SIR-X.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SIR-X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook exemplifies how Open-SIR can be used to fit the SIR-X model by [Maier and Dirk (2020)](https://science.sciencemag.org/content/early/2020/04/07/science.abb4557.full) to existing data and make predictions. The SIR-X model is a standard generalization of the Susceptible-Infectious-Removed (SIR) model, which includes the influence of exogenous factors such as policy changes, lockdown of the whole population and quarantine of the infectious individuals.\n",
    "\n",
    "The Open-SIR implementation of the SIR-X model will be validated reproducing the parameter fitting published in the [supplementary material](https://science.sciencemag.org/cgi/content/full/science.abb4557/DC1) of the original article published by [Maier and Brockmann (2020)](https://science.sciencemag.org/content/early/2020/04/07/science.abb4557.full). For simplicity, the validation will be performed only for the city of Guangdong, China."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import modules"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import packages\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data sourcing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will source data from the repository of the [John Hopkins University COVID-19 dashboard] (https://coronavirus.jhu.edu/map.html) published formally as a correspondence in [The Lancet](https://www.thelancet.com/journals/laninf/article/PIIS1473-3099(20)30120-1/fulltext#seccestitle10). This time series data contains the number of reported cases $C(t)$ per day for a number of cities.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Province/State</th>\n",
       "      <th>Country/Region</th>\n",
       "      <th>Lat</th>\n",
       "      <th>Long</th>\n",
       "      <th>1/22/20</th>\n",
       "      <th>1/23/20</th>\n",
       "      <th>1/24/20</th>\n",
       "      <th>1/25/20</th>\n",
       "      <th>1/26/20</th>\n",
       "      <th>1/27/20</th>\n",
       "      <th>...</th>\n",
       "      <th>7/5/20</th>\n",
       "      <th>7/6/20</th>\n",
       "      <th>7/7/20</th>\n",
       "      <th>7/8/20</th>\n",
       "      <th>7/9/20</th>\n",
       "      <th>7/10/20</th>\n",
       "      <th>7/11/20</th>\n",
       "      <th>7/12/20</th>\n",
       "      <th>7/13/20</th>\n",
       "      <th>7/14/20</th>\n",
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       "      <th>0</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>33.93911</td>\n",
       "      <td>67.709953</td>\n",
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       "      <td>34740</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Albania</td>\n",
       "      <td>41.15330</td>\n",
       "      <td>20.168300</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>2893</td>\n",
       "      <td>2964</td>\n",
       "      <td>3038</td>\n",
       "      <td>3106</td>\n",
       "      <td>3188</td>\n",
       "      <td>3278</td>\n",
       "      <td>3371</td>\n",
       "      <td>3454</td>\n",
       "      <td>3571</td>\n",
       "      <td>3667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Algeria</td>\n",
       "      <td>28.03390</td>\n",
       "      <td>1.659600</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>15941</td>\n",
       "      <td>16404</td>\n",
       "      <td>16879</td>\n",
       "      <td>17348</td>\n",
       "      <td>17808</td>\n",
       "      <td>18242</td>\n",
       "      <td>18712</td>\n",
       "      <td>19195</td>\n",
       "      <td>19689</td>\n",
       "      <td>20216</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Andorra</td>\n",
       "      <td>42.50630</td>\n",
       "      <td>1.521800</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>855</td>\n",
       "      <td>855</td>\n",
       "      <td>855</td>\n",
       "      <td>855</td>\n",
       "      <td>855</td>\n",
       "      <td>855</td>\n",
       "      <td>855</td>\n",
       "      <td>855</td>\n",
       "      <td>858</td>\n",
       "      <td>861</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Angola</td>\n",
       "      <td>-11.20270</td>\n",
       "      <td>17.873900</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>346</td>\n",
       "      <td>346</td>\n",
       "      <td>386</td>\n",
       "      <td>386</td>\n",
       "      <td>396</td>\n",
       "      <td>458</td>\n",
