estimating_infected.ipynb

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      "source": [
        "# Estimating The Infected Population From Deaths\n",
        "> Estimating the number of infected people by country based on the number of deaths and case fatality rate  Based on work done by Joao B. Duarte\n"
      ]
    },
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        "> Warning: This analysis contains the results of a predictive model. There are a number of assumptions made which include some speculation.  Furthermore, this analysis was not prepared or reviewed by an Epidimiologist. Therefore, the assumptions and methods presented should be scrutinized carefully before arriving at any conclusions. "
      ]
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      "source": [
        "#hide\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import altair as alt\n",
        "from datetime import timedelta, datetime, date\n",
        "%config InlineBackend.figure_format = 'retina'\n",
        "\n",
        "chart_width = 550\n",
        "chart_height= 400"
      ],
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      "source": [
        "#hide\n",
        "def plot(data, type1, levels):\n",
        "    data_countries_pc2 = data.copy()\n",
        "    for i in range(0,len(countries)):\n",
        "        data_countries_pc2[i] = data_countries_pc2[i].reset_index()\n",
        "        data_countries_pc2[i]['n_days'] = data_countries_pc2[i].index\n",
        "        if type1 == \"scatter\":\n",
        "            data_countries_pc2[i]['cases'] = data_countries_pc2[i][\"total_cases\"]\n",
        "        data_countries_pc2[i]['infected'] = data_countries_pc2[i][\"total_infected\"]\n",
        "    data_plot = data_countries_pc2[0]\n",
        "    for i in range(1, len(countries)):    \n",
        "        data_plot = pd.concat([data_plot, data_countries_pc2[i]], axis=0)\n",
        "    \n",
        "    if type1 == \"scatter\":\n",
        "        data_plot[\"45_line\"] = data_plot[\"cases\"]\n",
        "\n",
        "    # Plot it using Altair\n",
        "    source = data_plot\n",
        "    \n",
        "    if levels == True:\n",
        "        ylabel = \"Total\"\n",
        "    else :\n",
        "        ylabel = \"Per Million\"\n",
        "\n",
        "    scales = alt.selection_interval(bind='scales')\n",
        "    selection = alt.selection_multi(fields=['location'], bind='legend')\n",
        "\n",
        "    if type1 == \"line\": \n",
        "        base = alt.Chart(source, title =  \"Estimated Infected Population By Country\").encode(\n",
        "            x = alt.X('n_days:Q', title = \"Days since outbreak\"),\n",
        "            y = alt.Y(\"infected:Q\",title = ylabel),\n",
        "            color = alt.Color('location:N', legend=alt.Legend(title=\"Country\", labelFontSize=15, titleFontSize=17),\n",
        "                             scale=alt.Scale(scheme='tableau20'))\n",
        "        )\n",
        "        \n",
        "        shades = base.mark_area().encode(\n",
        "            x='n_days:Q',\n",
        "            y='total_infected_lower:Q',\n",
        "            y2='total_infected_upper:Q',\n",
        "            opacity = alt.condition(selection, alt.value(0.2), alt.value(0.05))\n",
        "        )\n",
        "    \n",
        "        lines = base.mark_line().encode(\n",
        "            opacity = alt.condition(selection, alt.value(1), alt.value(0.1))\n",
        "        ).add_selection(\n",
        "            scales\n",
        "        ).add_selection(\n",
        "            selection\n",
        "        ).properties(\n",
        "            width=chart_width,\n",
        "            height=chart_height\n",
        "        )\n",
        "        return(\n",
        "        ( lines + shades)\n",
        "        .configure_title(fontSize=20)\n",
        "        .configure_axis(labelFontSize=15,titleFontSize=18)\n",
        "        )\n",
        "    \n",
        "    if levels == True:\n",
        "        ylabel = \"Infected\"\n",
        "        xlabel = \"Cases\"\n",
        "    else :\n",
        "        ylabel = \"Per Million Infected\"\n",
        "        xlabel = \"Per Million Cases\"\n",
        "        \n",
        "    if type1 == \"scatter\":\n",
        "        base = alt.Chart(source, title = \"COVID-19 Cases VS Infected\").encode(\n",
        "            x = alt.X('cases:Q', title = xlabel),\n",
        "            y = alt.Y(\"infected:Q\",title = ylabel),\n",
        "            color = alt.Color('location:N', legend=alt.Legend(title=\"Country\", labelFontSize=15, titleFontSize=17),\n",
        "                             scale=alt.Scale(scheme='tableau20')),\n",
        "            opacity = alt.condition(selection, alt.value(1), alt.value(0.1))\n",
        "        )\n",
        "\n",
        "        \n",
        "        scatter = base.mark_point().add_selection(\n",
        "            scales\n",
        "        ).add_selection(\n",
        "            selection\n",
        "        ).properties(\n",
        "            width=chart_width,\n",
        "            height=chart_height\n",
        "        )\n",
        "\n",
        "        line_45 = alt.Chart(source).encode(\n",
        "            x = \"cases:Q\",\n",
        "            y = alt.Y(\"45_line:Q\",  scale=alt.Scale(domain=(0, max(data_plot[\"infected\"])))),\n",
        "        ).mark_line(color=\"grey\", strokeDash=[3,3])\n",
