Covid19-approx.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Аппроксимируем эпидемиологические данные (начало эпидемии)\n",
    "\n",
    "## 1. Подключаем необходимые библиотеки"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from scipy import optimize\n",
    "import pandas as pd\n",
    "import datetime"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Загружаем данные\n",
    "\n",
    "Данные о распространении эпидемии возьмем [здесь](https://github.com/CSSEGISandData/COVID-19/tree/master/csse_covid_19_data/csse_covid_19_time_series). Данные обновляются каждый день.\n",
    "\n",
    "Будем использовать [pandas](https://pandas.pydata.org/) - библиотеку, в которой реализованы полезные инструментарии для анализа данных. Основной тип данных в этой библиотеке - это таблицы (`dataframe`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "url = \"https://raw.githubusercontent.com/CSSEGISandData/COVID-19/master/csse_covid_19_data/csse_covid_19_time_series/\"\n",
    "covid19_confirmed = pd.read_csv(url + \"time_series_covid19_confirmed_global.csv\")\n",
    "covid19_deaths    = pd.read_csv(url + \"time_series_covid19_deaths_global.csv\")\n",
    "covid19_recovered = pd.read_csv(url + \"time_series_covid19_recovered_global.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Мы загрузили 3 таблицы, которые содержат данные по странам на данный день:\n",
    "* `covid19_confirmed` о количестве подтвержденных случаев\n",
    "* `covid19_deaths`    - суммарное количество\n",
    "* `covid19_recovered` - суммарное количество выздоровевших\n",
    "\n",
    "Рассмотрим, например, `covid19_confirmed`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
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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",
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       "      <th>3/23/20</th>\n",
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       "      <td>170</td>\n",
       "      <td>174</td>\n",
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       "    <tr>\n",
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       "      <td>Albania</td>\n",
       "      <td>41.153300</td>\n",
       "      <td>20.168300</td>\n",
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       "      <td>104</td>\n",
       "      <td>123</td>\n",
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       "      <td>186</td>\n",
       "      <td>197</td>\n",
       "      <td>212</td>\n",
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       "      <td>243</td>\n",
       "      <td>259</td>\n",
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       "      <th>2</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Algeria</td>\n",
       "      <td>28.033900</td>\n",
       "      <td>1.659600</td>\n",
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       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>230</td>\n",
       "      <td>264</td>\n",
       "      <td>302</td>\n",
       "      <td>367</td>\n",
       "      <td>409</td>\n",
       "      <td>454</td>\n",
       "      <td>511</td>\n",
       "      <td>584</td>\n",
       "      <td>716</td>\n",
       "      <td>847</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Andorra</td>\n",
       "      <td>42.506300</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>133</td>\n",
       "      <td>164</td>\n",
       "      <td>188</td>\n",
       "      <td>224</td>\n",
       "      <td>267</td>\n",
       "      <td>308</td>\n",
       "      <td>334</td>\n",
       "      <td>370</td>\n",
       "      <td>376</td>\n",
       "      <td>390</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Angola</td>\n",
       "      <td>-11.202700</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>3</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Antigua and Barbuda</td>\n",
       "      <td>17.060800</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>3</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Argentina</td>\n",
       "      <td>-38.416100</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>301</td>\n",
       "      <td>387</td>\n",
       "      <td>387</td>\n",
       "      <td>502</td>\n",
       "      <td>589</td>\n",
       "      <td>690</td>\n",
       "      <td>745</td>\n",
       "      <td>820</td>\n",
       "      <td>1054</td>\n",
       "      <td>1054</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Armenia</td>\n",
       "      <td>40.069100</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>235</td>\n",
       "      <td>249</td>\n",
       "      <td>265</td>\n",
       "      <td>290</td>\n",
       "      <td>329</td>\n",
       "      <td>407</td>\n",
       "      <td>424</td>\n",
       "      <td>482</td>\n",
       "      <td>532</td>\n",
       "      <td>571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>Australian Capital Territory</td>\n",
       "      <td>Australia</td>\n",
       "      <td>-35.473500</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>32</td>\n",
       "      <td>39</td>\n",
       "      <td>39</td>\n",
       "      <td>53</td>\n",
       "      <td>62</td>\n",
       "      <td>71</td>\n",
       "      <td>77</td>\n",
       "      <td>78</td>\n",
       "      <td>80</td>\n",
       "      <td>84</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>New South Wales</td>\n",
       "      <td>Australia</td>\n",
       "      <td>-33.868800</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>669</td>\n",
       "      <td>818</td>\n",
       "      <td>1029</td>\n",
       "      <td>1219</td>\n",
       "      <td>1405</td>\n",
       "      <td>1617</td>\n",
       "      <td>1791</td>\n",
       "      <td>2032</td>\n",
       "      <td>2032</td>\n",
       "      <td>2182</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>Northern Territory</td>\n",
       "      <td>Australia</td>\n",
       "      <td>-12.463400</td>\n",
