SIR_Model-Interactive.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/john-s-butler-dit/CaseStudy_PredatorPrey/blob/master/SIR_Model-Interactive.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "dSl3L5CBWmv5"
      },
      "source": [
        "# SIR Differential Equations"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kdwg7r4FWmv-"
      },
      "source": [
        "\n",
        "In this notebook we will model the spread of disease using the Kermack-McKendrick Model model which is a compartment model."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "bFdy8x_TWmv_"
      },
      "outputs": [],
      "source": [
        "## Library\n",
        "import numpy as np\n",
        "import math \n",
        "import matplotlib.pyplot as plt\n",
        "# @title Figure Settings\n",
        "import IPython.display as ipd\n",
        "from matplotlib import gridspec\n",
        "\n",
        "import ipywidgets as widgets  # interactive display\n",
        "%config InlineBackend.figure_format = 'retina'\n",
        "\n",
        "# use NMA plot style\n",
        "plt.style.use(\"https://raw.githubusercontent.com/NeuromatchAcademy/content-creation/main/nma.mplstyle\")\n",
        "my_layout = widgets.Layout()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MlEIJ72vWmwA"
      },
      "source": [
        "The model is a system of three non-linear first order differential equations:\n",
        "\\begin{equation}\n",
        "\\begin{array}{cl}\n",
        "\\frac{dS}{dt}=-\\frac{\\beta IS}{N},\\\\\n",
        "\\frac{dI}{dt}=\\frac{\\beta IS}{N}-\\gamma I,\\\\\n",
        "\\frac{dR}{dt}=\\gamma I\n",
        "\\end{array}\n",
        "\\end{equation}\n",
        "where \n",
        "S is the people who are susceptible in the population, \n",
        "I is the number of people infected, \n",
        "R is the number of removed population (either by death or recovery), and \n",
        "N is the sum of these three $$ N=S(t_0)+I(t_0)+R(t_0).$$\n",
        "$\\beta$ is the infection rate, and $\\gamma$ is the recovery rate.\n",
        "$$ R_{0}={\\frac{\\beta }{\\gamma }},$$\n",
        "\n",
        "the so-called basic reproduction number (also called basic reproduction ratio).\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2yALKnymWmwA"
      },
      "source": [
        "## Discrete Domain \n",
        "To numiercally approximate the solution we discretise the continuous domain using a step size, $h=0.001$, \n",
        "which gives\n",
        "\\begin{equation}\n",
        "t_i=0+i h,\n",
        "\\end{equation}\n",
        "for $i=0,...n$.\n",
        "The figure below illustrate the discrete domain."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 297
        },
        "id": "wjzZ8GRVWmwB",
        "outputId": "c561bd90-b48a-4708-a4d5-19b5780f1e85"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 360x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "image/png": {
              "width": 352,
              "height": 280
            },
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "h=0.001\n",
        "t=np.arange(0,10+h/2,h)\n",
        "fig = plt.figure(1,figsize=(5,4))\n",
        "ax = fig.add_subplot(1,1,1)\n",
        "ax.plot(t,0*t,'o:',color='k')\n",
        "ax.set_xlabel('Time (yrs)')\n",
        "plt.title('Discrete Time Domain')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "a0LVWnYcWmwD"
      },
      "source": [
        "We numerically approximate the differential equation using Eulers method to give the difference equation\n",
        "\\begin{equation}\n",
        "S[i+1] = S[i]+ h*\\big(-beta*S[i]*I[i]/N \\big)\n",
        "\\end{equation}\n",
        "\n",
        "\\begin{equation}\n",
        "I[i+1] = I[i]+ h*\\big(\\beta*S[i]*I[i] /N- gamma I[i] \\big)\n",
        "\\end{equation}\n",
        "\n",
        "\\begin{equation}\n",
        "R[i+1] = R[i]+ h*\\big(gamma I[i] \\big)\n",
        "\\end{equation}\n",
        "\n",
        "\n",
        "where $h$ is the stepsize and  $H[i]$ and $L[i]$ is the numerical approximation of the susceptible $S(t_i)$, infected $I(t_i)$  and recovered $R(t_i)$ at time $t_i$, for $i=0,...,n$\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "id": "idDCTRpuWmwD"