        "        \n",
        "        return(\n",
        "        (scatter + line_45)\n",
        "        .configure_title(fontSize=20)\n",
        "        .configure_axis(labelFontSize=15,titleFontSize=18)\n",
        "        )"
      ],
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      "source": [
        "#hide \n",
        "# Get data on deaths D_t\n",
        "data = pd.read_csv(\"https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_deaths_global.csv\", \n",
        "                   error_bad_lines=False)\n",
        "data = data.drop(columns=[\"Lat\", \"Long\"])\n",
        "data = data.melt(id_vars= [\"Province/State\", \"Country/Region\"])\n",
        "data = pd.DataFrame(data.groupby(['Country/Region', \"variable\"]).sum())\n",
        "data.reset_index(inplace=True)  \n",
        "data = data.rename(columns={\"Country/Region\": \"location\", \"variable\": \"date\", \"value\": \"total_deaths\"})\n",
        "data['date'] =pd.to_datetime(data.date)\n",
        "data = data.sort_values(by = \"date\")\n",
        "data.loc[data.location == \"US\",\"location\"] = \"United States\"\n",
        "data.loc[data.location == \"Korea, South\",\"location\"] = \"South Korea\"\n",
        "\n",
        "#hide\n",
        "# Get data and clean it\n",
        "data_cases = pd.read_csv(\"https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_confirmed_global.csv\", error_bad_lines=False)\n",
        "\n",
        "data_cases = data_cases.drop(columns=[\"Lat\", \"Long\"])\n",
        "data_cases = data_cases.melt(id_vars= [\"Province/State\", \"Country/Region\"])\n",
        "data_cases = pd.DataFrame(data_cases.groupby(['Country/Region', \"variable\"]).sum())\n",
        "data_cases.reset_index(inplace=True)  \n",
        "data_cases = data_cases.rename(columns={\"Country/Region\": \"location\", \"variable\": \"date\", \"value\": \"total_cases\"})\n",
        "data_cases['date'] =pd.to_datetime(data_cases.date)\n",
        "data_cases = data_cases.sort_values(by = \"date\")\n",
        "data_cases.loc[data_cases.location == \"US\",\"location\"] = \"United States\"\n",
        "data_cases.loc[data_cases.location == \"Korea, South\",\"location\"] = \"South Korea\"\n",
        "# Add countries\n",
        "countries = [\"China\", \"Italy\", \"Spain\", \"France\", \"United Kingdom\", \"Germany\", \n",
        "             \"Portugal\", \"United States\", \"Singapore\",\"South Korea\", \"Japan\", \n",
        "             \"Brazil\",\"Iran\", \"India\", \"Switzerland\", \"Canada\", \"Australia\", \n",
        "             \"Russia\", \"Belarus\", \"Ukraine\", \"India\"]\n",
        "\n",
        "data_final = pd.merge(data,\n",
        "                 data_cases\n",
        "                 )\n",
        "data_final[\"CFR\"] = data_final[\"total_deaths\"]/data_final[\"total_cases\"]\n",
        "\n",
        "\n",
        "data_final[\"total_infected\"] = np.NaN\n",
        "data_final = data_final.sort_values(by = ['location', 'date'])\n",
        "data_final = data_final.reset_index(drop = True)\n",
        "\n",
        "\n",
        "for j in countries:\n",
        "    for i in data_final[\"date\"].unique()[0:-8]:\n",
        "        data_final.loc[(data_final.date == i) & (data_final.location == j), \"total_infected\"] = data_final.loc[(data_final.date == i + np.timedelta64(8, 'D')) & (data_final.location == j), \"total_deaths\"].iloc[0]/data_final.loc[(data_final.date == i + np.timedelta64(8, 'D')) & (data_final.location == j), \"CFR\"].iloc[0]\n",
        "        \n",
        "\n",
        "# Estimate growth rate of infected, g        \n",
        "data_final['infected_g'] = np.log(data_final['total_infected'])\n",
        "data_final['infected_g'] = data_final['infected_g'].diff() \n",
        "\n",
        "# Estimate number of infected given g\n",
        "today = data_final.date.iloc[-1]\n",
        "for j in countries:\n",
        "    for i in range(7,-1,-1):\n",
        "        data_final.loc[(data_final.location == j) & (data_final.date == today - timedelta(i)), \"total_infected\"] = data_final.loc[data_final.location == j, \"total_infected\"].iloc[-i-2]*(1+data_final.loc[data_final.location == j, \"infected_g\"][-12:-8].aggregate(func = \"mean\"))\n",
        "    \n",
        "\n",
        "\n",
        "# Upper Bound\n",
        "data_final[\"total_infected_upper\"] = np.NaN\n",
        "data_final = data_final.sort_values(by = ['location', 'date'])\n",
        "data_final = data_final.reset_index(drop = True)\n",
        "for j in countries:\n",
        "    for i in data_final[\"date\"].unique()[0:-8]:\n",
        "        data_final.loc[(data_final.date == i) & (data_final.location == j), \"total_infected_upper\"] = data_final.loc[(data_final.date == i + np.timedelta64(8, 'D')) & (data_final.location == j), \"total_deaths\"].iloc[0]/(data_final.loc[(data_final.date == i + np.timedelta64(8, 'D')) & (data_final.location == j), \"CFR\"].iloc[0]*0.7)\n",
        "# Estimate growth rate of infected, g        \n",
        "data_final['infected_g'] = np.log(data_final['total_infected_upper'])\n",
        "data_final['infected_g'] = data_final['infected_g'].diff() \n",
        "# Estimate number of infected given g \n",
        "today = data_final.date.iloc[-1]\n",
        "for j in countries:\n",
        "    for i in range(7,-1,-1):\n",
