Epidemiology301.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"width: 100%; overflow: hidden;\">\n",
    "    <div style=\"width: 150px; float: left;\"> <img src=\"data/D4Sci_logo_ball.png\" alt=\"Data For Science, Inc\" align=\"left\" border=\"0\" width=160px> </div>\n",
    "    <div style=\"float: left; margin-left: 10px;\"> <h1>Epidemiology 301</h1>\n",
    "<h1>How to model the effects of vaccination</h1>\n",
    "        <p>Bruno Gonçalves<br/>\n",
    "        <a href=\"http://www.data4sci.com/\">www.data4sci.com</a><br/>\n",
    "            @bgoncalves, @data4sci</p></div>\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import Counter\n",
    "from pprint import pprint\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt \n",
    "\n",
    "import tqdm as tq\n",
    "from tqdm.notebook import tqdm\n",
    "\n",
    "import epidemik\n",
    "from epidemik import EpiModel\n",
    "\n",
    "import watermark\n",
    "\n",
    "%load_ext watermark\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start by print out the versions of the libraries we're using for future reference"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Python implementation: CPython\n",
      "Python version       : 3.13.2\n",
      "IPython version      : 8.32.0\n",
      "\n",
      "Compiler    : Clang 16.0.0 (clang-1600.0.26.6)\n",
      "OS          : Darwin\n",
      "Release     : 24.3.0\n",
      "Machine     : arm64\n",
      "Processor   : arm\n",
      "CPU cores   : 16\n",
      "Architecture: 64bit\n",
      "\n",
      "Git hash: 6d9f1a6eb4084a40d0e306ad0ba8a2eaa55e5c85\n",
      "\n",
      "epidemik  : 0.1.2\n",
      "pandas    : 2.2.3\n",
      "tqdm      : 4.67.1\n",
      "matplotlib: 3.10.0\n",
      "watermark : 2.5.0\n",
      "numpy     : 2.2.2\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%watermark -n -v -m -g -iv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load default figure style"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use('./d4sci.mplstyle')\n",
    "colors = plt.rcParams['axes.prop_cycle'].by_key()['color']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## SIR Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We start with the classical SIR model. It's not the most realistic, but it provides us with a simple model of a single wave epidemice (neglecting seasonality effects, social distancing measures, etc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "beta = 0.2\n",
    "mu = 0.1\n",
    "N = 1_000_000\n",
    "I0 = 10\n",
    "\n",
    "SIR = EpiModel()\n",
    "SIR.add_interaction('S', 'I', 'I', beta=beta)\n",
    "SIR.add_spontaneous('I', 'R', mu=mu)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# Epidemic Model with 3 compartments and 2 transitions:\n",
      "\n",
      "Parameters:\n",
      "  beta : 0.200000\n",
      "  mu : 0.100000\n",
      "\n",
      "\n",
      "Transitions:\n",
      "  - S + I = I beta\n",
      "  - I -> R mu\n",
      "\n",
      "# R0=2.00\n"
     ]
    }
   ],
   "source": [
    "print(SIR)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the dynamics are fairly simple as well:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "SIR.integrate(365, S=N-I0, I=I0, R=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the usual quick visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 3840x2640 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = SIR.plot('SIR Model', normed=True)\n",
    "ax.legend(['Susceptible', 'Infectious', 'Recovered'])\n",
    "ax.set_xlabel('Days')\n",
    "plt.gcf().patch.set_facecolor((1, 1, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The purple line is the number of currently infectious cases as a function of time. As we can see, not all of the population is infectious at the same time, and, in fact, only about $80\\%$ of the population is ever infected, as shown by the green curve representing the fraction of recovered."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The typical bell curve you're likely to see (as asked to flatten) is simply the number of infectious individuals as a function of time:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 3840x2640 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax=(SIR.I/N).plot(label='Infectious', color=colors[1])\n",
    "ax.set_xlabel('Days')\n",
    "ax.set_ylabel('Population')\n",
    "ax.legend()\n",