       "      <td>462</td>\n",
       "      <td>506</td>\n",
       "      <td>525</td>\n",
       "      <td>541</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Antigua and Barbuda</td>\n",
       "      <td>17.06080</td>\n",
       "      <td>-61.796400</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>68</td>\n",
       "      <td>70</td>\n",
       "      <td>70</td>\n",
       "      <td>70</td>\n",
       "      <td>73</td>\n",
       "      <td>74</td>\n",
       "      <td>74</td>\n",
       "      <td>74</td>\n",
       "      <td>74</td>\n",
       "      <td>74</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>-38.41610</td>\n",
       "      <td>-63.616700</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>77815</td>\n",
       "      <td>80447</td>\n",
       "      <td>83426</td>\n",
       "      <td>87030</td>\n",
       "      <td>90693</td>\n",
       "      <td>94060</td>\n",
       "      <td>97509</td>\n",
       "      <td>100166</td>\n",
       "      <td>103265</td>\n",
       "      <td>106910</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Armenia</td>\n",
       "      <td>40.06910</td>\n",
       "      <td>45.038200</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>28606</td>\n",
       "      <td>28936</td>\n",
       "      <td>29285</td>\n",
       "      <td>29820</td>\n",
       "      <td>30346</td>\n",
       "      <td>30903</td>\n",
       "      <td>31392</td>\n",
       "      <td>31969</td>\n",
       "      <td>32151</td>\n",
       "      <td>32490</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Australian Capital Territory</td>\n",
       "      <td>Australia</td>\n",
       "      <td>-35.47350</td>\n",
       "      <td>149.012400</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>108</td>\n",
       "      <td>108</td>\n",
       "      <td>111</td>\n",
       "      <td>112</td>\n",
       "      <td>113</td>\n",
       "      <td>113</td>\n",
       "      <td>113</td>\n",
       "      <td>113</td>\n",
       "      <td>113</td>\n",
       "      <td>113</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>New South Wales</td>\n",
       "      <td>Australia</td>\n",
       "      <td>-33.86880</td>\n",
       "      <td>151.209300</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>...</td>\n",
       "      <td>3429</td>\n",
       "      <td>3433</td>\n",
       "      <td>3440</td>\n",
       "      <td>3453</td>\n",
       "      <td>3467</td>\n",
       "      <td>3474</td>\n",
       "      <td>3478</td>\n",
       "      <td>3492</td>\n",
       "      <td>3505</td>\n",
       "      <td>3517</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10 rows × 179 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                 Province/State       Country/Region       Lat        Long  \\\n",
       "0                           NaN          Afghanistan  33.93911   67.709953   \n",
       "1                           NaN              Albania  41.15330   20.168300   \n",
       "2                           NaN              Algeria  28.03390    1.659600   \n",
       "3                           NaN              Andorra  42.50630    1.521800   \n",
       "4                           NaN               Angola -11.20270   17.873900   \n",
       "5                           NaN  Antigua and Barbuda  17.06080  -61.796400   \n",
       "6                           NaN            Argentina -38.41610  -63.616700   \n",
       "7                           NaN              Armenia  40.06910   45.038200   \n",
       "8  Australian Capital Territory            Australia -35.47350  149.012400   \n",
       "9               New South Wales            Australia -33.86880  151.209300   \n",
       "\n",
       "   1/22/20  1/23/20  1/24/20  1/25/20  1/26/20  1/27/20  ...  7/5/20  7/6/20  \\\n",
       "0        0        0        0        0        0        0  ...   32951   33190   \n",
       "1        0        0        0        0        0        0  ...    2893    2964   \n",
       "2        0        0        0        0        0        0  ...   15941   16404   \n",
       "3        0        0        0        0        0        0  ...     855     855   \n",
       "4        0        0        0        0        0        0  ...     346     346   \n",
       "5        0        0        0        0        0        0  ...      68      70   \n",
       "6        0        0        0        0        0        0  ...   77815   80447   \n",