      },
      "outputs": [],
      "source": [
        "def SIR(beta,gamma):\n",
        "    \"\"\"\n",
        "    Args:\n",
        "  \n",
        "    \"\"\"\n",
        "    h=0.001\n",
        "    t=np.arange(0,10+h/2,h)\n",
        "\n",
        "    n=len(t) # Number of Steps\n",
        "    S=np.zeros(n) # Numerical Solution Hares\n",
        "    S[0]=99 # Intial Hare population\n",
        "    I=np.zeros(n) # Numerical Solution Lynxes\n",
        "    I[0]=1# Initial Lynx population\n",
        "    R=np.zeros(n) # Numerical Solution Lynxes\n",
        "    R[0]=0# Initial Lynx population\n",
        "\n",
        "    N=100\n",
        "\n",
        "    for i in range (0,n-1):\n",
        "        S[i+1]=S[i]+h*(-beta*S[i]*I[i]/N) \n",
        "        I[i+1]=I[i]+h*(beta*S[i]*I[i]/N-gamma*I[i])# INSERT EQUATION HERE \n",
        "        R[i+1]=R[i]+h*gamma*I[i]\n",
        "    ## Plotting Figure\n",
        "        ## Plotting Figure\n",
        "    fig, [ax1, ax2] =plt.subplots(1,2,figsize=(16,4), gridspec_kw={'width_ratios': [2, 1]})\n",
        "    ax1.plot(t,S,':',color='green',label='Sus')\n",
        "    ax1.plot(t,I,':',color='red',label='Inf')\n",
        "    ax1.plot(t,R,':',color='blue',label='Rec')\n",
        "    ax1.legend()\n",
        "    ax1.set_xlabel('Time (yrs)')\n",
        "    ax1.set_ylabel('Population (tens of thousands)')\n",
        "\n",
        "    ax2.plot(I,S,'-',color='black',label='I vs S')\n",
        "    ax2.plot(I,R,'-',color='red',label='I vs R')\n",
        "    ax2.set_xlabel('Infected Population (tens of thousands)')\n",
        "    ax2.set_ylabel('Population (tens of thousands)')\n",
        "    ax2.legend(loc='best')\n",
        "    plt.tight_layout()\n",
        "\n",
        "    plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RNO2SdzJWmwE"
      },
      "source": [
        "## Results\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 361,
          "referenced_widgets": [
            "720165ced72f433198ea1a4b18f2022f",
            "6687d69ac8134944a7fe05373b283ba9",
            "cd2d59e77fc14cb4b17c6dff2121e042",
            "7ffd5ca272804e58b43b839c2635901c",
            "9b09602bf16e4c42a6b31d6d1fc4447f",
            "2b2a5689f3e8497db7bc633b8cd61e2d",
            "f6ce804b1d514b00bec81adc0dab5e8f",
            "dc89f3f348894d6b909186e9deabf114",
            "8dde668001d34d45b417173a1f5ea469"
          ]
        },
        "id": "CcOmOPI1WmwE",
        "outputId": "ce52d0c7-c86e-4c7b-beb5-816a363f441d"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "application/vnd.jupyter.widget-view+json": {
              "model_id": "720165ced72f433198ea1a4b18f2022f",
              "version_minor": 0,
              "version_major": 2
            },
            "text/plain": [
              "interactive(children=(FloatSlider(value=1.1, description='beta', layout=Layout(width='450px'), max=2.0), Float…"
            ]
          },
          "metadata": {}
        }
      ],
      "source": [
        "my_layout.width = '450px'\n",
        "@widgets.interact(\n",
        "    beta=widgets.FloatSlider(1.1, min=0., max=2., step=.1, layout=my_layout),\n",
        "    gamma=widgets.FloatSlider(0.4, min=0.00, max=2.0, step=.1, layout=my_layout)\n",
        ")\n",
        "def Pop_widget(beta,gamma):\n",
        "  SIR(beta,gamma)\n",
        "  plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "i0ck25p0WmwF"
      },
      "source": [
        "# References\n",
        "\n",
        "[1] Weisstein, Eric W. \"Kermack-McKendrick Model.\" From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Kermack-McKendrickModel.html\n",
        "\n",
        "[2]  Wikipedia contributors. (2021, February 28). Compartmental models in epidemiology. In Wikipedia, The Free Encyclopedia. Retrieved 18:12, March 15, 2021, from https://en.wikipedia.org/w/index.php?title=Compartmental_models_in_epidemiology&oldid=1009414539\n"
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