    "plt.gcf().patch.set_facecolor((1, 1, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Vaccination"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A simple way to add vaccination to this model is to just spontaneously move individuals from the 'Susceptible' compartiment to a new 'Vaccinated' compartment at a fixed rate, say, 1% per day. To make it more realistic, we only turn on this transition after a few steps (to simulate the vaccine development process)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "daily_vaccination_rate = 0.01\n",
    "vaccination_start = 75"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "# Epidemic Model with 4 compartments and 3 transitions:\n",
      "Name: Vaccine_SIR\n",
      "\n",
      "Parameters:\n",
      "  beta : 0.200000\n",
      "  mu : 0.100000\n",
      "\n",
      "\n",
      "Transitions:\n",
      "  - S + I = I beta\n",
      "  - S -> V mu starting at 75 days\n",
      "  - I -> R mu\n",
      "\n"
     ]
    }
   ],
   "source": [
    "Vaccine_SIR = EpiModel()\n",
    "Vaccine_SIR.add_interaction('S', 'I', 'I', beta=beta)\n",
    "Vaccine_SIR.add_spontaneous('I', 'R', mu=mu)\n",
    "\n",
    "# Add the vaccination transition\n",
    "Vaccine_SIR.add_vaccination('S', 'V', \n",
    "                            daily_vaccination_rate, \n",
    "                            vaccination_start)\n",
    "Vaccine_SIR.name = \"Vaccine_SIR\"\n",
    "\n",
    "print(Vaccine_SIR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "capi_return is NULL\n",
      "Call-back cb_f_in_lsoda__user__routines failed.\n"
     ]
    },
    {
     "ename": "KeyError",
     "evalue": "0.01",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "Cell \u001b[0;32mIn[11], line 1\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mVaccine_SIR\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mintegrate\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m365\u001b[39;49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mS\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mN\u001b[49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[43mI0\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mI\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mI0\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mR\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/Library/Caches/pypoetry/virtualenvs/epidemiology101-UtPQcdCX-py3.13/lib/python3.13/site-packages/epidemik/EpiModel.py:510\u001b[0m, in \u001b[0;36mEpiModel.integrate\u001b[0;34m(self, timesteps, t_min, seasonality, **kwargs)\u001b[0m\n\u001b[1;32m    506\u001b[0m time \u001b[38;5;241m=\u001b[39m np\u001b[38;5;241m.\u001b[39marange(t_min, t_min \u001b[38;5;241m+\u001b[39m timesteps, \u001b[38;5;241m1\u001b[39m)\n\u001b[1;32m    508\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mseasonality \u001b[38;5;241m=\u001b[39m seasonality\n\u001b[1;32m    509\u001b[0m values \u001b[38;5;241m=\u001b[39m pd\u001b[38;5;241m.\u001b[39mDataFrame(\n\u001b[0;32m--> 510\u001b[0m     \u001b[43mscipy\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mintegrate\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43msolve_ivp\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m    511\u001b[0m \u001b[43m        \u001b[49m\u001b[43mfun\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_new_cases\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    512\u001b[0m \u001b[43m        \u001b[49m\u001b[43mt_span\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mtime\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mtime\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m-\u001b[39;49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    513\u001b[0m \u001b[43m        \u001b[49m\u001b[43my0\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mpopulation\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    514\u001b[0m \u001b[43m        \u001b[49m\u001b[43mt_eval\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mtime\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    515\u001b[0m \u001b[43m        \u001b[49m\u001b[43margs\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mpos\u001b[49m\u001b[43m,\u001b[49m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    516\u001b[0m \u001b[43m        \u001b[49m\u001b[43mmethod\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mLSODA\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m,\u001b[49m\n\u001b[1;32m    517\u001b[0m \u001b[43m    \u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241m.\u001b[39my\u001b[38;5;241m.\u001b[39mT,\n\u001b[1;32m    518\u001b[0m     columns\u001b[38;5;241m=\u001b[39mpos\u001b[38;5;241m.\u001b[39mkeys(),\n\u001b[1;32m    519\u001b[0m     index\u001b[38;5;241m=\u001b[39mtime,\n\u001b[1;32m    520\u001b[0m )\n\u001b[1;32m    522\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mpopulation \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m    523\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mvalues_ \u001b[38;5;241m=\u001b[39m values\n",
