python/samples/sir/sir_model_simulation.ipynb

{
 "cells": [
  {
   "cell_type": "raw",
   "id": "ea27a3dd-bccc-4bb3-b28f-4c0317b45c97",
   "metadata": {},
   "source": [
    "---\n",
    "title: \"SIR Model Equations Demo\"\n",
    "author: \"Meikang Wu\"\n",
    "date: \"2024-08-30\"\n",
    "output:\n",
    "  html:\n",
    "    math: katex\n",
    "---\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff221105-6a8e-4072-90bf-486911c75bd0",
   "metadata": {},
   "source": [
    "# SIR Model Simulation\n",
    "\n",
    "In this notebook, we will simulate a simple SIR model to understand how infectious diseases spread over time in a closed population. The model divides the population into three compartments:\n",
    "\n",
    "- **S**: The number of susceptible individuals.\n",
    "- **I**: The number of infected individuals.\n",
    "- **R**: The number of recovered individuals.\n",
    "\n",
    "The equations governing the SIR model are as follows:\n",
    "\n",
    "$$\n",
    "\\frac{dS}{dt} = -\\beta SI\n",
    "$$\n",
    "$$\n",
    "\\frac{dI}{dt} = \\beta SI - \\gamma I\n",
    "$$\n",
    "$$\n",
    "\\frac{dR}{dt} = \\gamma I\n",
    "$$\n",
    "\n",
    "Where:\n",
    "\n",
    "- $\\beta$ is the infection rate.\n",
    "- $\\gamma$ is the recovery rate.\n"
   ]
  },
  {
   "metadata": {},
   "cell_type": "code",
   "source": [
    "#| eval: false\n",
    "#| echo: false\n",
    "#| include: false\n",
    "%pip install -r requirements.txt"
   ],
   "id": "9d67ea2a26799bd6",
   "outputs": [],
   "execution_count": null
  },
  {
   "cell_type": "code",
   "id": "88293b16-acc0-439b-8a95-3c6be72fe3c0",
   "metadata": {},
   "source": [
    "import numpy as np\n",
    "from scipy.integrate import odeint\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.animation import FuncAnimation\n",
    "from IPython.display import HTML\n",
    "\n",
    "# %matplotlib inline\n",
    "\n",
    "# SIR model differential equations.\n",
    "def sir_model(y, t, beta, gamma):\n",
    "    S, I, R = y\n",
    "    dS_dt = -beta * S * I\n",
    "    dI_dt = beta * S * I - gamma * I\n",
    "    dR_dt = gamma * I\n",
    "    return [dS_dt, dI_dt, dR_dt]\n",
    "\n",
    "# Initial conditions: 99% susceptible, 1% infected, 0% recovered\n",
    "S0, I0, R0 = 0.99, 0.01, 0.0\n",
    "y0 = [S0, I0, R0]\n",
    "\n",
    "# Parameters\n",
    "beta = 0.3  # infection rate\n",
    "gamma = 0.1  # recovery rate\n",
    "\n",
    "# Time points\n",
    "t = np.linspace(0, 100, 100)\n",
    "\n",
    "# Integrate the SIR equations over the time grid, t.\n",
    "solution = odeint(sir_model, y0, t, args=(beta, gamma))\n",
    "S, I, R = solution.T\n",
    "\n",
    "# Create a plot\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_xlabel('Time')\n",
    "ax.set_ylabel('Proportion')\n",
    "line1, = ax.plot([], [], 'b-', label='Susceptible')\n",
    "line2, = ax.plot([], [], 'r-', label='Infected')\n",
    "line3, = ax.plot([], [], 'g-', label='Recovered')\n",
    "ax.set_xlim(0, 100)\n",
    "ax.set_ylim(0, 1)\n",
    "ax.legend()\n",
    "\n",
    "def init():\n",
    "    line1.set_data([], [])\n",
    "    line2.set_data([], [])\n",
    "    line3.set_data([], [])\n",
    "    return line1, line2, line3\n",
    "\n",
    "def update(frame):\n",
    "    line1.set_data(t[:frame], S[:frame])\n",
    "    line2.set_data(t[:frame], I[:frame])\n",
    "    line3.set_data(t[:frame], R[:frame])\n",
    "    return line1, line2, line3\n",
    "\n",
    "HTML(FuncAnimation(fig, update, frames=len(t), init_func=init, blit=True).to_html5_video())\n"
   ],
   "outputs": [
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 4
  },
  {
   "cell_type": "markdown",
   "id": "ce73d651-82f7-40cc-8034-10995bfd7b58",
   "metadata": {},
   "source": [
    "# Explanation of the SIR Model Simulation\n",
    "In this simulation, the initial conditions are set such that 99% of the population is susceptible, 1% is infected, and 0% has recovered. The infection rate $\\beta$ is set to 0.3, and the recovery rate $\\gamma$ is set to 0.1.\n",
    "\n",
    "As time progresses, the number of susceptible individuals decreases, the number of infected individuals initially increases and then decreases as individuals recover, and the number of recovered individuals increases. This is a typical behavior of an infectious disease in a closed population without births or deaths."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}