        "        data_final.loc[(data_final.location == j) & (data_final.date == today - timedelta(i)), \"total_infected_upper\"] = data_final.loc[data_final.location == j, \"total_infected_upper\"].iloc[-i-2]*(1+data_final.loc[data_final.location == j, \"infected_g\"][-12:-8].aggregate(func = \"mean\"))\n",
        "\n",
        "# Lower Bound\n",
        "data_final[\"total_infected_lower\"] = np.NaN\n",
        "data_final = data_final.sort_values(by = ['location', 'date'])\n",
        "data_final = data_final.reset_index(drop = True)\n",
        "for j in countries:\n",
        "    for i in data_final[\"date\"].unique()[0:-8]:\n",
        "        data_final.loc[(data_final.date == i) & (data_final.location == j), \"total_infected_lower\"] = data_final.loc[(data_final.date == i + np.timedelta64(8, 'D')) & (data_final.location == j), \"total_deaths\"].iloc[0]/(data_final.loc[(data_final.date == i + np.timedelta64(8, 'D')) & (data_final.location == j), \"CFR\"].iloc[0]*1.3)\n",
        "# Estimate growth rate of infected, g        \n",
        "data_final['infected_g'] = np.log(data_final['total_infected_lower'])\n",
        "data_final['infected_g'] = data_final['infected_g'].diff() \n",
        "# Estimate number of infected given g \n",
        "today = data_final.date.iloc[-1]\n",
        "for j in countries:\n",
        "    for i in range(7,-1,-1):\n",
        "        data_final.loc[(data_final.location == j) & (data_final.date == today - timedelta(i)), \"total_infected_lower\"] = data_final.loc[data_final.location == j, \"total_infected_lower\"].iloc[-i-2]*(1+data_final.loc[data_final.location == j, \"infected_g\"][-12:-8].aggregate(func = \"mean\"))\n",
        "data_final.loc[data_final.total_infected_lower < data_final.total_cases, \"total_infected_lower\"] = data_final.loc[data_final.total_infected_lower < data_final.total_cases, \"total_cases\"]\n",
        "\n",
        "\n",
        "data_pc = data_final[['location', 'date', 'total_infected', 'total_infected_lower', 'total_infected_upper']].copy()\n",
        "\n",
        "#countries = [\"China\", \"Italy\", \"Spain\", \"France\", \"United Kingdom\", \"Germany\", \n",
        "#             \"Portugal\", \"United States\", \"South Korea\", \"Japan\", \n",
        "#             \"Brazil\",\"Iran\",\"India\"]\n",
        "\n",
        "\n",
        "countries = [\"China\", \"Italy\", \"France\", \"Iran\", \"Germany\", \"Singapore\",\"South Korea\", \"Japan\", \n",
        "             \"Iran\",\"India\",\"United States\"]\n",
        "data_countries = []\n",
        "data_countries_pc = []\n",
        "\n",
        "for i in countries:\n",
        "    data_pc.loc[data_pc.location == i,\"total_infected\"] = data_pc.loc[data_pc.location == i,\"total_infected\"]\n",
        "\n",
        "# Get each country time series\n",
        "filter1 = data_pc[\"total_infected\"] > 1\n",
        "for i in countries:\n",
        "    filter_country = data_pc[\"location\"]== i\n",
        "    data_countries_pc.append(data_pc[filter_country & filter1])      "
      ],
      "execution_count": 18,
      "outputs": [
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      "source": [
        "## Estimated Infected Population By Country\n",
        "\n",
        "with respect to days since outbreak\n",
        "\n",
        "> Tip: Click (Shift+ for multiple) on countries in the legend to filter the visualization. "
      ]
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      "source": [
        "#hide_input\n",
        "# Plot estimated absolute number of infected\n",
        "plot1 = plot(data_countries_pc, \"line\", True)\n",
        "#plot1.save(\"../images/covid-estimate-infections.png\")\n",
        "plot1"
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\"2020-04-22T00:00:00\", \"total_infected\": 1069424.0, \"total_infected_lower\": 840351.0, \"total_infected_upper\": 1527748.5714285716, \"n_days\": 61, \"infected\": 1069424.0}, {\"index\": 19562, \"location\": \"United States\", \"date\": \"2020-04-23T00:00:00\", \"total_infected\": 1103461.0, \"total_infected_lower\": 869170.0, \"total_infected_upper\": 1576372.8571428573, \"n_days\": 62, \"infected\": 1103461.0}, {\"index\": 19563, \"location\": \"United States\", \"date\": \"2020-04-24T00:00:00\", \"total_infected\": 1132539.0, \"total_infected_lower\": 905358.0, \"total_infected_upper\": 1617912.857142857, \"n_days\": 63, \"infected\": 1132539.0}, {\"index\": 19564, \"location\": \"United States\", \"date\": \"2020-04-25T00:00:00\", \"total_infected\": 1158040.0, \"total_infected_lower\": 938154.0, \"total_infected_upper\": 1654342.8571428573, \"n_days\": 64, \"infected\": 1158040.0}, {\"index\": 19565, \"location\": \"United States\", \"date\": \"2020-04-26T00:00:00\", \"total_infected\": 1180375.0, \"total_infected_lower\": 965785.0, \"total_infected_upper\": 1686250.0, \"n_days\": 65, \"infected\": 1180375.0}, {\"index\": 19566, \"location\": \"United States\", \"date\": \"2020-04-27T00:00:00\", \"total_infected\": 1204351.0, \"total_infected_lower\": 988197.0, \"total_infected_upper\": 1720501.4285714289, \"n_days\": 66, \"infected\": 1204351.0}, {\"index\": 19567, \"location\": \"United States\", \"date\": \"2020-04-28T00:00:00\", \"total_infected\": 1229331.0, \"total_infected_lower\": 1012582.0, \"total_infected_upper\": 1756187.142857143, \"n_days\": 67, \"infected\": 1229331.0}, {\"index\": 19568, \"location\": \"United States\", \"date\": \"2020-04-29T00:00:00\", \"total_infected\": 1257023.0, \"total_infected_lower\": 1039909.0, \"total_infected_upper\": 1795747.1428571427, \"n_days\": 68, \"infected\": 1257023.0}, {\"index\": 