       "      <td>130.845600</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>5</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>12</td>\n",
       "      <td>12</td>\n",
       "      <td>15</td>\n",
       "      <td>15</td>\n",
       "      <td>15</td>\n",
       "      <td>17</td>\n",
       "      <td>19</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>Queensland</td>\n",
       "      <td>Australia</td>\n",
       "      <td>-28.016700</td>\n",
       "      <td>153.400000</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>319</td>\n",
       "      <td>397</td>\n",
       "      <td>443</td>\n",
       "      <td>493</td>\n",
       "      <td>555</td>\n",
       "      <td>625</td>\n",
       "      <td>656</td>\n",
       "      <td>689</td>\n",
       "      <td>743</td>\n",
       "      <td>781</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>South Australia</td>\n",
       "      <td>Australia</td>\n",
       "      <td>-34.928500</td>\n",
       "      <td>138.600700</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>134</td>\n",
       "      <td>170</td>\n",
       "      <td>170</td>\n",
       "      <td>235</td>\n",
       "      <td>257</td>\n",
       "      <td>287</td>\n",
       "      <td>299</td>\n",
       "      <td>305</td>\n",
       "      <td>337</td>\n",
       "      <td>367</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>Tasmania</td>\n",
       "      <td>Australia</td>\n",
       "      <td>-41.454500</td>\n",
       "      <td>145.970700</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>28</td>\n",
       "      <td>28</td>\n",
       "      <td>36</td>\n",
       "      <td>47</td>\n",
       "      <td>47</td>\n",
       "      <td>62</td>\n",
       "      <td>66</td>\n",
       "      <td>66</td>\n",
       "      <td>69</td>\n",
       "      <td>69</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>Victoria</td>\n",
       "      <td>Australia</td>\n",
       "      <td>-37.813600</td>\n",
       "      <td>144.963100</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>...</td>\n",
       "      <td>355</td>\n",
       "      <td>411</td>\n",
       "      <td>466</td>\n",
       "      <td>520</td>\n",
       "      <td>574</td>\n",
       "      <td>685</td>\n",
       "      <td>769</td>\n",
       "      <td>821</td>\n",
       "      <td>917</td>\n",
       "      <td>968</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>Western Australia</td>\n",
       "      <td>Australia</td>\n",
       "      <td>-31.950500</td>\n",
       "      <td>115.860500</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>140</td>\n",
       "      <td>175</td>\n",
       "      <td>175</td>\n",
       "      <td>231</td>\n",
       "      <td>231</td>\n",
       "      <td>278</td>\n",
       "      <td>311</td>\n",
       "      <td>355</td>\n",
       "      <td>364</td>\n",
       "      <td>392</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Austria</td>\n",
       "      <td>47.516200</td>\n",
       "      <td>14.550100</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>4474</td>\n",
       "      <td>5283</td>\n",
       "      <td>5588</td>\n",
       "      <td>6909</td>\n",
       "      <td>7657</td>\n",
       "      <td>8271</td>\n",
       "      <td>8788</td>\n",
       "      <td>9618</td>\n",
       "      <td>10180</td>\n",
       "      <td>10711</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Azerbaijan</td>\n",
       "      <td>40.143100</td>\n",
       "      <td>47.576900</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>72</td>\n",
       "      <td>87</td>\n",
       "      <td>93</td>\n",
       "      <td>122</td>\n",
       "      <td>165</td>\n",
       "      <td>182</td>\n",
       "      <td>209</td>\n",
       "      <td>273</td>\n",
       "      <td>298</td>\n",
       "      <td>359</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Bahamas</td>\n",
       "      <td>25.034300</td>\n",
       "      <td>-77.396300</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>4</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "      <td>11</td>\n",
       "      <td>14</td>\n",
       "      <td>14</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Bahrain</td>\n",
       "      <td>26.027500</td>\n",
       "      <td>50.550000</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>377</td>\n",
       "      <td>392</td>\n",
       "      <td>419</td>\n",
       "      <td>458</td>\n",
       "      <td>466</td>\n",
       "      <td>476</td>\n",
       "      <td>499</td>\n",
       "      <td>515</td>\n",
       "      <td>567</td>\n",
       "      <td>569</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Bangladesh</td>\n",
       "      <td>23.685000</td>\n",
       "      <td>90.356300</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>33</td>\n",
       "      <td>39</td>\n",
       "      <td>39</td>\n",
       "      <td>44</td>\n",
       "      <td>48</td>\n",
       "      <td>48</td>\n",
       "      <td>48</td>\n",
       "      <td>49</td>\n",
       "      <td>51</td>\n",
       "      <td>54</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Barbados</td>\n",
       "      <td>13.193900</td>\n",
       "      <td>-59.543200</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>17</td>\n",
       "      <td>18</td>\n",
       "      <td>18</td>\n",
       "      <td>18</td>\n",
       "      <td>24</td>\n",
       "      <td>26</td>\n",
       "      <td>33</td>\n",
       "      <td>33</td>\n",
       "      <td>34</td>\n",
       "      <td>34</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Belarus</td>\n",
       "      <td>53.709800</td>\n",
       "      <td>27.953400</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>81</td>\n",
       "      <td>81</td>\n",
       "      <td>86</td>\n",
       "      <td>86</td>\n",
       "      <td>94</td>\n",
       "      <td>94</td>\n",
       "      <td>94</td>\n",
       "      <td>152</td>\n",
       "      <td>152</td>\n",