       "7        0        0        0        0        0        0  ...   28606   28936   \n",
       "8        0        0        0        0        0        0  ...     108     108   \n",
       "9        0        0        0        0        3        4  ...    3429    3433   \n",
       "\n",
       "   7/7/20  7/8/20  7/9/20  7/10/20  7/11/20  7/12/20  7/13/20  7/14/20  \n",
       "0   33384   33594   33908    34194    34366    34451    34455    34740  \n",
       "1    3038    3106    3188     3278     3371     3454     3571     3667  \n",
       "2   16879   17348   17808    18242    18712    19195    19689    20216  \n",
       "3     855     855     855      855      855      855      858      861  \n",
       "4     386     386     396      458      462      506      525      541  \n",
       "5      70      70      73       74       74       74       74       74  \n",
       "6   83426   87030   90693    94060    97509   100166   103265   106910  \n",
       "7   29285   29820   30346    30903    31392    31969    32151    32490  \n",
       "8     111     112     113      113      113      113      113      113  \n",
       "9    3440    3453    3467     3474     3478     3492     3505     3517  \n",
       "\n",
       "[10 rows x 179 columns]"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Source data from John Hokpins university reposotiry\n",
    "# jhu_link = \"https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/who_covid_19_situation_reports/who_covid_19_sit_rep_time_series/who_covid_19_sit_rep_time_series.csv\"\n",
    "jhu_link = \"https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_global.csv\"\n",
    "jhu_df = pd.read_csv(jhu_link)\n",
    "# Explore the dataset\n",
    "jhu_df.head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is observed that the column \"Province/States\" contains the name of the cities, and since the forth column a time series stamp (or index) is provided to record daily data of reported cases. Additionally, there are many days without recorded data for a number of chinese cities. This won't be an issue for parameter fitting as Open-SIR doesn't require uniform spacement of the observed data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data preparation\n",
    "\n",
    "In the following lines, the time series for Guangdong reported cases $C(t)$ is extracted from the original dataframe. Thereafter, the columns are converted to a pandas date time index in order to perform further data preparation steps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "China = jhu_df[jhu_df[jhu_df.columns[1]]==\"China\"]\n",
    "city_name = \"Guangdong\"\n",
    "city = China[China[\"Province/State\"] == city_name]\n",
    "city = city.drop(columns=[\"Province/State\", \"Country/Region\", \"Lat\",\"Long\"])\n",
    "time_index = pd.to_datetime(city.columns)\n",
    "data = city.values\n",
    "# Visualize the time\n",
    "ts = pd.Series(data = city.values[0], index = time_index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the function ts.plot() a quick visualization of the dataset is obtained:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ts.plot()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Data cleaning"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "ts_clean = ts.dropna()\n",
    "# Extract data\n",
    "ts_fit = ts_clean['2020-01-21':\"2020-02-12\"]\n",
    "# Convert index to numeric\n",
    "ts_num = pd.to_numeric(ts_fit.index)\n",
    "t0 = ts_num[0]\n",
    "# Convert datetime to days\n",
    "t_days = (ts_num-t0)/(10**9*86400)\n",
    "t_days = t_days.astype(int).values\n",
    "# t_days is an input for SIR"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the X number\n",
    "nX = ts_fit.values # Number of infected\n",
    "N = 104.3e6 # Population size of Guangdong"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Exploration of the dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ts_fit.plot(style='ro')\n",
    "plt.xlabel(\"Number of infected\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Setting up SIR and SIR-X models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The population $N$ of the city is a necessary input for the model. In this notebook, this was hardocded, but it can be sourced directly from a web source.\n",
    "\n",
    "Note that whilst the SIR model estimates directly the number of infected people, $N I(t)$, SIR-X estimates the number of infected people based on the number of tested cases that are in quarantine or in an hospital $N X(t)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# These lines are required only if opensir wasn't installed using pip install, or if opensir is running in the pipenv virtual environment\n",
