AC_tissueInfection_toSIR.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "toc": true
   },
   "source": [
    "<h1>Table of Contents<span class=\"tocSkip\"></span></h1>\n",
    "<div class=\"toc\"><ul class=\"toc-item\"><li><span><a href=\"#Activity\" data-toc-modified-id=\"Activity-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Activity</a></span></li><li><span><a href=\"#Libraries\" data-toc-modified-id=\"Libraries-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>Libraries</a></span></li><li><span><a href=\"#Setting-up-the-data\" data-toc-modified-id=\"Setting-up-the-data-3\"><span class=\"toc-item-num\">3&nbsp;&nbsp;</span>Setting up the data</a></span></li><li><span><a href=\"#Modeling-changes-to-a-tissue-during-infection\" data-toc-modified-id=\"Modeling-changes-to-a-tissue-during-infection-4\"><span class=\"toc-item-num\">4&nbsp;&nbsp;</span>Modeling changes to a tissue during infection</a></span></li><li><span><a href=\"#Run-simulation-and-visualize\" data-toc-modified-id=\"Run-simulation-and-visualize-5\"><span class=\"toc-item-num\">5&nbsp;&nbsp;</span>Run simulation and visualize</a></span></li><li><span><a href=\"#How-immune-cells-affect-infection\" data-toc-modified-id=\"How-immune-cells-affect-infection-6\"><span class=\"toc-item-num\">6&nbsp;&nbsp;</span>How immune cells affect infection</a></span></li><li><span><a href=\"#Plot-infection-with-immune-system-over-time\" data-toc-modified-id=\"Plot-infection-with-immune-system-over-time-7\"><span class=\"toc-item-num\">7&nbsp;&nbsp;</span>Plot infection with immune system over time</a></span></li></ul></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Activity"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    \n",
    "    Imagine a tissue with n x n cells with different states:\n",
    "    \n",
    "    H: Healthy\n",
    "    VA: Viral assembly\n",
    "    VR: Viral release\n",
    "    D: Dead\n",
    "    \n",
    "    INFECT_PROB = probability of infection (i.e. the likelihood of a cell becoming infected)\n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import sys\n",
    "# !{sys.executable} -m pip install plotly"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Libraries"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-23T23:08:43.096574Z",
     "start_time": "2021-02-23T23:08:03.934821Z"
    }
   },
   "outputs": [],
   "source": [
    "#Importing libraries: computer code 'cookbooks'\n",
    "\n",
    "import matplotlib.pyplot\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import random\n",
    "import plotly as py\n",
    "import plotly.graph_objs as go\n",
    "import copy\n",
    "\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Setting up the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
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       "      <td>S</td>\n",
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       "      <td>-</td>\n",
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       "   0  1  2  3  4  5  6  7  8  9\n",
       "0  -  -  -  -  -  -  -  -  -  -\n",
       "1  -  -  -  -  -  -  -  -  -  I\n",
       "2  -  -  -  -  -  -  -  -  S  -\n",
       "3  -  -  -  -  -  -  -  -  -  -\n",
       "4  -  -  -  -  -  -  S  -  -  -\n",
       "5  -  -  -  -  -  -  -  -  -  -\n",
       "6  -  -  -  -  -  -  -  S  -  -\n",
       "7  -  -  I  -  S  S  -  -  -  S\n",
       "8  -  -  S  -  -  -  -  -  S  -\n",
       "9  -  -  -  -  -  -  -  -  -  -"