       "      <td>163</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Belgium</td>\n",
       "      <td>50.833300</td>\n",
       "      <td>4.000000</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>3743</td>\n",
       "      <td>4269</td>\n",
       "      <td>4937</td>\n",
       "      <td>6235</td>\n",
       "      <td>7284</td>\n",
       "      <td>9134</td>\n",
       "      <td>10836</td>\n",
       "      <td>11899</td>\n",
       "      <td>12775</td>\n",
       "      <td>13964</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Benin</td>\n",
       "      <td>9.307700</td>\n",
       "      <td>2.315800</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>5</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>9</td>\n",
       "      <td>13</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Bhutan</td>\n",
       "      <td>27.514200</td>\n",
       "      <td>90.433600</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>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Bolivia</td>\n",
       "      <td>-16.290200</td>\n",
       "      <td>-63.588700</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>27</td>\n",
       "      <td>29</td>\n",
       "      <td>32</td>\n",
       "      <td>43</td>\n",
       "      <td>61</td>\n",
       "      <td>74</td>\n",
       "      <td>81</td>\n",
       "      <td>97</td>\n",
       "      <td>107</td>\n",
       "      <td>115</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Bosnia and Herzegovina</td>\n",
       "      <td>43.915900</td>\n",
       "      <td>17.679100</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>136</td>\n",
       "      <td>166</td>\n",
       "      <td>176</td>\n",
       "      <td>191</td>\n",
       "      <td>237</td>\n",
       "      <td>258</td>\n",
       "      <td>323</td>\n",
       "      <td>368</td>\n",
       "      <td>420</td>\n",
       "      <td>459</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Brazil</td>\n",
       "      <td>-14.235000</td>\n",
       "      <td>-51.925300</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>1924</td>\n",
       "      <td>2247</td>\n",
       "      <td>2554</td>\n",
       "      <td>2985</td>\n",
       "      <td>3417</td>\n",
       "      <td>3904</td>\n",
       "      <td>4256</td>\n",
       "      <td>4579</td>\n",
       "      <td>5717</td>\n",
       "      <td>6836</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Brunei</td>\n",
       "      <td>4.535300</td>\n",
       "      <td>114.727700</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>91</td>\n",
       "      <td>104</td>\n",
       "      <td>109</td>\n",
       "      <td>114</td>\n",
       "      <td>115</td>\n",
       "      <td>120</td>\n",
       "      <td>126</td>\n",
       "      <td>127</td>\n",
       "      <td>129</td>\n",
       "      <td>131</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>226</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Uzbekistan</td>\n",
       "      <td>41.377500</td>\n",
       "      <td>64.585300</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>46</td>\n",
       "      <td>50</td>\n",
       "      <td>60</td>\n",
       "      <td>75</td>\n",
       "      <td>88</td>\n",
       "      <td>104</td>\n",
       "      <td>144</td>\n",
       "      <td>149</td>\n",
       "      <td>172</td>\n",
       "      <td>181</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>227</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Venezuela</td>\n",
       "      <td>6.423800</td>\n",
       "      <td>-66.589700</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>77</td>\n",
       "      <td>84</td>\n",
       "      <td>91</td>\n",
       "      <td>107</td>\n",
       "      <td>107</td>\n",
       "      <td>119</td>\n",
       "      <td>119</td>\n",
       "      <td>135</td>\n",
       "      <td>135</td>\n",
       "      <td>143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>228</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Vietnam</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>108.000000</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>...</td>\n",
       "      <td>123</td>\n",
       "      <td>134</td>\n",
       "      <td>141</td>\n",
       "      <td>153</td>\n",
       "      <td>163</td>\n",
       "      <td>174</td>\n",
       "      <td>188</td>\n",
       "      <td>203</td>\n",
       "      <td>212</td>\n",
       "      <td>218</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>229</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Zambia</td>\n",
       "      <td>-15.416700</td>\n",
       "      <td>28.283300</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>3</td>\n",
       "      <td>3</td>\n",
       "      <td>12</td>\n",
       "      <td>16</td>\n",
       "      <td>22</td>\n",
       "      <td>28</td>\n",
       "      <td>29</td>\n",
       "      <td>35</td>\n",
       "      <td>35</td>\n",
       "      <td>36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>230</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Zimbabwe</td>\n",
       "      <td>-20.000000</td>\n",
       "      <td>30.000000</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>3</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>231</th>\n",
       "      <td>Diamond Princess</td>\n",
       "      <td>Canada</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</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>0</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>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>232</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Dominica</td>\n",
       "      <td>15.415000</td>\n",
       "      <td>-61.371000</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>2</td>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "      <td>11</td>\n",
       "      <td>11</td>\n",
       "      <td>11</td>\n",
       "      <td>11</td>\n",
       "      <td>11</td>\n",
       "      <td>12</td>\n",