19569, \"location\": \"United States\", \"date\": \"2020-04-30T00:00:00\", \"total_infected\": 1283929.0, \"total_infected_lower\": 1069424.0, \"total_infected_upper\": 1834184.2857142857, \"n_days\": 69, \"infected\": 1283929.0}, {\"index\": 19570, \"location\": \"United States\", \"date\": \"2020-05-01T00:00:00\", \"total_infected\": 1309550.0, \"total_infected_lower\": 1103461.0, \"total_infected_upper\": 1870785.714285714, \"n_days\": 70, \"infected\": 1309550.0}, {\"index\": 19571, \"location\": \"United States\", \"date\": \"2020-05-02T00:00:00\", \"total_infected\": 1329260.0, \"total_infected_lower\": 1132539.0, \"total_infected_upper\": 1898942.8571428573, \"n_days\": 71, \"infected\": 1329260.0}, {\"index\": 19572, \"location\": \"United States\", \"date\": \"2020-05-03T00:00:00\", \"total_infected\": 1355231.1740763457, \"total_infected_lower\": 1158040.0, \"total_infected_upper\": 1936044.53439478, \"n_days\": 72, \"infected\": 1355231.1740763457}, {\"index\": 19573, \"location\": \"United States\", \"date\": \"2020-05-04T00:00:00\", \"total_infected\": 1381709.7747531338, \"total_infected_lower\": 1180375.0, \"total_infected_upper\": 1973871.1067901915, \"n_days\": 73, \"infected\": 1381709.7747531338}, {\"index\": 19574, \"location\": \"United States\", \"date\": \"2020-05-05T00:00:00\", \"total_infected\": 1408705.716166478, \"total_infected_lower\": 1204351.0, \"total_infected_upper\": 2012436.7373806837, \"n_days\": 74, \"infected\": 1408705.716166478}, {\"index\": 19575, \"location\": \"United States\", \"date\": \"2020-05-06T00:00:00\", \"total_infected\": 1436229.106155572, \"total_infected_lower\": 1229331.0, \"total_infected_upper\": 2051755.8659365322, \"n_days\": 75, \"infected\": 1436229.106155572}, {\"index\": 19576, \"location\": \"United States\", \"date\": \"2020-05-07T00:00:00\", \"total_infected\": 1464290.2500472718, \"total_infected_lower\": 1257023.0, \"total_infected_upper\": 2091843.2143532461, \"n_days\": 76, \"infected\": 1464290.2500472718}, {\"index\": 19577, \"location\": \"United States\", \"date\": \"2020-05-08T00:00:00\", \"total_infected\": 1492899.654514625, \"total_infected_lower\": 1283929.0, \"total_infected_upper\": 2132713.7921637506, \"n_days\": 77, \"infected\": 1492899.654514625}, {\"index\": 19578, \"location\": \"United States\", \"date\": \"2020-05-09T00:00:00\", \"total_infected\": 1522068.0315107852, \"total_infected_lower\": 1309550.0, \"total_infected_upper\": 2174382.902158265, \"n_days\": 78, \"infected\": 1522068.0315107852}, {\"index\": 19579, \"location\": \"United States\", \"date\": \"2020-05-10T00:00:00\", \"total_infected\": 1551806.3022797902, \"total_infected_lower\": 1329260.0, \"total_infected_upper\": 2216866.1461139866, \"n_days\": 79, \"infected\": 1551806.3022797902}]}}, {\"mode\": \"vega-lite\"});\n",
              "</script>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 19
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    {
      "cell_type": "markdown",
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      "source": [
        "Latest Country Estimates"
      ]
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    {
      "cell_type": "code",
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        "execution": {
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        },
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        "id": "QP-HqCOxij7K",
        "colab_type": "code",
        "outputId": "cdf1ac62-efa0-4bf8-a069-342f01096483",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 394
        }
      },
      "source": [
        "#hide_input    \n",
        "label = 'Estimated Infected'\n",
        "temp = pd.concat([x.copy() for x in data_countries_pc]).loc[lambda x: x.date >= '3/1/2020']\n",
        "\n",
        "metric_name = f'{label}'\n",
        "temp.columns = ['Country', 'Date', metric_name, \"Lower Bound Estimates\", \"Upper Bound Estimates\"]\n",
        "temp.loc[:, \"Estimated Infected\"] = temp.loc[:, \"Estimated Infected\"].round(0).map('{:,.0f}'.format) \n",
        "temp.loc[:, \"Lower Bound Estimates\"] = temp.loc[:, \"Lower Bound Estimates\"].round(0).map('{:,.0f}'.format) \n",
        "temp.loc[:, \"Upper Bound Estimates\"] = temp.loc[:, \"Upper Bound Estimates\"].round(0).map('{:,.0f}'.format) \n",
        "temp.groupby('Country').last()"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        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>Date</th>\n",
              "      <th>Estimated Infected</th>\n",
              "      <th>Lower Bound Estimates</th>\n",
              "      <th>Upper Bound Estimates</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Country</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>China</th>\n",
              "      <td>2020-05-10</td>\n",
              "      <td>84,090</td>\n",
              "      <td>84,010</td>\n",
              "      <td>120,129</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>France</th>\n",
              "      <td>2020-05-10</td>\n",
              "      <td>182,964</td>\n",
              "      <td>177,094</td>\n",
              "      <td>261,378</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Germany</th>\n",
              "      <td>2020-05-10</td>\n",
              "      <td>179,540</td>\n",
              "      <td>171,879</td>\n",
              "      <td>256,486</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>India</th>\n",
              "      <td>2020-05-10</td>\n",