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     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def setUpData(n, max_starting_infected, popSize, infect_prob):\n",
    "    \"\"\"\n",
    "    n size of tissue\n",
    "    max_starting_infected: max number of cells in tissue that could start as infected, all others are healthy\n",
    "    infect_prob: probality that a healthy cell that is next to a VR cell gets infected on one timestep\n",
    "    \n",
    "    returns: pop: list of individuals in population, where an individual [row, col, state, susptablity, infectivity, ageInfect]\n",
    "    S: susptablity of 1, infectivity: 0\n",
    "    I: susptablity of 0, infectivity: infect_prob\n",
    "    R: susptablity of 0.2, infectivity: 0\n",
    "    \n",
    "    \"\"\"\n",
    "    \n",
    "    pop = []\n",
    "    \n",
    "    n_starting_infected = random.randint(0, max_starting_infected) \n",
    "    points_I = set()\n",
    "    while len(points_I) < n_starting_infected:\n",
    "        points_I.add((random.randint(0, n-1), random.randint(0, n-1))) \n",
    "    for cord in points_I:\n",
    "        pop.append([cord[0], cord[1], \"I\", 0, infect_prob, 0])\n",
    "        \n",
    "    n_susceptible = popSize - n_starting_infected\n",
    "    points_S = set()\n",
    "    while len(points_S) < n_susceptible:\n",
    "        points_S.add((random.randint(0, n-1), random.randint(0, n-1))) \n",
    "    for cord in points_S:\n",
    "        pop.append([cord[0], cord[1], \"S\", 1, 0, 0])\n",
    "        \n",
    "    return pop\n",
    "\n",
    "\n",
    "def assignTissue(n, pop):\n",
    "    tissue = pd.DataFrame(\"-\", index = range(n), columns = range(n))\n",
    "    for person in pop:\n",
    "        tissue.iloc[person[0], person[1]] = person[2]\n",
    "    return tissue\n",
    "\n",
    "pop = setUpData(10, 3, 10, 0.9) \n",
    "assignTissue(n, pop)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modeling changes to a tissue during infection"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "    Next stages for:\n",
    "    \n",
    "        Healthy cell: \n",
    "            If adjacent to cells releasing viruses (i.e. \"VR\"), give a random probability between 0 and 1.\n",
    "            If probability <= INFECT_PROB, healthy cell is infected and becomes H -> VA\n",
    "            \n",
    "        Viral assembly:\n",
    "            Release of viruses (i.e. VA -> VR)\n",
    "            \n",
    "        Viral release:\n",
    "            Dies (i.e. VR -> D)\n",
    "            \n",
    "        Dead cell:\n",
    "            No change\n",
    "            \n",
    "            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "def one_time_step(n, pop):\n",
    "    \"\"\"\n",
    "    check all population if infectivity next to susptablity; and infect based on prob\n",
    "    [row, col, state, susptablity, infectivity, ageInfect]\n",
    "    TODO move individuals randomly\n",
    "    \"\"\"\n",
    "    pop_new = copy.deepcopy(pop)\n",
    "    for p1 in pop:\n",
    "        p1_infect = p1[4]\n",
    "        for i in range(len(pop)):\n",
    "            p2 = pop[i]\n",
    "            if abs(p1[0]-p2[0]) <= 3:\n",
    "                if abs(p1[1]-p2[1]) <= 3:\n",
    "                    if random.random() < p1_infect*p2[3]: #infectivity of p1 times susptablity of p2\n",
    "                        pop_new[i][2] = \"I\"\n",
    "                        pop_new[i][3] = 0\n",
