04_Covid_SEIR_Analysis.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.integrate\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initial Conditions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "S0 = 0.9\n",
    "I0 = 1\n",
    "R0 = 2.20\n",
    "\n",
    "#beta = 0.3 # The parameter controlling how often a susceptible-infected contact results in a new infection.\n",
    "#gamma = 0.1 # The rate an infected recovers and moves into the resistant phase.\n",
    "#sigma = 0.1 # The rate at which an exposed person becomes infective.\n",
    "\n",
    "\n",
    "InterventionTime = 100\n",
    "OMInterventionAmt = 2/3\n",
    "InterventionAmt = 1 - OMInterventionAmt\n",
    "\n",
    "CFR = 0.02 # Case Fatality Rate\n",
    "\n",
    "P_SEVERE = 0.2 #Hospitalization Rate \n",
    "\n",
    "Time_to_death = 32 # Time from end of incubation to death.\n",
    "\n",
    "D_incubation = 5.2 #Length of incubation period\n",
    "D_infectious = 2.9 # Duration patient is infectious\n",
    "D_recovery_mild   = (14 - 2.9)  # Recovery time for mild cases\n",
    "D_recovery_severe = (31.5 - 2.9) # Recovery time for severe Cases - Length of hopital Stay\n",
    "D_hospital_lag = 5 # Time to hospitalization.\n",
    "D_death = Time_to_death - D_infectious \n",
    "\n",
    "daysTotal = 360 # total days to model\n",
    "days0 = 57  #days before lockdown measures\n",
    "\n",
    "population = 7000000\n",
    "\n",
    "E0 = 1  # exposed at initial time step\n",
    "duration = 7*12*1e10\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### SEIR MODEL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "  def model(y, t, N):\n",
    "    # :param array t: Time step (days)\n",
    "    # :param int N: Population\n",
    "    # :param float beta: The parameter controlling how often a susceptible-infected contact results in a new infection.\n",
    "    # :param float gamma: The rate an infected recovers and moves into the resistant phase.\n",
    "    # :param float sigma: The rate at which an exposed person becomes infective.\n",
    "    \n",
    "    # Beta, Gamma and Sigma calculation\n",
    "    if t > InterventionTime and t < InterventionTime + duration:\n",
    "        beta = InterventionAmt * R0/ D_infectious\n",
    "    elif t > InterventionTime + duration:\n",
    "        beta = 0.5*R0/(D_infectious)\n",
    "    else:\n",
    "        beta = R0/D_infectious\n",
    "      \n",
    "    sigma = 1/D_incubation\n",
    "    gamma = 1/D_infectious\n",
    "    \n",
    "    # S = Susceptible\n",
    "    # E = Exposed\n",
    "    # I = Infectious\n",
    "    # Mild - Recovering (Mild)     \n",
    "    # Severe -  Recovering (Severe at home)\n",
    "    # Severe_H - Recovering (Severe in hospital)\n",
    "    # Fatal - Recovering (Fatal)\n",
    "    # R_Mild - Recovered\n",
    "    # R_Severe - Recovered\n",
    "    # R_Fatal - Dead\n",
    "    S, E, I, R, Mild, Severe, Severe_H, Fatal, R_Mild, R_Severe, R_Fatal  = y\n",
    "    \n",
    "    p_severe = P_SEVERE\n",
    "    p_fatal  = CFR\n",
    "    p_mild   = 1 - P_SEVERE - CFR\n",
    "\n",
    "    #beta = beta0 if x < days0 else beta1\n",
    "    \n",
    "    dS = -beta * S * I / N\n",
    "    dE = beta * S * I / N - sigma * E\n",
    "    dI = sigma * E - gamma * I\n",
    "    dR = gamma * I\n",
    "    \n",
    "    dMild     =  p_mild*gamma*I   - (1/D_recovery_mild)*Mild\n",
    "    dSevere   =  p_severe*gamma*I - (1/D_hospital_lag)*Severe\n",
    "    dSevere_H =  (1/D_hospital_lag)*Severe - (1/D_recovery_severe)*Severe_H\n",
    "    dFatal    =  p_fatal*gamma*I  - (1/D_death)*Fatal\n",
    "    dR_Mild   =  (1/D_recovery_mild)*Mild\n",
    "    dR_Severe =  (1/D_recovery_severe)*Severe_H\n",
    "    dR_Fatal  =  (1/D_death)*Fatal\n",
    "    \n",
    "    return ([dS, dE, dI, dR, dMild, dSevere, dSevere_H, dFatal, dR_Mild, dR_Severe, dR_Fatal])\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### SOLVE SEIR MODEL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "def solve(model, population, E0):\n",
    "    X = np.arange(daysTotal)  # time steps array\n",
    "    N0 = population - E0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0  # S, E, I, R at initial step\n",
    "\n",
    "    y_data_var = scipy.integrate.odeint(model, N0, X, args=(population,))\n",
    "\n",
    "    S, E, I, R, Mild, Severe, Severe_H, Fatal, R_Mild, R_Severe, R_Fatal = y_data_var.T  # transpose and unpack\n",