              "      <td>106,449</td>\n",
              "      <td>81,884</td>\n",
              "      <td>152,070</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Iran</th>\n",
              "      <td>2020-05-10</td>\n",
              "      <td>120,479</td>\n",
              "      <td>107,603</td>\n",
              "      <td>172,112</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Italy</th>\n",
              "      <td>2020-05-10</td>\n",
              "      <td>228,570</td>\n",
              "      <td>219,070</td>\n",
              "      <td>326,529</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Japan</th>\n",
              "      <td>2020-05-10</td>\n",
              "      <td>16,875</td>\n",
              "      <td>15,777</td>\n",
              "      <td>24,107</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Singapore</th>\n",
              "      <td>2020-05-10</td>\n",
              "      <td>30,992</td>\n",
              "      <td>23,840</td>\n",
              "      <td>44,274</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>South Korea</th>\n",
              "      <td>2020-05-10</td>\n",
              "      <td>11,109</td>\n",
              "      <td>10,909</td>\n",
              "      <td>15,871</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>United States</th>\n",
              "      <td>2020-05-10</td>\n",
              "      <td>1,551,806</td>\n",
              "      <td>1,329,260</td>\n",
              "      <td>2,216,866</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                    Date  ... Upper Bound Estimates\n",
              "Country                   ...                      \n",
              "China         2020-05-10  ...               120,129\n",
              "France        2020-05-10  ...               261,378\n",
              "Germany       2020-05-10  ...               256,486\n",
              "India         2020-05-10  ...               152,070\n",
              "Iran          2020-05-10  ...               172,112\n",
              "Italy         2020-05-10  ...               326,529\n",
              "Japan         2020-05-10  ...                24,107\n",
              "Singapore     2020-05-10  ...                44,274\n",
              "South Korea   2020-05-10  ...                15,871\n",
              "United States 2020-05-10  ...             2,216,866\n",
              "\n",
              "[10 rows x 4 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "papermill": {
          "duration": 0.015181,
          "end_time": "2020-04-17T06:14:00.081109",
          "exception": false,
          "start_time": "2020-04-17T06:14:00.065928",
          "status": "completed"
        },
        "tags": [],
        "id": "GQyekcJBij7S",
        "colab_type": "text"
      },
      "source": [
        "## Infected vs. number of confirmed cases\n",
        "> Allows you to compare how countries have been tracking the true number of infected people. The smaller deviation from the dashed line (45 degree line) the better job at tracking the true number of infected people."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "papermill": {
          "duration": 0.014833,
          "end_time": "2020-04-17T06:14:00.111757",
          "exception": false,
          "start_time": "2020-04-17T06:14:00.096924",
          "status": "completed"
        },
        "tags": [],
        "id": "teKItoeaij7U",
        "colab_type": "text"
      },
      "source": [
        "> Tip: Click (Shift+ for multiple) on countries in the legend to filter the visualization. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "execution": {
          "iopub.execute_input": "2020-04-17T06:14:00.150933Z",
          "iopub.status.busy": "2020-04-17T06:14:00.150162Z",
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        },
        "papermill": {
          "duration": 0.26932,
          "end_time": "2020-04-17T06:14:00.396061",
          "exception": false,
          "start_time": "2020-04-17T06:14:00.126741",
          "status": "completed"
        },
        "tags": [],
        "id": "Szb9vm5cij7W",
        "colab_type": "code",
        "outputId": "22828a0c-3941-403a-8809-4ff4a905be04",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 507
        }
      },
      "source": [
        "#hide_input\n",
        "# Plot it using Altair\n",
        "data_pc = data_final[['location', 'date', 'total_cases', 'total_infected']].copy()\n",
        "\n",
        "countries = [\"China\", \"Italy\", \"Spain\", \"France\", \"United Kingdom\", \"Germany\", \n",
        "             \"Portugal\", \"Singapore\",\"South Korea\", \"Japan\", \n",
        "             \"Brazil\",\"Iran\",\"India\"]\n",
        "data_countries = []\n",
        "data_countries_pc = []\n",
        "\n",
        "for i in countries:\n",
        "    data_pc.loc[data_pc.location == i,\"total_infected\"] = data_pc.loc[data_pc.location == i,\"total_infected\"]\n",
        "    data_pc.loc[data_pc.location == i,\"total_cases\"] = data_pc.loc[data_pc.location == i,\"total_cases\"]\n",
        "    # get each country time series\n",
        "filter1 = data_pc[\"total_infected\"] > 1\n",
        "for i in countries:\n",
        "    filter_country = data_pc[\"location\"]== i\n",
        "    data_countries_pc.append(data_pc[filter_country & filter1])\n",
        "\n",
        "\n",
        "plot(data_countries_pc, \"scatter\", True)"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "alt.LayerChart(...)"