    "import sys\n",
    "path_opensir = '../../'\n",
    "sys.path.append(path_opensir)\n",
    "\n",
    "# Import SIR and SIRX models\n",
    "from opensir.models import SIR, SIRX\n",
    "nX = ts_fit.values # Number of observed infections of the time series\n",
    "N = 104.3e6 # Population size of Guangdong\n",
    "params = [0.95, 0.38]\n",
    "w0 = (N-nX[0], nX[0], 0)\n",
    "\n",
    "G_sir = SIR()\n",
    "G_sir.set_params(p=params, initial_conds=w0)\n",
    "G_sir.fit_input=2\n",
    "G_sir.fit(t_days, nX)\n",
    "G_sir.solve(t_days[-1], t_days[-1]+1)\n",
    "t_SIR = G_sir.fetch()[:,0]\n",
    "I_SIR = G_sir.fetch()[:,2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Try to fit a SIR model to Guangdong data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = plt.axes()\n",
    "ax.tick_params(axis=\"both\", which=\"major\", labelsize= 14 )\n",
    "plt.plot(t_SIR, I_SIR)\n",
    "plt.plot(t_days, nX, 'ro')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The SIR model is clearly not appropriate to fit this data, as it cannot resolve the effect of exogeneous containment efforts such as quarantines or lockdown. We will repeat the process with a SIR-X model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "g_sirx = SIRX()\n",
    "params = [6.2/8, 1/8, 0.05, 0.05, 5]\n",
    "# X_0 can be directly ontained from the statistics\n",
    "n_x0 = nX[0]            # Number of people tested positive\n",
    "n_i0 = nX[0]\n",
    "\n",
    "w0 = (N-n_x0-n_i0, n_i0, 0, n_x0)\n",
    "g_sirx.set_params(p=params, initial_conds=w0)\n",
    "# Fit all parameters\n",
    "fit_index=[False, False, True, True, True]\n",
    "g_sirx.fit(t_days, nX, fit_index = fit_index)\n",
    "g_sirx.solve(t_days[-1], t_days[-1]+1)\n",
    "t_sirx = g_sirx.fetch()[:,0]\n",
    "inf_sirx = g_sirx.fetch()[:,4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[6,6])\n",
    "ax = plt.axes()\n",
    "plt.plot(t_sirx, inf_sirx, 'b-', linewidth=2)\n",
    "plt.plot(t_SIR, I_SIR,'g-', linewidth=2)\n",
    "plt.plot(t_days, nX, 'ro')\n",
    "plt.legend([\"SIR-X model fit\", \"SIR model fit\", \"Number of reported cases\"], fontsize=13)\n",
    "plt.title(\"SARS-CoV-2 evolution in Guangdong, China\", size=15)\n",
    "plt.xlabel('Days', fontsize=14)\n",
    "plt.ylabel('COVID-19 confirmed cases', fontsize=14)\n",
    "ax.tick_params(axis='both', which='major', labelsize=14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After fitting the parameters, the effective infectious period $T_{I,eff}$ and the effective reproduction rate $R_{0,eff}$ can be obtained from the model properties\n",
    "\n",
    "$$T_{I,eff} = (\\beta + \\kappa + \\kappa_0)^{-1}$$\n",
    "$$R_{0,eff} = \\alpha T_{I,eff}$$\n",
    "\n",
    "Aditionally, the Public containment leverage $P$ and the quarantine probability $Q$ can be calculated through:\n",
    "\n",
    "$$P = \\frac{\\kappa_0}{\\kappa_0 + \\kappa}$$\n",
    "$$Q = \\frac{\\kappa_0 + \\kappa}{\\beta + \\kappa_0 + \\kappa}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Effective infectious period T_I_eff =  3.88 days \n",
      "Effective reproduction rate R_0_eff =  3.01, Maier and Brockmann = 3.02\n",
      "Public containment leverage =  0.79, Maier and Brockmann = 0.75\n",
      "Quarantine probability =  0.52, Maier and Brockmann = 0.51\n"
     ]
    }
   ],
   "source": [
    "print(\"Effective infectious period T_I_eff =  %.2f days \" % g_sirx.t_inf_eff )\n",
    "print(\"Effective reproduction rate R_0_eff =  %.2f, Maier and Brockmann = %.2f\" % (g_sirx.r0_eff, 3.02))\n",
    "print(\"Public containment leverage =  %.2f, Maier and Brockmann = %.2f\" % (g_sirx.pcl, 0.75))\n",
    "print(\"Quarantine probability =  %.2f, Maier and Brockmann = %.2f\" % (g_sirx.q_prob, 0.51))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Calculation of predictive confidence intervals\n",
    "\n",
    "The confidence intervals on the predictions of the SIR-X model can be calculated using a block cross validation. This technique is widely used in Time Series Analysis. In the open-sir API, the function `model.ci_block_cv` calculates the average mean squared error of the predictions, a list of the rolling mean squared errors and the list of parameters which shows how much each parameter changes taking different number of days for making predictions.\n",