      "File \u001b[0;32m~/Library/Caches/pypoetry/virtualenvs/epidemiology101-UtPQcdCX-py3.13/lib/python3.13/site-packages/scipy/integrate/_ivp/ivp.py:655\u001b[0m, in \u001b[0;36msolve_ivp\u001b[0;34m(fun, t_span, y0, method, t_eval, dense_output, events, vectorized, args, **options)\u001b[0m\n\u001b[1;32m    653\u001b[0m status \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mNone\u001b[39;00m\n\u001b[1;32m    654\u001b[0m \u001b[38;5;28;01mwhile\u001b[39;00m status \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[0;32m--> 655\u001b[0m     message \u001b[38;5;241m=\u001b[39m \u001b[43msolver\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mstep\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    657\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m solver\u001b[38;5;241m.\u001b[39mstatus \u001b[38;5;241m==\u001b[39m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mfinished\u001b[39m\u001b[38;5;124m'\u001b[39m:\n\u001b[1;32m    658\u001b[0m         status \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m0\u001b[39m\n",
      "File \u001b[0;32m~/Library/Caches/pypoetry/virtualenvs/epidemiology101-UtPQcdCX-py3.13/lib/python3.13/site-packages/scipy/integrate/_ivp/base.py:197\u001b[0m, in \u001b[0;36mOdeSolver.step\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    195\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[1;32m    196\u001b[0m     t \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mt\n\u001b[0;32m--> 197\u001b[0m     success, message \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_step_impl\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    199\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m success:\n\u001b[1;32m    200\u001b[0m         \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mstatus \u001b[38;5;241m=\u001b[39m \u001b[38;5;124m'\u001b[39m\u001b[38;5;124mfailed\u001b[39m\u001b[38;5;124m'\u001b[39m\n",
      "File \u001b[0;32m~/Library/Caches/pypoetry/virtualenvs/epidemiology101-UtPQcdCX-py3.13/lib/python3.13/site-packages/scipy/integrate/_ivp/lsoda.py:161\u001b[0m, in \u001b[0;36mLSODA._step_impl\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    159\u001b[0m itask \u001b[38;5;241m=\u001b[39m integrator\u001b[38;5;241m.\u001b[39mcall_args[\u001b[38;5;241m2\u001b[39m]\n\u001b[1;32m    160\u001b[0m integrator\u001b[38;5;241m.\u001b[39mcall_args[\u001b[38;5;241m2\u001b[39m] \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m5\u001b[39m\n\u001b[0;32m--> 161\u001b[0m solver\u001b[38;5;241m.\u001b[39m_y, solver\u001b[38;5;241m.\u001b[39mt \u001b[38;5;241m=\u001b[39m \u001b[43mintegrator\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrun\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m    162\u001b[0m \u001b[43m    \u001b[49m\u001b[43msolver\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mf\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43msolver\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mjac\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;129;43;01mor\u001b[39;49;00m\u001b[43m \u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;28;43;01mlambda\u001b[39;49;00m\u001b[43m:\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43;01mNone\u001b[39;49;00m\u001b[43m)\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43msolver\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_y\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43msolver\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mt\u001b[49m\u001b[43m,\u001b[49m\n\u001b[1;32m    163\u001b[0m \u001b[43m    \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mt_bound\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43msolver\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mf_params\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43msolver\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mjac_params\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    164\u001b[0m integrator\u001b[38;5;241m.\u001b[39mcall_args[\u001b[38;5;241m2\u001b[39m] \u001b[38;5;241m=\u001b[39m itask\n\u001b[1;32m    166\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m solver\u001b[38;5;241m.\u001b[39msuccessful():\n",