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              "\n",
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18539}, {\"index\": 8780, \"location\": \"India\", \"date\": \"2020-04-21T00:00:00\", \"total_cases\": 20080, \"total_infected\": 33062.0, \"n_days\": 49, \"cases\": 20080, \"infected\": 33062.0, \"45_line\": 20080}, {\"index\": 8781, \"location\": \"India\", \"date\": \"2020-04-22T00:00:00\", \"total_cases\": 21370, \"total_infected\": 34863.0, \"n_days\": 50, \"cases\": 21370, \"infected\": 34863.0, \"45_line\": 21370}, {\"index\": 8782, \"location\": \"India\", \"date\": \"2020-04-23T00:00:00\", \"total_cases\": 23077, \"total_infected\": 37257.0, \"n_days\": 51, \"cases\": 23077, \"infected\": 37257.0, \"45_line\": 23077}, {\"index\": 8783, \"location\": \"India\", \"date\": \"2020-04-24T00:00:00\", \"total_cases\": 24530, \"total_infected\": 39699.0, \"n_days\": 52, \"cases\": 24530, \"infected\": 39699.0, \"45_line\": 24530}, {\"index\": 8784, \"location\": \"India\", \"date\": \"2020-04-25T00:00:00\", \"total_cases\": 26283, \"total_infected\": 42505.0, \"n_days\": 53, \"cases\": 26283, \"infected\": 42505.0, \"45_line\": 26283}, {\"index\": 8785, \"location\": \"India\", \"date\": \"2020-04-26T00:00:00\", \"total_cases\": 27890, \"total_infected\": 46437.0, \"n_days\": 54, \"cases\": 27890, \"infected\": 46437.0, \"45_line\": 27890}, {\"index\": 8786, \"location\": \"India\", \"date\": \"2020-04-27T00:00:00\", \"total_cases\": 29451, \"total_infected\": 49400.00000000001, \"n_days\": 55, \"cases\": 29451, \"infected\": 49400.00000000001, \"45_line\": 29451}, {\"index\": 8787, \"location\": \"India\", \"date\": \"2020-04-28T00:00:00\", \"total_cases\": 31324, \"total_infected\": 52986.99999999999, \"n_days\": 56, \"cases\": 31324, \"infected\": 52986.99999999999, \"45_line\": 31324}, {\"index\": 8788, \"location\": \"India\", \"date\": \"2020-04-29T00:00:00\", \"total_cases\": 33062, \"total_infected\": 56351.0, \"n_days\": 57, \"cases\": 33062, \"infected\": 56351.0, \"45_line\": 33062}, {\"index\": 8789, \"location\": \"India\", \"date\": \"2020-04-30T00:00:00\", \"total_cases\": 34863, \"total_infected\": 59694.99999999999, \"n_days\": 58, \"cases\": 34863, \"infected\": 59694.99999999999, \"45_line\": 34863}, {\"index\": 8790, \"location\": \"India\", \"date\": \"2020-05-01T00:00:00\", \"total_cases\": 37257, \"total_infected\": 62808.0, \"n_days\": 59, \"cases\": 37257, \"infected\": 62808.0, \"45_line\": 37257}, {\"index\": 8791, \"location\": \"India\", \"date\": \"2020-05-02T00:00:00\", \"total_cases\": 39699, \"total_infected\": 67161.0, \"n_days\": 60, \"cases\": 39699, \"infected\": 67161.0, \"45_line\": 39699}, {\"index\": 8792, \"location\": \"India\", \"date\": \"2020-05-03T00:00:00\", \"total_cases\": 42505, \"total_infected\": 71141.063640968, \"n_days\": 61, \"cases\": 42505, \"infected\": 71141.063640968, \"45_line\": 42505}, {\"index\": 8793, \"location\": \"India\", \"date\": \"2020-05-04T00:00:00\", \"total_cases\": 46437, \"total_infected\": 75356.99194425721, \"n_days\": 62, \"cases\": 46437, \"infected\": 75356.99194425721, \"45_line\": 46437}, {\"index\": 8794, \"location\": \"India\", \"date\": \"2020-05-05T00:00:00\", \"total_cases\": 49400, \"total_infected\": 79822.76261071627, \"n_days\": 63, \"cases\": 49400, \"infected\": 79822.76261071627, \"45_line\": 49400}, {\"index\": 8795, \"location\": \"India\", \"date\": \"2020-05-06T00:00:00\", \"total_cases\": 52987, \"total_infected\": 84553.18168113707, \"n_days\": 64, \"cases\": 52987, \"infected\": 84553.18168113707, \"45_line\": 52987}, {\"index\": 8796, \"location\": \"India\", \"date\": \"2020-05-07T00:00:00\", \"total_cases\": 56351, \"total_infected\": 89563.93262494754, \"n_days\": 65, \"cases\": 56351, \"infected\": 89563.93262494754, \"45_line\": 56351}, {\"index\": 8797, \"location\": \"India\", \"date\": \"2020-05-08T00:00:00\", \"total_cases\": 59695, \"total_infected\": 94871.62833797536, \"n_days\": 66, \"cases\": 59695, \"infected\": 94871.62833797536, \"45_line\": 59695}, {\"index\": 8798, \"location\": \"India\", \"date\": \"2020-05-09T00:00:00\", \"total_cases\": 62808, \"total_infected\": 100493.86622167878, \"n_days\": 67, \"cases\": 62808, \"infected\": 100493.86622167878, \"45_line\": 62808}, {\"index\": 8799, \"location\": \"India\", \"date\": \"2020-05-10T00:00:00\", \"total_cases\": 67161, \"total_infected\": 106449.28652645694, \"n_days\": 68, \"cases\": 67161, \"infected\": 106449.28652645694, \"45_line\": 67161}]}}, {\"mode\": \"vega-lite\"});\n",
              "</script>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 21
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      "source": [
        "Latest Observed vs. Estimate of Infected Cases"
      ]
    },
    {
      "cell_type": "code",
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        "execution": {
          "iopub.execute_input": "2020-04-17T06:14:00.474092Z",
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          "shell.execute_reply": "2020-04-17T06:14:00.495202Z"