    "\n",
    "The three first parameters are the same as the fit function, while the last two parameters are the `lags` and the `min_sample`. The `lags` parameter indicates how many periods in the future will be forecasted in order to calculate the mean squared error of the model prediction. The `min_sample` parameter indicates the initial number of observations and days that will be taken to perform the block cross validation.\n",
    "\n",
    "In the following example, `model.ci_block_cv` is used to estimate the average mean squared error of *1-day* predictions taking *6* observations as the starting point of the cross validation. For Guangdong, a `min_sample=6` higher than the default 3 is required to handle well the missing data. This way, both the data on the four first days, and two days after the data starts again, are considered for cross validation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Calculate confidence intervals\n",
    "mse_avg, mse_list, p_list, pred_data = g_sirx.block_cv(lags = 1, min_sample = 6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If it is assumed that the residuals distribute normally, then a good estimation of a 95% confidence interval on the one-day prediction of the number of confirmed cases is \n",
    "\n",
    "$$\\sigma \\sim \\mathrm{MSE} \\rightarrow n_{X,{t+1}} \\sim \\hat{n}_{X,{t+1}} \\pm 2 \\sigma$$ \n",
    "\n",
    "Where $n_{X,{t+1}}$ is the real number of confirmed cases in the next day, and $\\hat{n}_{X,{t+1}}$ is the estimation using the SIR-X model using cross validation. We can use the `PredictionResults` instance `pred_data` functionality to explore the mean-squared errors and the predictions confidence intervals:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average MSE for 0-day predictions = 18.21, MSE sample size = 16\n",
      "Average MSE for 1-day predictions = 28.94, MSE sample size = 15\n",
      "Average MSE for 2-day predictions = 40.50, MSE sample size = 14\n",
      "Average MSE for 3-day predictions = 55.46, MSE sample size = 13\n",
      "Average MSE for 4-day predictions = 74.75, MSE sample size = 12\n",
      "Average MSE for 5-day predictions = 96.88, MSE sample size = 11\n",
      "Average MSE for 6-day predictions = 121.33, MSE sample size = 10\n",
      "Average MSE for 7-day predictions = 148.01, MSE sample size = 9\n",
      "Average MSE for 8-day predictions = 176.33, MSE sample size = 8\n",
      "Average MSE for 9-day predictions = 204.69, MSE sample size = 7\n",
      "Average MSE for 10-day predictions = 231.87, MSE sample size = 6\n",
      "Average MSE for 11-day predictions = 255.87, MSE sample size = 5\n",
      "Average MSE for 12-day predictions = 298.53, MSE sample size = 4\n",
      "Average MSE for 13-day predictions = 289.29, MSE sample size = 3\n",
      "Average MSE for 14-day predictions = 92.49, MSE sample size = 2\n",
      "Average MSE for 15-day predictions = 196.88, MSE sample size = 1\n"
     ]
    }
   ],
   "source": [
    "pred_data.print_mse()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The predictive accuracy of the model is quite impressive, even for 9-day predictions. Let's take advantage of the relatively low mean squared error to forecast a 10 days horizon with confidence intervals using `pred_data.plot_predictions(n_days=9)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pred_data.plot_predictions(n_days=9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If it is assumed that the residuals distribute normally, then a good estimation of a 95% confidence interval on the one-day prediction of the number of confirmed cases is \n",
    "\n",
    "$$\\sigma \\sim \\mathrm{MSE} \\rightarrow n_{X,{t+1}} \\sim \\hat{n}_{X,{t+1}} \\pm 2 \\sigma$$ \n",
    "\n",
    "Where $n_{X,{t+1}}$ is the real number of confirmed cases in the next day, and $\\hat{n}_{X,{t+1}}$ is the estimation using the SIR-X model using cross validation. We use solve to make a 1-day prediction and append the 95% confidence interval."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Estimation of n_X_{t+1} = 1268 +- 36 \n"
     ]
    }
   ],
   "source": [
    "# Predict\n",
    "g_sirx.solve(t_days[-1]+1,t_days[-1]+2)\n",
    "n_X_tplusone = g_sirx.fetch()[-1,4]\n",
    "print(\"Estimation of n_X_{t+1} = %.0f +- %.0f \" % (n_X_tplusone, 2*mse_avg[0]) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>alpha</th>\n",
       "      <th>beta</th>\n",
       "      <th>kappa_0</th>\n",