       "      <td>12</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>233</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Grenada</td>\n",
       "      <td>12.116500</td>\n",
       "      <td>-61.679000</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>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>9</td>\n",
       "      <td>9</td>\n",
       "      <td>9</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>234</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Mozambique</td>\n",
       "      <td>-18.665695</td>\n",
       "      <td>35.529562</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>1</td>\n",
       "      <td>3</td>\n",
       "      <td>5</td>\n",
       "      <td>7</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>235</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Syria</td>\n",
       "      <td>34.802075</td>\n",
       "      <td>38.996815</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>1</td>\n",
       "      <td>1</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>236</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Timor-Leste</td>\n",
       "      <td>-8.874217</td>\n",
       "      <td>125.727539</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>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>237</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Belize</td>\n",
       "      <td>13.193900</td>\n",
       "      <td>-59.543200</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>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>238</th>\n",
       "      <td>Recovered</td>\n",
       "      <td>Canada</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</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>0</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>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>239</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Laos</td>\n",
       "      <td>19.856270</td>\n",
       "      <td>102.495496</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>0</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>6</td>\n",
       "      <td>6</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>240</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Libya</td>\n",
       "      <td>26.335100</td>\n",
       "      <td>17.228331</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>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>10</td>\n",
       "      <td>10</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>241</th>\n",
       "      <td>NaN</td>\n",
       "      <td>West Bank and Gaza</td>\n",
       "      <td>31.952200</td>\n",
       "      <td>35.233200</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>59</td>\n",
       "      <td>59</td>\n",
       "      <td>59</td>\n",
       "      <td>84</td>\n",
       "      <td>91</td>\n",
       "      <td>98</td>\n",
       "      <td>109</td>\n",
       "      <td>116</td>\n",
       "      <td>119</td>\n",
       "      <td>134</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>242</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Guinea-Bissau</td>\n",
       "      <td>11.803700</td>\n",
       "      <td>-15.180400</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>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>243</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Mali</td>\n",
       "      <td>17.570692</td>\n",
       "      <td>-3.996166</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>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>4</td>\n",
       "      <td>11</td>\n",
       "      <td>18</td>\n",
       "      <td>18</td>\n",
       "      <td>25</td>\n",
       "      <td>28</td>\n",
       "      <td>31</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>244</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Saint Kitts and Nevis</td>\n",
       "      <td>17.357822</td>\n",
       "      <td>-62.782998</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>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>245</th>\n",
       "      <td>Northwest Territories</td>\n",
       "      <td>Canada</td>\n",
       "      <td>64.825500</td>\n",
       "      <td>-124.845700</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>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>246</th>\n",
       "      <td>Yukon</td>\n",
       "      <td>Canada</td>\n",
       "      <td>64.282300</td>\n",
       "      <td>-135.000000</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>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>247</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Kosovo</td>\n",
       "      <td>42.602636</td>\n",
       "      <td>20.902977</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>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>71</td>\n",
       "      <td>86</td>\n",
       "      <td>91</td>\n",
       "      <td>94</td>\n",
       "      <td>94</td>\n",
       "      <td>112</td>\n",
       "      <td>125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>248</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Burma</td>\n",
       "      <td>21.916200</td>\n",
       "      <td>95.956000</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>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>8</td>\n",
       "      <td>8</td>\n",
       "      <td>10</td>\n",
       "      <td>14</td>\n",
       "      <td>15</td>\n",
       "      <td>15</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>249</th>\n",
       "      <td>Anguilla</td>\n",
       "      <td>United Kingdom</td>\n",
       "      <td>18.220600</td>\n",
       "      <td>-63.068600</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>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>250</th>\n",
       "      <td>British Virgin Islands</td>\n",
       "      <td>United Kingdom</td>\n",
       "      <td>18.420700</td>\n",
       "      <td>-64.640000</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>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>251</th>\n",