    "    return X, S, E, I, R, Mild, Severe, Severe_H, Fatal, R_Mild, R_Severe, R_Fatal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, S, E, I, R, Mild, Severe, Severe_H, Fatal, R_Mild, R_Severe, R_Fatal = solve(model, population, 1)\n",
    "Hospitalized = np.array([Severe_H, Fatal]).sum(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Peak day is [127] With  74677.1227473301 Hospitalized\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1080x864 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "peak = np.amax(Hospitalized)\n",
    "day = np.where(Hospitalized == peak)\n",
    "print('Peak day is', day[0], 'With ', peak, 'Hospitalized')\n",
    "\n",
    "plt.figure(figsize=[15,12])\n",
    "#plt.plot(X,S, label=\"Susceptible\")\n",
    "plt.plot(X,E, label=\"Exposed\")\n",
    "plt.plot(X,I, label=\"Infected\")\n",
    "#plt.plot(X,R, label=\"Recovered with immunity\")\n",
    "plt.plot(X, Hospitalized , label=\"Hospitalized\")\n",
    "plt.plot(X, R_Fatal , label=\"Fatalities\")\n",
    "\n",
    "\n",
    "plt.grid()\n",
    "plt.legend()\n",
    "plt.xlabel(\"Time\")\n",
    "plt.ylabel(\"Proportions\")\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    " E[100]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Appendix\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### RK 45 - Attempted different model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "def model_beta(t, y):\n",
    "    # :param array t: Time step (days)\n",
    "    # :param int N: Population\n",
    "    # :param float beta: The parameter controlling how often a susceptible-infected contact results in a new infection.\n",
    "    # :param float gamma: The rate an infected recovers and moves into the resistant phase.\n",
    "    # :param float sigma: The rate at which an exposed person becomes infective.\n",
    "    \n",
    "    # Beta, Gamma and Sigma calculation\n",
    "    N = population\n",
    "    if t > InterventionTime and t < InterventionTime + duration:\n",
    "        beta = InterventionAmt * R0/ D_infectious\n",
    "    elif t > InterventionTime + duration:\n",
    "        beta = 0.5*R0/(D_infectious)\n",
    "    else:\n",
    "        beta = R0/D_infectious\n",
    "      \n",
    "    sigma = 1/D_incubation\n",
    "    gamma = 1/D_infectious\n",
    "    \n",
    "    # S = Susceptible\n",
    "    # E = Exposed\n",
    "    # I = Infectious\n",
    "    # Mild - Recovering (Mild)     \n",
    "    # Severe -  Recovering (Severe at home)\n",
    "    # Severe_H - Recovering (Severe in hospital)\n",
    "    # Fatal - Recovering (Fatal)\n",
    "    # R_Mild - Recovered\n",
    "    # R_Severe - Recovered\n",
    "    # R_Fatal - Dead\n",
    "    S, E, I, R, Mild, Severe, Severe_H, Fatal, R_Mild, R_Severe, R_Fatal  = y\n",
    "    \n",
    "    p_severe = P_SEVERE\n",
    "    p_fatal  = CFR\n",
    "    p_mild   = 1 - P_SEVERE - CFR\n",
    "\n",
    "    #beta = beta0 if x < days0 else beta1\n",
    "    \n",
    "    dS = -beta * S * I / N\n",
    "    dE = beta * S * I / N - sigma * E\n",
    "    dI = sigma * E - gamma * I\n",
    "    dR = gamma * I\n",
    "    \n",
    "    dMild     =  p_mild*gamma*I   - (1/D_recovery_mild)*Mild\n",
    "    dSevere   =  p_severe*gamma*I - (1/D_hospital_lag)*Severe\n",
    "    dSevere_H =  (1/D_hospital_lag)*Severe - (1/D_recovery_severe)*Severe_H\n",
    "    dFatal    =  p_fatal*gamma*I  - (1/D_death)*Fatal\n",
    "    dR_Mild   =  (1/D_recovery_mild)*Mild\n",
    "    dR_Severe =  (1/D_recovery_severe)*Severe_H\n",
    "    dR_Fatal  =  (1/D_death)*Fatal\n",
    "    \n",
    "    return ([dS, dE, dI, dR, dMild, dSevere, dSevere_H, dFatal, dR_Mild, dR_Severe, dR_Fatal])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "def solve_beta(model, population, E0):\n",
    "    X = np.arange(daysTotal)  # time steps array\n",
    "    N0 = population - E0, E0, 0, 0, 0, 0, 0, 0, 0, 0, 0  # S, E, I, R at initial step\n",
    "\n",
    "    y_data_var = scipy.integrate.solve_ivp(model, [0,360], N0, method='RK45', t_eval=X, first_step=0.2)\n",
    "    S, E, I, R, Mild, Severe, Severe_H, Fatal, R_Mild, R_Severe, R_Fatal = y_data_var.y  # transpose and unpack\n",
    "    return y_data_var.t, S, E, I, R, Mild, Severe, Severe_H, Fatal, R_Mild, R_Severe, R_Fatal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, S, E, I, R, Mild, Severe, Severe_H, Fatal, R_Mild, R_Severe, R_Fatal = solve_beta(model_beta, population, 1)\n",
    "Hospitalized = np.array([Severe_H, Fatal]).sum(axis=0)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
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