        },
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          "status": "completed"
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        "id": "2-EORfuUij7d",
        "colab_type": "code",
        "outputId": "b1bb6e47-39cc-4ca6-97cb-357bea3fe080",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 489
        }
      },
      "source": [
        "#hide_input\n",
        "label1 = 'Observed Cases'\n",
        "label2 = 'Estimated Infected'\n",
        "temp = pd.concat([x.copy() for x in data_countries_pc]).loc[lambda x: x.date >= '3/1/2020']\n",
        "\n",
        "metric_name1 = f'{label1}'\n",
        "metric_name2 = f'{label2}'\n",
        "temp.columns = ['Country', 'Date', metric_name1, metric_name2]\n",
        "# temp.loc[:, 'month'] = temp.date.dt.strftime('%Y-%m')\n",
        "temp.loc[:, \"Observed Cases\"] = temp.loc[:, \"Observed Cases\"].round(0).map('{:,.0f}'.format)\n",
        "temp.loc[:, \"Estimated Infected\"] = temp.loc[:, \"Estimated Infected\"].round(0).map('{:,.0f}'.format)\n",
        "temp.groupby('Country').last()"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        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>Date</th>\n",
              "      <th>Observed Cases</th>\n",
              "      <th>Estimated Infected</th>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Country</th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "      <th></th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>Brazil</th>\n",
              "      <td>2020-05-10</td>\n",
              "      <td>162,699</td>\n",
              "      <td>264,640</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>China</th>\n",
              "      <td>2020-05-10</td>\n",
              "      <td>84,010</td>\n",
              "      <td>84,090</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>France</th>\n",
              "      <td>2020-05-10</td>\n",
              "      <td>177,094</td>\n",
              "      <td>182,964</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Germany</th>\n",
              "      <td>2020-05-10</td>\n",
              "      <td>171,879</td>\n",
              "      <td>179,540</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>India</th>\n",
              "      <td>2020-05-10</td>\n",
              "      <td>67,161</td>\n",
              "      <td>106,449</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Iran</th>\n",
              "      <td>2020-05-10</td>\n",
              "      <td>107,603</td>\n",
              "      <td>120,479</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Italy</th>\n",
              "      <td>2020-05-10</td>\n",
              "      <td>219,070</td>\n",
              "      <td>228,570</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Japan</th>\n",
              "      <td>2020-05-10</td>\n",
              "      <td>15,777</td>\n",
              "      <td>16,875</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Portugal</th>\n",
              "      <td>2020-05-10</td>\n",
              "      <td>27,581</td>\n",
              "      <td>30,587</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Singapore</th>\n",
              "      <td>2020-05-10</td>\n",
              "      <td>23,336</td>\n",
              "      <td>30,992</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>South Korea</th>\n",
              "      <td>2020-05-10</td>\n",
              "      <td>10,909</td>\n",
              "      <td>11,109</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>Spain</th>\n",
              "      <td>2020-05-10</td>\n",
              "      <td>224,350</td>\n",
              "      <td>232,603</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>United Kingdom</th>\n",
              "      <td>2020-05-10</td>\n",
              "      <td>220,449</td>\n",
              "      <td>261,153</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "                     Date Observed Cases Estimated Infected\n",
              "Country                                                    \n",
              "Brazil         2020-05-10        162,699            264,640\n",
              "China          2020-05-10         84,010             84,090\n",
              "France         2020-05-10        177,094            182,964\n",
              "Germany        2020-05-10        171,879            179,540\n",
              "India          2020-05-10         67,161            106,449\n",
              "Iran           2020-05-10        107,603            120,479\n",
              "Italy          2020-05-10        219,070            228,570\n",
              "Japan          2020-05-10         15,777             16,875\n",
              "Portugal       2020-05-10         27,581             30,587\n",
              "Singapore      2020-05-10         23,336             30,992\n",
              "South Korea    2020-05-10         10,909             11,109\n",
              "Spain          2020-05-10        224,350            232,603\n",