       "      <td>Turks and Caicos Islands</td>\n",
       "      <td>United Kingdom</td>\n",
       "      <td>21.694000</td>\n",
       "      <td>-71.797900</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>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>5</td>\n",
       "      <td>5</td>\n",
       "      <td>6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>252</th>\n",
       "      <td>NaN</td>\n",
       "      <td>MS Zaandam</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</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>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>253</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Botswana</td>\n",
       "      <td>-22.328500</td>\n",
       "      <td>24.684900</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>0</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>3</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>254</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Burundi</td>\n",
       "      <td>-3.373100</td>\n",
       "      <td>29.918900</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>0</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>0</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>255</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Sierra Leone</td>\n",
       "      <td>8.460555</td>\n",
       "      <td>-11.779889</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>0</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>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>256 rows × 75 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "                   Province/State          Country/Region        Lat  \\\n",
       "0                             NaN             Afghanistan  33.000000   \n",
       "1                             NaN                 Albania  41.153300   \n",
       "2                             NaN                 Algeria  28.033900   \n",
       "3                             NaN                 Andorra  42.506300   \n",
       "4                             NaN                  Angola -11.202700   \n",
       "5                             NaN     Antigua and Barbuda  17.060800   \n",
       "6                             NaN               Argentina -38.416100   \n",
       "7                             NaN                 Armenia  40.069100   \n",
       "8    Australian Capital Territory               Australia -35.473500   \n",
       "9                 New South Wales               Australia -33.868800   \n",
       "10             Northern Territory               Australia -12.463400   \n",
       "11                     Queensland               Australia -28.016700   \n",
       "12                South Australia               Australia -34.928500   \n",
       "13                       Tasmania               Australia -41.454500   \n",
       "14                       Victoria               Australia -37.813600   \n",
       "15              Western Australia               Australia -31.950500   \n",
       "16                            NaN                 Austria  47.516200   \n",
       "17                            NaN              Azerbaijan  40.143100   \n",
       "18                            NaN                 Bahamas  25.034300   \n",
       "19                            NaN                 Bahrain  26.027500   \n",
       "20                            NaN              Bangladesh  23.685000   \n",
       "21                            NaN                Barbados  13.193900   \n",
       "22                            NaN                 Belarus  53.709800   \n",
       "23                            NaN                 Belgium  50.833300   \n",
       "24                            NaN                   Benin   9.307700   \n",
       "25                            NaN                  Bhutan  27.514200   \n",
       "26                            NaN                 Bolivia -16.290200   \n",
       "27                            NaN  Bosnia and Herzegovina  43.915900   \n",
       "28                            NaN                  Brazil -14.235000   \n",
       "29                            NaN                  Brunei   4.535300   \n",
       "..                            ...                     ...        ...   \n",
       "226                           NaN              Uzbekistan  41.377500   \n",
       "227                           NaN               Venezuela   6.423800   \n",
       "228                           NaN                 Vietnam  16.000000   \n",
       "229                           NaN                  Zambia -15.416700   \n",
       "230                           NaN                Zimbabwe -20.000000   \n",
       "231              Diamond Princess                  Canada   0.000000   \n",
       "232                           NaN                Dominica  15.415000   \n",
       "233                           NaN                 Grenada  12.116500   \n",
       "234                           NaN              Mozambique -18.665695   \n",
       "235                           NaN                   Syria  34.802075   \n",
       "236                           NaN             Timor-Leste  -8.874217   \n",
       "237                           NaN                  Belize  13.193900   \n",
       "238                     Recovered                  Canada   0.000000   \n",
       "239                           NaN                    Laos  19.856270   \n",
       "240                           NaN                   Libya  26.335100   \n",
       "241                           NaN      West Bank and Gaza  31.952200   \n",
       "242                           NaN           Guinea-Bissau  11.803700   \n",
       "243                           NaN                    Mali  17.570692   \n",
       "244                           NaN   Saint Kitts and Nevis  17.357822   \n",
       "245         Northwest Territories                  Canada  64.825500   \n",
       "246                         Yukon                  Canada  64.282300   \n",