       "      <th>kappa</th>\n",
       "      <th>inf_over_test</th>\n",
       "      <th>Day</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.775</td>\n",
       "      <td>0.125</td>\n",
       "      <td>0.115900</td>\n",
       "      <td>2.472714e-13</td>\n",
       "      <td>2.705770</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.775</td>\n",
       "      <td>0.125</td>\n",
       "      <td>0.109540</td>\n",
       "      <td>8.640802e-10</td>\n",
       "      <td>2.774669</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.775</td>\n",
       "      <td>0.125</td>\n",
       "      <td>0.065223</td>\n",
       "      <td>1.206344e-01</td>\n",
       "      <td>1.764604</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.775</td>\n",
       "      <td>0.125</td>\n",
       "      <td>0.082934</td>\n",
       "      <td>6.629895e-02</td>\n",
       "      <td>2.099931</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.775</td>\n",
       "      <td>0.125</td>\n",
       "      <td>0.104995</td>\n",
       "      <td>1.792900e-14</td>\n",
       "      <td>2.822296</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.775</td>\n",
       "      <td>0.125</td>\n",
       "      <td>0.089924</td>\n",
       "      <td>4.695617e-02</td>\n",
       "      <td>2.263911</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.775</td>\n",
       "      <td>0.125</td>\n",
       "      <td>0.092797</td>\n",
       "      <td>3.732302e-02</td>\n",
       "      <td>2.355464</td>\n",
       "      <td>11</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.775</td>\n",
       "      <td>0.125</td>\n",
       "      <td>0.104239</td>\n",
       "      <td>2.828441e-07</td>\n",
       "      <td>2.824631</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.775</td>\n",
       "      <td>0.125</td>\n",
       "      <td>0.105290</td>\n",
       "      <td>1.722384e-13</td>\n",
       "      <td>2.843347</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.775</td>\n",
       "      <td>0.125</td>\n",
       "      <td>0.106338</td>\n",
       "      <td>1.838751e-10</td>\n",
       "      <td>2.866021</td>\n",
       "      <td>14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.775</td>\n",
       "      <td>0.125</td>\n",
       "      <td>0.107281</td>\n",
       "      <td>1.555796e-10</td>\n",
       "      <td>2.889821</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.775</td>\n",
       "      <td>0.125</td>\n",
       "      <td>0.108249</td>\n",
       "      <td>1.054350e-08</td>\n",
       "      <td>2.917514</td>\n",
       "      <td>16</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.775</td>\n",
       "      <td>0.125</td>\n",
       "      <td>0.108956</td>\n",
       "      <td>2.717790e-11</td>\n",
       "      <td>2.939901</td>\n",
       "      <td>17</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.775</td>\n",
       "      <td>0.125</td>\n",
       "      <td>0.110043</td>\n",
       "      <td>9.489022e-11</td>\n",
       "      <td>2.977371</td>\n",
       "      <td>18</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.775</td>\n",
       "      <td>0.125</td>\n",
       "      <td>0.109950</td>\n",
       "      <td>4.382709e-03</td>\n",
       "      <td>2.957901</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.775</td>\n",
       "      <td>0.125</td>\n",
       "      <td>0.106470</td>\n",
       "      <td>2.058907e-02</td>\n",
       "      <td>2.798665</td>\n",
       "      <td>20</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.775</td>\n",
       "      <td>0.125</td>\n",
       "      <td>0.104943</td>\n",
       "      <td>2.795106e-02</td>\n",
       "      <td>2.740668</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    alpha   beta   kappa_0         kappa  inf_over_test  Day\n",
       "0   0.775  0.125  0.115900  2.472714e-13       2.705770    5\n",
       "1   0.775  0.125  0.109540  8.640802e-10       2.774669    6\n",
       "2   0.775  0.125  0.065223  1.206344e-01       1.764604    7\n",
       "3   0.775  0.125  0.082934  6.629895e-02       2.099931    8\n",
       "4   0.775  0.125  0.104995  1.792900e-14       2.822296    9\n",
       "5   0.775  0.125  0.089924  4.695617e-02       2.263911   10\n",
       "6   0.775  0.125  0.092797  3.732302e-02       2.355464   11\n",
       "7   0.775  0.125  0.104239  2.828441e-07       2.824631   12\n",
       "8   0.775  0.125  0.105290  1.722384e-13       2.843347   13\n",
