new"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
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       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
       "}\n",
       ".anim-state label {\n",
       "    margin-right: 8px;\n",
       "}\n",
       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
       "  <img id=\"_anim_img8cfa750f91be476caaa4606945c1254d\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_slider8cfa750f91be476caaa4606945c1254d\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"anim8cfa750f91be476caaa4606945c1254d.set_frame(parseInt(this.value));\"></input>\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button onclick=\"anim8cfa750f91be476caaa4606945c1254d.slower()\"><i class=\"fa fa-minus\"></i></button>\n",
       "      <button onclick=\"anim8cfa750f91be476caaa4606945c1254d.first_frame()\"><i class=\"fa fa-fast-backward\">\n",
       "          </i></button>\n",
       "      <button onclick=\"anim8cfa750f91be476caaa4606945c1254d.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button onclick=\"anim8cfa750f91be476caaa4606945c1254d.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button onclick=\"anim8cfa750f91be476caaa4606945c1254d.pause_animation()\"><i class=\"fa fa-pause\">\n",
       "          </i></button>\n",
       "      <button onclick=\"anim8cfa750f91be476caaa4606945c1254d.play_animation()\"><i class=\"fa fa-play\"></i>\n",
       "          </button>\n",
       "      <button onclick=\"anim8cfa750f91be476caaa4606945c1254d.next_frame()\"><i class=\"fa fa-step-forward\">\n",
       "          </i></button>\n",
       "      <button onclick=\"anim8cfa750f91be476caaa4606945c1254d.last_frame()\"><i class=\"fa fa-fast-forward\">\n",
       "          </i></button>\n",
       "      <button onclick=\"anim8cfa750f91be476caaa4606945c1254d.faster()\"><i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form action=\"#n\" name=\"_anim_loop_select8cfa750f91be476caaa4606945c1254d\" class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_8cfa750f91be476caaa4606945c1254d\"\n",
       "             >\n",
       "      <label for=\"_anim_radio1_8cfa750f91be476caaa4606945c1254d\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_8cfa750f91be476caaa4606945c1254d\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio2_8cfa750f91be476caaa4606945c1254d\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_8cfa750f91be476caaa4606945c1254d\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_8cfa750f91be476caaa4606945c1254d\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\n",
       "</div>\n",
       "\n",
       "\n",
       "<script language=\"javascript\">\n",
       "  /* Instantiate the Animation class. */\n",
       "  /* The IDs given should match those used in the template above. */\n",
       "  (function() {\n",
       "    var img_id = \"_anim_img8cfa750f91be476caaa4606945c1254d\";\n",
       "    var slider_id = \"_anim_slider8cfa750f91be476caaa4606945c1254d\";\n",
       "    var loop_select_id = \"_anim_loop_select8cfa750f91be476caaa4606945c1254d\";\n",
       "    var frames = new Array(60);\n",
       "    \n",
       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAtAAAAJACAYAAACkMVHfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\\\n",
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       "uTerFjoEj/0AAAAASUVORK5CYII=\\\n",
       "\"\n",
       "\n",
       "\n",
       "    /* set a timeout to make sure all the above elements are created before\n",
       "       the object is initialized. */\n",
       "    setTimeout(function() {\n",
       "        anim8cfa750f91be476caaa4606945c1254d = new Animation(frames, img_id, slider_id, 200.0,\n",
       "                                 loop_select_id);\n",
       "    }, 0);\n",
       "  })()\n",
       "</script>\n"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x7f8a5bdad410>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 720x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "\n",
    "initial_infected = 5\n",
    "encounters_per_person = 2\n",
    "infection_probability = 0.3\n",
    "beta = encounters_per_person * infection_probability\n",
    "\n",
    "D = 5 # Duration of the disease\n",
    "gamma = 1/D\n",
    "\n",
    "N = 10000\n",
    "\n",
    "timeline = np.arange(60)\n",
    "susceptible = [N-initial_infected]\n",
    "infected = [initial_infected]\n",
    "recovered = [0]\n",
    "\n",
    "\n",
    "for step in timeline[1:]:\n",
    "    s, i, r = SRI_step(susceptible[-1], infected[-1], recovered[-1], beta=beta, gamma=gamma)\n",
    "    susceptible.append(s)\n",
    "    infected.append(i)\n",
    "    recovered.append(r)\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(10, 8))\n",
    "l1, = ax.plot(timeline, susceptible, color=\"blue\", label=\"Susceptible\")\n",
    "l2, = ax.plot(timeline, infected, color=\"red\", label=\"Infected\")\n",
    "l3, = ax.plot(timeline, recovered, color=\"green\", label=\"Recovered\")\n",
    "ax.legend()\n",
    "\n",
    "\n",
    "def animate_step(i):\n",
    "    l1.set_data(timeline[:i], susceptible[:i])\n",
    "    l2.set_data(timeline[:i], infected[:i])\n",
    "    l3.set_data(timeline[:i], recovered[:i])\n",
    "\n",
    "ani = matplotlib.animation.FuncAnimation(fig, animate_step, frames=len(timeline))\n",
    "ani"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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