       "247                           NaN                  Kosovo  42.602636   \n",
       "248                           NaN                   Burma  21.916200   \n",
       "249                      Anguilla          United Kingdom  18.220600   \n",
       "250        British Virgin Islands          United Kingdom  18.420700   \n",
       "251      Turks and Caicos Islands          United Kingdom  21.694000   \n",
       "252                           NaN              MS Zaandam   0.000000   \n",
       "253                           NaN                Botswana -22.328500   \n",
       "254                           NaN                 Burundi  -3.373100   \n",
       "255                           NaN            Sierra Leone   8.460555   \n",
       "\n",
       "           Long  1/22/20  1/23/20  1/24/20  1/25/20  1/26/20  1/27/20  ...  \\\n",
       "0     65.000000        0        0        0        0        0        0  ...   \n",
       "1     20.168300        0        0        0        0        0        0  ...   \n",
       "2      1.659600        0        0        0        0        0        0  ...   \n",
       "3      1.521800        0        0        0        0        0        0  ...   \n",
       "4     17.873900        0        0        0        0        0        0  ...   \n",
       "5    -61.796400        0        0        0        0        0        0  ...   \n",
       "6    -63.616700        0        0        0        0        0        0  ...   \n",
       "7     45.038200        0        0        0        0        0        0  ...   \n",
       "8    149.012400        0        0        0        0        0        0  ...   \n",
       "9    151.209300        0        0        0        0        3        4  ...   \n",
       "10   130.845600        0        0        0        0        0        0  ...   \n",
       "11   153.400000        0        0        0        0        0        0  ...   \n",
       "12   138.600700        0        0        0        0        0        0  ...   \n",
       "13   145.970700        0        0        0        0        0        0  ...   \n",
       "14   144.963100        0        0        0        0        1        1  ...   \n",
       "15   115.860500        0        0        0        0        0        0  ...   \n",
       "16    14.550100        0        0        0        0        0        0  ...   \n",
       "17    47.576900        0        0        0        0        0        0  ...   \n",
       "18   -77.396300        0        0        0        0        0        0  ...   \n",
       "19    50.550000        0        0        0        0        0        0  ...   \n",
       "20    90.356300        0        0        0        0        0        0  ...   \n",
       "21   -59.543200        0        0        0        0        0        0  ...   \n",
       "22    27.953400        0        0        0        0        0        0  ...   \n",
       "23     4.000000        0        0        0        0        0        0  ...   \n",
       "24     2.315800        0        0        0        0        0        0  ...   \n",
       "25    90.433600        0        0        0        0        0        0  ...   \n",
       "26   -63.588700        0        0        0        0        0        0  ...   \n",
       "27    17.679100        0        0        0        0        0        0  ...   \n",
       "28   -51.925300        0        0        0        0        0        0  ...   \n",
       "29   114.727700        0        0        0        0        0        0  ...   \n",
       "..          ...      ...      ...      ...      ...      ...      ...  ...   \n",
       "226   64.585300        0        0        0        0        0        0  ...   \n",
       "227  -66.589700        0        0        0        0        0        0  ...   \n",
       "228  108.000000        0        2        2        2        2        2  ...   \n",
       "229   28.283300        0        0        0        0        0        0  ...   \n",
       "230   30.000000        0        0        0        0        0        0  ...   \n",
       "231    0.000000        0        0        0        0        0        0  ...   \n",
       "232  -61.371000        0        0        0        0        0        0  ...   \n",
       "233  -61.679000        0        0        0        0        0        0  ...   \n",
       "234   35.529562        0        0        0        0        0        0  ...   \n",
       "235   38.996815        0        0        0        0        0        0  ...   \n",
       "236  125.727539        0        0        0        0        0        0  ...   \n",
       "237  -59.543200        0        0        0        0        0        0  ...   \n",
       "238    0.000000        0        0        0        0        0        0  ...   \n",
       "239  102.495496        0        0        0        0        0        0  ...   \n",
       "240   17.228331        0        0        0        0        0        0  ...   \n",
       "241   35.233200        0        0        0        0        0        0  ...   \n",
       "242  -15.180400        0        0        0        0        0        0  ...   \n",
       "243   -3.996166        0        0        0        0        0        0  ...   \n",
       "244  -62.782998        0        0        0        0        0        0  ...   \n",
       "245 -124.845700        0        0        0        0        0        0  ...   \n",
       "246 -135.000000        0        0        0        0        0        0  ...   \n",
       "247   20.902977        0        0        0        0        0        0  ...   \n",
       "248   95.956000        0        0        0        0        0        0  ...   \n",
       "249  -63.068600        0        0        0        0        0        0  ...   \n",
       "250  -64.640000        0        0        0        0        0        0  ...   \n",
       "251  -71.797900        0        0        0        0        0        0  ...   \n",