       "9   0.775  0.125  0.106338  1.838751e-10       2.866021   14\n",
       "10  0.775  0.125  0.107281  1.555796e-10       2.889821   15\n",
       "11  0.775  0.125  0.108249  1.054350e-08       2.917514   16\n",
       "12  0.775  0.125  0.108956  2.717790e-11       2.939901   17\n",
       "13  0.775  0.125  0.110043  9.489022e-11       2.977371   18\n",
       "14  0.775  0.125  0.109950  4.382709e-03       2.957901   19\n",
       "15  0.775  0.125  0.106470  2.058907e-02       2.798665   20\n",
       "16  0.775  0.125  0.104943  2.795106e-02       2.740668   21"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Transform parameter list into a DataFrame\n",
    "par_block_cv = pd.DataFrame(p_list)\n",
    "# Rename dataframe columns based on SIR-X parameter names\n",
    "par_block_cv.columns = g_sirx.PARAMS\n",
    "# Add the day. Note that we take the days from min_sample until the end of the array, as days\n",
    "# 0,1,2 are used for the first sampling in the block cross-validation\n",
    "par_block_cv['Day'] = t_days[5:]\n",
    "# Explore formatted dataframe for parametric analysis\n",
    "par_block_cv.head(len(p_list))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = [5,5])\n",
    "ax = plt.axes()\n",
    "ax.tick_params(axis = \"both\", which = \"major\", labelsize = 14 )\n",
    "plt.plot(mse_list[0],'ro')\n",
    "plt.xlabel('Number of days used to predict the next day', size = 14)\n",
    "plt.ylabel('MSE', size = 14)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is an outlier on day 1, as this is when the missing date starts. A more reliable approach would be to take the last 8 values of the mean squared error to calculate a new average assuming that there will be no more missing data."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Variation of fitted parameters\n",
    "\n",
    "Finally, it is possible to observe how the model parameters change as more days and number of confirmed cases are introduced in the block cross validation. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is clear to observe that after day 15 all parameters except kappa begin to converge. Therefore, care must be taken when performing inference over the parameter kappa."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Long term prediction\n",
    "Now we can use the model to predict when the peak will occur and what will be the maximum number of infected"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Predict\n",
    "plt.figure(figsize=[6,6])\n",
    "ax = plt.axes()\n",
    "ax.tick_params(axis=\"both\", which=\"major\", labelsize= 14 )\n",
    "g_sirx.solve(40,41)\n",
    "# Plot\n",
    "plt.plot(g_sirx.fetch()[:,4], 'b-', linewidth=2) # X(t)\n",
    "plt.plot(g_sirx.fetch()[:,2], 'b--', linewidth=2) # I(t)\n",
    "plt.xlabel('Day', size=14)\n",
    "plt.ylabel('Number of people', size=14)\n",
    "plt.legend([\"X(t): Confirmed\",\"I(t) = Infected\"], fontsize=13)\n",
    "plt.title(city_name)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model was trained with a limited amount of data. It is clear to observe that since the measures took place in Guangdong, at least 6 weeks of quarantine were necessary to control the pandemics. Note that a limitation of this model is that it predicts an equilibrium where the number of infected, denoted by the yellow line in the figure above, is 0 after a short time. In reality, this amount will decrease to a small number.\n",
    "\n",
    "After the peak of infections is reached, it is necessary to keep the quarantine and effective contact tracing for at least 30 days more."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Validate using model.plot()\n",
    "\n",
    "The function `model.plot()` offers a handy way to visualize model fitting and predictions. Custom visualizations can be validated against the `model.plot()` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "g_sirx.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at the values of the number of infected and quarantined individuals, as well as the time of the peak, it is clear that both plots are in good agreement, which validates the customized plot created by the code cell below \"long term prediction\"."
   ]
  }
 ],
 "metadata": {
  "file_extension": ".py",
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.6"
  },
  "mimetype": "text/x-python",
  "name": "python",
  "npconvert_exporter": "python",
  "pygments_lexer": "ipython3",
  "version": 3
 },
 "nbformat": 4,
 "nbformat_minor": 2
}