    "                        pop_new[i][4] = p1_infect\n",
    "                        pop_new[i][5] = 0\n",
    "                        \n",
    "    for p1 in pop_new:\n",
    "        if p1[2] == \"I\":\n",
    "            if p1[5] == 10:\n",
    "                p1[2] = \"R\"\n",
    "                p1[3] = 0.2\n",
    "                p1[4] = 0\n",
    "                p1[5] = 0\n",
    "            else:\n",
    "                p1[5] += 1 #update ageInfect counter\n",
    "        row = p1[0] +  random.randint(-1, 1)\n",
    "        if row < 0:\n",
    "            row = 0\n",
    "        if row >= n:\n",
    "            row = n-1\n",
    "        p1[0] = row\n",
    "        col = p1[1] +  random.randint(-1, 1)\n",
    "        if col < 0:\n",
    "            col = 0\n",
    "        if col >= n:\n",
    "            col = n-1\n",
    "        p1[1] = col \n",
    "    return pop_new\n",
    "        \n",
    "# pop = setUpData(10, 3, 10, 0.9) \n",
    "# print(assignTissue(n, pop))\n",
    "# pop = one_time_step(n, copy.deepcopy(pop))\n",
    "# print(assignTissue(n, pop))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "def t_time_step(t, n, pop):\n",
    "    tissue = assignTissue(n, pop) \n",
    "    out_tissue = [tissue]\n",
    "    out_pop = [pop]\n",
    "    for step in range(t):\n",
    "        pop = one_time_step(n, copy.deepcopy(pop))\n",
    "        updated_tissue = assignTissue(n, pop) \n",
    "        out_tissue.append(updated_tissue.values)\n",
    "        out_pop.append(pop)\n",
    "    return out_tissue, out_pop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NEXT STEP\n",
      "[[1, 2, 'S', 1, 0, 0], [3, 2, 'S', 1, 0, 0], [0, 0, 'S', 1, 0, 0], [1, 3, 'S', 1, 0, 0], [3, 3, 'S', 1, 0, 0], [3, 0, 'S', 1, 0, 0], [0, 2, 'S', 1, 0, 0], [1, 0, 'S', 1, 0, 0], [3, 1, 'S', 1, 0, 0], [2, 1, 'S', 1, 0, 0], [1, 4, 'S', 1, 0, 0], [2, 0, 'S', 1, 0, 0], [1, 1, 'S', 1, 0, 0], [4, 3, 'S', 1, 0, 0], [2, 2, 'S', 1, 0, 0], [3, 4, 'S', 1, 0, 0], [0, 3, 'S', 1, 0, 0], [4, 1, 'S', 1, 0, 0], [2, 4, 'S', 1, 0, 0], [4, 0, 'S', 1, 0, 0]]\n",
      "NEXT STEP\n",
      "[[2, 1, 'S', 1, 0, 0], [4, 3, 'S', 1, 0, 0], [1, 0, 'S', 1, 0, 0], [0, 2, 'S', 1, 0, 0], [4, 3, 'S', 1, 0, 0], [4, 0, 'S', 1, 0, 0], [0, 3, 'S', 1, 0, 0], [2, 0, 'S', 1, 0, 0], [3, 0, 'S', 1, 0, 0], [2, 1, 'S', 1, 0, 0], [1, 4, 'S', 1, 0, 0], [2, 0, 'S', 1, 0, 0], [2, 0, 'S', 1, 0, 0], [4, 4, 'S', 1, 0, 0], [3, 1, 'S', 1, 0, 0], [3, 4, 'S', 1, 0, 0], [1, 4, 'S', 1, 0, 0], [4, 2, 'S', 1, 0, 0], [1, 3, 'S', 1, 0, 0], [4, 0, 'S', 1, 0, 0]]\n",
      "NEXT STEP\n",
      "[[2, 1, 'S', 1, 0, 0], [4, 3, 'S', 1, 0, 0], [1, 1, 'S', 1, 0, 0], [1, 3, 'S', 1, 0, 0], [4, 3, 'S', 1, 0, 0], [4, 1, 'S', 1, 0, 0], [1, 2, 'S', 1, 0, 0], [3, 0, 'S', 1, 0, 0], [3, 0, 'S', 1, 0, 0], [3, 1, 'S', 1, 0, 0], [2, 3, 'S', 1, 0, 0], [2, 0, 'S', 1, 0, 0], [3, 1, 'S', 1, 0, 0], [4, 4, 'S', 1, 0, 0], [3, 0, 'S', 1, 0, 0], [2, 3, 'S', 1, 0, 0], [1, 4, 'S', 1, 0, 0], [4, 1, 'S', 1, 0, 0], [0, 3, 'S', 1, 0, 0], [4, 1, 'S', 1, 0, 0]]\n",
      "NEXT STEP\n",
      "[[3, 1, 'S', 1, 0, 0], [4, 4, 'S', 1, 0, 0], [0, 0, 'S', 1, 0, 0], [2, 4, 'S', 1, 0, 0], [4, 2, 'S', 1, 0, 0], [4, 2, 'S', 1, 0, 0], [0, 1, 'S', 1, 0, 0], [2, 1, 'S', 1, 0, 0], [2, 1, 'S', 1, 0, 0], [3, 1, 'S', 1, 0, 0], [1, 3, 'S', 1, 0, 0], [1, 0, 'S', 1, 0, 0], [2, 1, 'S', 1, 0, 0], [3, 3, 'S', 1, 0, 0], [2, 1, 'S', 1, 0, 0], [1, 4, 'S', 1, 0, 0], [1, 3, 'S', 1, 0, 0], [4, 2, 'S', 1, 0, 0], [0, 4, 'S', 1, 0, 0], [4, 2, 'S', 1, 0, 0]]\n",