       "252    0.000000        0        0        0        0        0        0  ...   \n",
       "253   24.684900        0        0        0        0        0        0  ...   \n",
       "254   29.918900        0        0        0        0        0        0  ...   \n",
       "255  -11.779889        0        0        0        0        0        0  ...   \n",
       "\n",
       "     3/23/20  3/24/20  3/25/20  3/26/20  3/27/20  3/28/20  3/29/20  3/30/20  \\\n",
       "0         40       74       84       94      110      110      120      170   \n",
       "1        104      123      146      174      186      197      212      223   \n",
       "2        230      264      302      367      409      454      511      584   \n",
       "3        133      164      188      224      267      308      334      370   \n",
       "4          3        3        3        4        4        5        7        7   \n",
       "5          3        3        3        7        7        7        7        7   \n",
       "6        301      387      387      502      589      690      745      820   \n",
       "7        235      249      265      290      329      407      424      482   \n",
       "8         32       39       39       53       62       71       77       78   \n",
       "9        669      818     1029     1219     1405     1617     1791     2032   \n",
       "10         5        6        6       12       12       15       15       15   \n",
       "11       319      397      443      493      555      625      656      689   \n",
       "12       134      170      170      235      257      287      299      305   \n",
       "13        28       28       36       47       47       62       66       66   \n",
       "14       355      411      466      520      574      685      769      821   \n",
       "15       140      175      175      231      231      278      311      355   \n",
       "16      4474     5283     5588     6909     7657     8271     8788     9618   \n",
       "17        72       87       93      122      165      182      209      273   \n",
       "18         4        5        5        9       10       10       11       14   \n",
       "19       377      392      419      458      466      476      499      515   \n",
       "20        33       39       39       44       48       48       48       49   \n",
       "21        17       18       18       18       24       26       33       33   \n",
       "22        81       81       86       86       94       94       94      152   \n",
       "23      3743     4269     4937     6235     7284     9134    10836    11899   \n",
       "24         5        6        6        6        6        6        6        6   \n",
       "25         2        2        2        2        3        3        4        4   \n",
       "26        27       29       32       43       61       74       81       97   \n",
       "27       136      166      176      191      237      258      323      368   \n",
       "28      1924     2247     2554     2985     3417     3904     4256     4579   \n",
       "29        91      104      109      114      115      120      126      127   \n",
       "..       ...      ...      ...      ...      ...      ...      ...      ...   \n",
       "226       46       50       60       75       88      104      144      149   \n",
       "227       77       84       91      107      107      119      119      135   \n",
       "228      123      134      141      153      163      174      188      203   \n",
       "229        3        3       12       16       22       28       29       35   \n",
       "230        3        3        3        3        5        7        7        7   \n",
       "231        0        0        0        0        0        0        0        0   \n",
       "232        2        2        7       11       11       11       11       11   \n",
       "233        1        1        1        7        7        7        9        9   \n",
       "234        1        3        5        7        7        8        8        8   \n",
       "235        1        1        5        5        5        5        9       10   \n",
       "236        1        1        1        1        1        1        1        1   \n",
       "237        1        1        2        2        2        2        2        3   \n",
       "238        0        0        0        0        0        0        0        0   \n",
       "239        0        2        3        6        6        8        8        8   \n",
       "240        0        1        1        1        1        3        8        8   \n",
       "241       59       59       59       84       91       98      109      116   \n",
       "242        0        0        2        2        2        2        2        8   \n",
       "243        0        0        2        4       11       18       18       25   \n",
       "244        0        0        2        2        2        2        2        7   \n",
       "245        0        0        0        1        1        1        1        1   \n",
       "246        0        0        0        3        3        4        4        4   \n",
       "247        0        0        0       71       86       91       94       94   \n",
       "248        0        0        0        0        8        8       10       14   \n",
       "249        0        0        0        0        0        2        2        2   \n",
       "250        0        0        0        0        0        2        2        2   \n",
       "251        0        0        0        0        0        4        4        5   \n",
       "252        0        0        0        0        0        2        2        2   \n",
       "253        0        0        0        0        0        0        0        3   \n",
       "254        0        0        0        0        0        0        0        0   \n",
       "255        0        0        0        0        0        0        0        0   \n",
       "\n",
       "     3/31/20  4/1/20  \n",
       "0        174     237  \n",