              "United Kingdom 2020-05-10        220,449            261,153"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "papermill": {
          "duration": 0.017932,
          "end_time": "2020-04-17T06:14:00.532004",
          "exception": false,
          "start_time": "2020-04-17T06:14:00.514072",
          "status": "completed"
        },
        "tags": [],
        "id": "JnxCf98cij7k",
        "colab_type": "text"
      },
      "source": [
        "## Methodology"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "papermill": {
          "duration": 0.016951,
          "end_time": "2020-04-17T06:14:00.566489",
          "exception": false,
          "start_time": "2020-04-17T06:14:00.549538",
          "status": "completed"
        },
        "tags": [],
        "id": "x1TXHdWBij7m",
        "colab_type": "text"
      },
      "source": [
        "We argue that the number of infected in the past can be inferred using today's number of deaths and average fatality rate from confirmed cases in the following way:\n",
        "\n",
        "{%raw%}$$I_{t-j} = \\frac{D_t}{{CFR}_t}$${%endraw%}\n",
        "\n",
        "where {% raw %}$I_t${% endraw %} = number of infected, {% raw %}$D_t${% endraw %} = number of deaths, and {% raw %}${CFR}_t ${% endraw %} = case fatality rate = {% raw %}$\\frac{D}{C}${% endraw %}. The {% raw %}$j${% endraw %} depends on the average number of days that covid patients die after having the first symptoms."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "papermill": {
          "duration": 0.018565,
          "end_time": "2020-04-17T06:14:00.606823",
          "exception": false,
          "start_time": "2020-04-17T06:14:00.588258",
          "status": "completed"
        },
        "tags": [],
        "id": "D_PBqb13ij7m",
        "colab_type": "text"
      },
      "source": [
        "**Assumption 1**: The case fatality rate is a good proxy for the fatality rate of the infected population\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "papermill": {
          "duration": 0.018523,
          "end_time": "2020-04-17T06:14:00.644291",
          "exception": false,
          "start_time": "2020-04-17T06:14:00.625768",
          "status": "completed"
        },
        "tags": [],
        "id": "J4timt5Oij7n",
        "colab_type": "text"
      },
      "source": [
        "Then, in order to estimate the current number of infected {% raw %}$I_t${% endraw %} we need to estimate its growth rate from {% raw %}$t-j${% endraw %} to {% raw %}$t${% endraw %}.\n",
        "\n",
        "{% raw %}$$I_t = (1+\\hat{g})^j I_{t-j}$${% endraw %}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "papermill": {
          "duration": 0.017294,
          "end_time": "2020-04-17T06:14:00.680235",
          "exception": false,
          "start_time": "2020-04-17T06:14:00.662941",
          "status": "completed"
        },
        "tags": [],
        "id": "HQbubhK4ij7p",
        "colab_type": "text"
      },
      "source": [
        "**Assumption 2**: The growth rate of infected $\\hat{g}$ is an unbiased estimate of $g$ .\n",
        "\n",
        "For now we estimate $g$ using the average growth rate since having the first infected person."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "papermill": {
          "duration": 0.016698,
          "end_time": "2020-04-17T06:14:00.714440",
          "exception": false,
          "start_time": "2020-04-17T06:14:00.697742",
          "status": "completed"
        },
        "tags": [],
        "id": "ohL7DRquij7q",
        "colab_type": "text"
      },
      "source": [
        "**Assumption 3**: It takes on average 8 days to die after having the first symptoms."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "papermill": {
          "duration": 0.017621,
          "end_time": "2020-04-17T06:14:00.749034",
          "exception": false,
          "start_time": "2020-04-17T06:14:00.731413",
          "status": "completed"
        },
        "tags": [],
        "id": "Ha9RKN55ij7r",
        "colab_type": "text"
      },
      "source": [
        "This analysis was conducted by [Joao B. Duarte](http://jbduarte.com). Relevant sources are listed below: \n",
        "\n",
        "\n",
        "1. [2019 Novel Coronavirus COVID-19 (2019-nCoV) Data Repository by Johns Hopkins CSSE](https://systems.jhu.edu/research/public-health/ncov/) [GitHub repository](https://github.com/CSSEGISandData/COVID-19). \n",
        "\n",
        "2. [Feenstra, Robert C., Robert Inklaar and Marcel P. Timmer (2015), \"The Next Generation of the Penn World Table\" American Economic Review, 105(10), 3150-3182](https://www.rug.nl/ggdc/productivity/pwt/related-research)\n"
      ]
    },
    {
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          "status": "completed"
        },
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        "id": "qiRkVqMTij7s",
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      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}