      "FIRST POP\n",
      "   0  1  2  3  4\n",
      "0  S  -  S  S  -\n",
      "1  S  S  S  S  S\n",
      "2  S  S  S  -  S\n",
      "3  S  S  S  S  S\n",
      "4  S  S  -  S  -\n",
      "LAST POP\n",
      "   0  1  2  3  4\n",
      "0  S  S  -  -  S\n",
      "1  S  -  -  S  S\n",
      "2  -  S  -  -  S\n",
      "3  -  S  -  S  -\n",
      "4  -  -  S  -  S\n"
     ]
    }
   ],
   "source": [
    "INFECT_PROB = 0.9 \n",
    "n = 5 # size of tissue\n",
    "max_starting_infected = 3 \n",
    "t = 3\n",
    "    \n",
    "pop = setUpData(n, max_starting_infected, popSize, INFECT_PROB)\n",
    "\n",
    "out_tissue, out_pop = t_time_step(t, n, copy.deepcopy(pop))\n",
    "\n",
    "\n",
    "for h in out_pop:\n",
    "    print(\"NEXT STEP\")\n",
    "    print(h)\n",
    "    \n",
    "print(\"FIRST POP\")\n",
    "print(assignTissue(n, out_pop[0]))   \n",
    "print(\"LAST POP\")\n",
    "print(assignTissue(n, out_pop[-1]))   \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "tissue"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Run simulation and visualize"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-23T23:48:32.357140Z",
     "start_time": "2021-02-23T23:48:28.886878Z"
    }
   },
   "outputs": [],
   "source": [
    "INFECT_PROB = 1\n",
    "n = 25 # size of tissue\n",
    "max_starting_infected = 5 \n",
    "t = 20\n",
    "popSize = 20\n",
    "\n",
    "\n",
    "pop = setUpData(n, max_starting_infected, popSize, INFECT_PROB)\n",
    "tissue_frames, pop_frames = t_time_step(t, n, copy.deepcopy(pop))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "INFECT_PROB = 1\n",
    "n = 25 # size of tissue\n",
    "max_starting_infected = 10\n",
    "t = 20\n",
    "popSize = 30\n",
    "\n",
    "\n",
    "pop = setUpData(n, max_starting_infected, popSize, INFECT_PROB)\n",
    "tissue_frames, pop_frames = t_time_step(t, n, copy.deepcopy(pop))\n",
    "\n",
    "\n",
    "S_l = []\n",
    "I_l = []\n",
    "R_l = []\n",
    "for pop in pop_frames:\n",
    "    Scount = 0\n",
    "    Icount = 0\n",
    "    Rcount = 0\n",
    "    for p1 in pop:\n",
    "        if p1[2] == \"S\":\n",
    "            Scount += 1\n",
    "        if p1[2] == \"I\":\n",
    "            Icount += 1\n",
    "        if p1[2] == \"R\":\n",
    "            Rcount += 1\n",
    "    S_l.append(Scount)\n",
    "    I_l.append(Icount)\n",
    "    R_l.append(Rcount)\n",
    "times_l = list(range(len(pop_frames)))\n",
    "    \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[25, 19, 12, 10, 8, 8, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c39c1606a0>]"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "times_l\n",
    "print(S_l)\n",
    "plt.plot(times_l, S_l, color = \"blue\")\n",
    "plt.plot(times_l, I_l, color = \"red\")\n",
    "plt.plot(times_l, R_l, color = \"purple\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[7, 4, 'S', 1, 0, 0],\n",
       " [15, 18, 'S', 1, 0, 0],\n",
       " [22, 17, 'S', 1, 0, 0],\n",
       " [4, 13, 'S', 1, 0, 0],\n",
       " [3, 19, 'S', 1, 0, 0],\n",
       " [18, 4, 'S', 1, 0, 0],\n",
       " [9, 24, 'S', 1, 0, 0],\n",
       " [17, 18, 'S', 1, 0, 0],\n",
       " [4, 17, 'S', 1, 0, 0],\n",
       " [16, 0, 'S', 1, 0, 0],\n",
       " [9, 16, 'S', 1, 0, 0],\n",
       " [20, 16, 'S', 1, 0, 0],\n",
       " [13, 21, 'S', 1, 0, 0],\n",
       " [1, 22, 'S', 1, 0, 0],\n",
       " [2, 16, 'S', 1, 0, 0],\n",