      "File \u001b[0;32m~/Library/Caches/pypoetry/virtualenvs/epidemiology101-UtPQcdCX-py3.13/lib/python3.13/site-packages/scipy/integrate/_ode.py:1358\u001b[0m, in \u001b[0;36mlsoda.run\u001b[0;34m(self, f, jac, y0, t0, t1, f_params, jac_params)\u001b[0m\n\u001b[1;32m   1354\u001b[0m args \u001b[38;5;241m=\u001b[39m [f, y0, t0, t1] \u001b[38;5;241m+\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcall_args[:\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m] \u001b[38;5;241m+\u001b[39m \\\n\u001b[1;32m   1355\u001b[0m        [jac, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcall_args[\u001b[38;5;241m-\u001b[39m\u001b[38;5;241m1\u001b[39m], f_params, \u001b[38;5;241m0\u001b[39m, jac_params]\n\u001b[1;32m   1357\u001b[0m \u001b[38;5;28;01mwith\u001b[39;00m LSODA_LOCK:\n\u001b[0;32m-> 1358\u001b[0m     y1, t, istate \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mrunner\u001b[49m\u001b[43m(\u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m   1360\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mistate \u001b[38;5;241m=\u001b[39m istate\n\u001b[1;32m   1361\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m istate \u001b[38;5;241m<\u001b[39m \u001b[38;5;241m0\u001b[39m:\n",
      "File \u001b[0;32m~/Library/Caches/pypoetry/virtualenvs/epidemiology101-UtPQcdCX-py3.13/lib/python3.13/site-packages/scipy/integrate/_ivp/base.py:154\u001b[0m, in \u001b[0;36mOdeSolver.__init__.<locals>.fun\u001b[0;34m(t, y)\u001b[0m\n\u001b[1;32m    152\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;21mfun\u001b[39m(t, y):\n\u001b[1;32m    153\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mnfev \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m \u001b[38;5;241m1\u001b[39m\n\u001b[0;32m--> 154\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mfun_single\u001b[49m\u001b[43m(\u001b[49m\u001b[43mt\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43my\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/Library/Caches/pypoetry/virtualenvs/epidemiology101-UtPQcdCX-py3.13/lib/python3.13/site-packages/scipy/integrate/_ivp/base.py:23\u001b[0m, in \u001b[0;36mcheck_arguments.<locals>.fun_wrapped\u001b[0;34m(t, y)\u001b[0m\n\u001b[1;32m     22\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;21mfun_wrapped\u001b[39m(t, y):\n\u001b[0;32m---> 23\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m np\u001b[38;5;241m.\u001b[39masarray(\u001b[43mfun\u001b[49m\u001b[43m(\u001b[49m\u001b[43mt\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43my\u001b[49m\u001b[43m)\u001b[49m, dtype\u001b[38;5;241m=\u001b[39mdtype)\n",
      "File \u001b[0;32m~/Library/Caches/pypoetry/virtualenvs/epidemiology101-UtPQcdCX-py3.13/lib/python3.13/site-packages/scipy/integrate/_ivp/ivp.py:593\u001b[0m, in \u001b[0;36msolve_ivp.<locals>.fun\u001b[0;34m(t, x, fun)\u001b[0m\n\u001b[1;32m    592\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m\u001b[38;5;250m \u001b[39m\u001b[38;5;21mfun\u001b[39m(t, x, fun\u001b[38;5;241m=\u001b[39mfun):\n\u001b[0;32m--> 593\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[43mfun\u001b[49m\u001b[43m(\u001b[49m\u001b[43mt\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mx\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43margs\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/Library/Caches/pypoetry/virtualenvs/epidemiology101-UtPQcdCX-py3.13/lib/python3.13/site-packages/epidemik/EpiModel.py:254\u001b[0m, in \u001b[0;36mEpiModel._new_cases\u001b[0;34m(self, time, population, pos)\u001b[0m\n\u001b[1;32m    251\u001b[0m target \u001b[38;5;241m=\u001b[39m edge[\u001b[38;5;241m1\u001b[39m]\n\u001b[1;32m    252\u001b[0m trans \u001b[38;5;241m=\u001b[39m edge[\u001b[38;5;241m2\u001b[39m]\n\u001b[0;32m--> 254\u001b[0m rate_val \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mparams\u001b[49m\u001b[43m[\u001b[49m\u001b[43mtrans\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[38;5;124;43mrate\u001b[39;49m\u001b[38;5;124;43m\"\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m]\u001b[49m\n\u001b[1;32m    255\u001b[0m rate \u001b[38;5;241m=\u001b[39m rate_val \u001b[38;5;241m*\u001b[39m population[pos[source]]\n\u001b[1;32m    257\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mstart\u001b[39m\u001b[38;5;124m\"\u001b[39m \u001b[38;5;129;01min\u001b[39;00m trans \u001b[38;5;129;01mand\u001b[39;00m trans[\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mstart\u001b[39m\u001b[38;5;124m\"\u001b[39m] \u001b[38;5;241m>\u001b[39m\u001b[38;5;241m=\u001b[39m time:\n",
      "\u001b[0;31mKeyError\u001b[0m: 0.01"
     ]
    }
   ],
   "source": [
    "Vaccine_SIR.integrate(365, S=N-I0, I=I0, R=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ax=(Vaccine_SIR).plot()\n",
    "ax.axvline(x=vaccination_start, \n",
    "           label='Vaccination Starts', linestyle='--', color='darkgray')\n",
    "ax.set_xlabel('Days')\n",
    "ax.set_ylabel('Population')\n",
    "plt.gcf().patch.set_facecolor((1, 1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ax=(SIR.I/N).plot(label='SIR Model', color=colors[1])\n",
    "(Vaccine_SIR.I/N).plot(label='Vaccine SIR Model', color=colors[1], linestyle=':')\n",
    "ax.axvline(x=vaccination_start, \n",
    "           label='Vaccination Starts', linestyle='--', color='darkgray')\n",
    "ax.set_xlabel('Days')\n",
    "ax.set_ylabel('Population')\n",
    "ax.legend()\n",
    "plt.gcf().patch.set_facecolor((1, 1, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So far we've been assuming that the vaccine offers 100% protection, however, that's not necessarily true. If instead we have a vaccine with just 90% efficacy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "efficacy = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Vaccine_SIVIR = EpiModel()\n",
    "Vaccine_SIVIR.add_interaction('S', 'I', 'I', beta)\n",
    "Vaccine_SIVIR.add_spontaneous('I', 'R', mu)\n",
    "Vaccine_SIVIR.add_vaccination('S', 'V', daily_vaccination_rate, vaccination_start)\n",
    "Vaccine_SIVIR.add_interaction('V', 'VI', 'VI', beta*(1-efficacy))\n",
    "Vaccine_SIVIR.add_interaction('V', 'VI', 'I', beta*(1-efficacy))\n",
    "Vaccine_SIVIR.add_interaction('S', 'I', 'VI', beta*(1-efficacy))\n",
    "Vaccine_SIVIR.add_spontaneous('VI', 'VR', mu)\n",
    "\n",
    "\n",
    "print(Vaccine_SIVIR)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "Vaccine_SIVIR.integrate(365, S=N-I0, I=I0, R=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "compartment_colors = [*colors[:4], colors[5], colors[8]]\n",
    "color_dict = dict(zip(Vaccine_SIVIR.transitions.nodes, compartment_colors))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ax = (Vaccine_SIVIR).plot(color=compartment_colors)\n",
    "ax.axvline(x=vaccination_start, \n",
    "           label='Vaccination Starts', linestyle='--', color='darkgray')\n",
    "ax.legend(loc='upper right')\n",
    "ax.set_xlabel('Days')\n",
    "ax.set_ylabel('Population')\n",
    "fig = plt.gcf()\n",
    "fig.patch.set_facecolor((1, 1, 1))\n",
    "fig.savefig('SIRVVIVR.png', dpi=300, facecolor='white')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ax = (Vaccine_SIVIR[['I', 'VI']]/N).plot(color=[color_dict['I'], color_dict['VI']])\n",
    "(SIR.I/N).plot(ax=ax, label='SIR', color=colors[1], linestyle=':')\n",
    "ax.axvline(x=vaccination_start, \n",
    "           label='Vaccination Starts', linestyle='--', color='darkgray')\n",
    "\n",
    "ax.legend()\n",
    "ax.set_xlabel('Days')\n",
    "ax.set_ylabel('Population')\n",
    "plt.gcf().patch.set_facecolor((1, 1, 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "proportion = Vaccine_SIVIR[['I', 'VI']].copy()\n",
    "proportion = proportion.T.div(proportion.sum(axis=1)).T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "ax = proportion.plot(color=[color_dict['I'], color_dict['VI']])\n",
    "ax.axvline(x=vaccination_start, \n",
    "           label='Vaccination Starts', linestyle='--', color='darkgray')\n",
    "ax.legend(loc='lower right')\n",
    "ax.set_xlabel('Days')\n",
    "ax.set_ylabel('Proportion')\n",
    "plt.gcf().patch.set_facecolor((1, 1, 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<center>\n",
    "     <img src=\"data/D4Sci_logo_full.png\" alt=\"Data For Science, Inc\" align=\"center\" border=\"0\" width=300px> \n",
    "</center>"
   ]
  }
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