       " [23, 2, 'S', 1, 0, 0],\n",
       " [13, 19, 'S', 1, 0, 0],\n",
       " [3, 0, 'S', 1, 0, 0],\n",
       " [22, 23, 'S', 1, 0, 0],\n",
       " [1, 10, 'S', 1, 0, 0]]"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2021-02-23T23:50:40.173924Z",
     "start_time": "2021-02-23T23:50:39.935567Z"
    }
   },
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "colorbar": {
          "thickness": 25,
          "ticktext": [
           " ",
           "Suseptible",
           "Infecious",
           "Recovered"
          ],
          "tickvals": [
           0,
           0.25,
           0.5,
           0.75
          ]
         },
         "colorscale": [
          [
           0,
           "#56B4E9"
          ],
          [
           0.25,
           "#56B4E9"
          ],
          [
           0.25,
           "#F0E442"
          ],
          [
           0.5,
           "#F0E442"
          ],
          [
           0.5,
           "#D55E00"
          ],
          [
           0.75,
           "#D55E00"
          ],
          [
           0.75,
           "#000000"
          ],
          [
           1,
           "#000000"
          ]
         ],
         "type": "heatmap",
         "z": [
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       "                        }).then(function(){\n",
       "                            \n",
       "var gd = document.getElementById('4a25ab68-dee1-49f9-9002-96e439753914');\n",
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       "        var display = window.getComputedStyle(gd).display;\n",
       "        if (!display || display === 'none') {{\n",
       "            console.log([gd, 'removed!']);\n",
       "            Plotly.purge(gd);\n",
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       "\n",
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   "source": [
    "#Plot simulation - do not worry about what is happening in code here, just what movie it makes\n",
    "numerify = {'-': 0, 'S': 0.25, 'I': 0.5, 'R': 0.75}\n",
    "\n",
    "legend_colors = [\n",
    "    [0, \"#56B4E9\"],\n",
    "    [0.25,  \"#56B4E9\"],\n",
    "    [0.25, \"#F0E442\"],\n",
    "    [0.5, \"#F0E442\"],\n",
    "    [0.5, \"#D55E00\"],\n",
    "    [0.75, \"#D55E00\"],\n",
    "    [0.75, \"#000000\"],\n",
    "    [1.0, \"#000000\"]\n",
    "]\n",
    "\n",
    "numbers = [0, 0.25, 0.5, 0.75]\n",
    "names   = [' ', 'Suseptible', 'Infecious', 'Recovered']\n",
    "\n",
    "\n",
    "# Numerify the cells for plotting\n",
    "tissue_frames_numeric = []\n",
    "for t in range(len(tissue_frames)):\n",
    "    tissue_frames_numeric.append(tissue_frames[t].copy())\n",
    "    for i in range(tissue_frames[t].shape[0]):\n",
    "        for j in range(tissue_frames[t].shape[1]):\n",
    "            tissue_frames_numeric[t][i][j] = numerify[tissue_frames[t][i][j]]\n",
    "            \n",
    "fig = go.Figure(data=go.Heatmap(z=tissue_frames_numeric[0], colorscale=legend_colors, colorbar=dict(tickvals=numbers, ticktext=names, thickness=25)),\n",
    "               frames=[go.Frame(data=go.Heatmap(z=tissue_frames_numeric[i])) for i in range(len(tissue_frames_numeric))])\n",
    "fig.update_layout(\n",
    "    updatemenus=[\n",
    "        dict(type=\"buttons\", visible=True,\n",
    "        buttons=[dict(label=\"Play\", method=\"animate\", args=[None])]\n",
    "            )])\n",
    "fig.show()"
   ]
  }
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