       "1        243     259  \n",
       "2        716     847  \n",
       "3        376     390  \n",
       "4          7       8  \n",
       "5          7       7  \n",
       "6       1054    1054  \n",
       "7        532     571  \n",
       "8         80      84  \n",
       "9       2032    2182  \n",
       "10        17      19  \n",
       "11       743     781  \n",
       "12       337     367  \n",
       "13        69      69  \n",
       "14       917     968  \n",
       "15       364     392  \n",
       "16     10180   10711  \n",
       "17       298     359  \n",
       "18        14      21  \n",
       "19       567     569  \n",
       "20        51      54  \n",
       "21        34      34  \n",
       "22       152     163  \n",
       "23     12775   13964  \n",
       "24         9      13  \n",
       "25         4       4  \n",
       "26       107     115  \n",
       "27       420     459  \n",
       "28      5717    6836  \n",
       "29       129     131  \n",
       "..       ...     ...  \n",
       "226      172     181  \n",
       "227      135     143  \n",
       "228      212     218  \n",
       "229       35      36  \n",
       "230        8       8  \n",
       "231        0       0  \n",
       "232       12      12  \n",
       "233        9       9  \n",
       "234        8      10  \n",
       "235       10      10  \n",
       "236        1       1  \n",
       "237        3       3  \n",
       "238        0       0  \n",
       "239        9      10  \n",
       "240       10      10  \n",
       "241      119     134  \n",
       "242        8       9  \n",
       "243       28      31  \n",
       "244        8       8  \n",
       "245        1       2  \n",
       "246        5       5  \n",
       "247      112     125  \n",
       "248       15      15  \n",
       "249        2       2  \n",
       "250        3       3  \n",
       "251        5       6  \n",
       "252        2       9  \n",
       "253        4       4  \n",
       "254        2       2  \n",
       "255        1       2  \n",
       "\n",
       "[256 rows x 75 columns]"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "covid19_confirmed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Мы видим, что данные по каждой стране или провинции расположены по строкам. `NaN` соответствует пропущенным значениям. Для каждой страны указаны географические координаты, а затем, начиная с 4-го столбца (столбцы нумеруются с нуля) - конкретные значения зарегестрированных случаев."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Названия столбцов можно получить следующим образом:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Index(['Province/State', 'Country/Region', 'Lat', 'Long', '1/22/20', '1/23/20',\n",
       "       '1/24/20', '1/25/20', '1/26/20', '1/27/20', '1/28/20', '1/29/20',\n",
       "       '1/30/20', '1/31/20', '2/1/20', '2/2/20', '2/3/20', '2/4/20', '2/5/20',\n",
       "       '2/6/20', '2/7/20', '2/8/20', '2/9/20', '2/10/20', '2/11/20', '2/12/20',\n",
       "       '2/13/20', '2/14/20', '2/15/20', '2/16/20', '2/17/20', '2/18/20',\n",
       "       '2/19/20', '2/20/20', '2/21/20', '2/22/20', '2/23/20', '2/24/20',\n",
       "       '2/25/20', '2/26/20', '2/27/20', '2/28/20', '2/29/20', '3/1/20',\n",
       "       '3/2/20', '3/3/20', '3/4/20', '3/5/20', '3/6/20', '3/7/20', '3/8/20',\n",
       "       '3/9/20', '3/10/20', '3/11/20', '3/12/20', '3/13/20', '3/14/20',\n",
       "       '3/15/20', '3/16/20', '3/17/20', '3/18/20', '3/19/20', '3/20/20',\n",
       "       '3/21/20', '3/22/20', '3/23/20', '3/24/20', '3/25/20', '3/26/20',\n",
       "       '3/27/20', '3/28/20', '3/29/20', '3/30/20', '3/31/20', '4/1/20'],\n",
       "      dtype='object')"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "covid19_confirmed.columns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Извлечь данные по конкретной стране можно так:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "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>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>3/23/20</th>\n",
       "      <th>3/24/20</th>\n",
       "      <th>3/25/20</th>\n",
       "      <th>3/26/20</th>\n",
       "      <th>3/27/20</th>\n",
       "      <th>3/28/20</th>\n",
       "      <th>3/29/20</th>\n",
       "      <th>3/30/20</th>\n",
       "      <th>3/31/20</th>\n",
       "      <th>4/1/20</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>187</th>\n",
       "      <td>NaN</td>\n",
       "      <td>Russia</td>\n",
       "      <td>60.0</td>\n",
       "      <td>90.0</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>438</td>\n",
       "      <td>495</td>\n",
       "      <td>658</td>\n",
       "      <td>840</td>\n",
       "      <td>1036</td>\n",
       "      <td>1264</td>\n",
       "      <td>1534</td>\n",
       "      <td>1836</td>\n",
       "      <td>2337</td>\n",
       "      <td>2777</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>1 rows × 75 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "    Province/State Country/Region   Lat  Long  1/22/20  1/23/20  1/24/20  \\\n",
       "187            NaN         Russia  60.0  90.0        0        0        0   \n",
       "\n",
       "     1/25/20  1/26/20  1/27/20  ...  3/23/20  3/24/20  3/25/20  3/26/20  \\\n",
       "187        0        0        0  ...      438      495      658      840   \n",
       "\n",
       "     3/27/20  3/28/20  3/29/20  3/30/20  3/31/20  4/1/20  \n",
       "187     1036     1264     1534     1836     2337    2777  \n",
       "\n",
       "[1 rows x 75 columns]"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "covid19_confirmed[covid19_confirmed['Country/Region']=='Russia']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Скопируем данные для России, получим три `numpy`-массива:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "Russia_confirmed = np.array(covid19_confirmed[covid19_confirmed['Country/Region']=='Russia'].iloc[0,4:], dtype=float)\n",
    "Russia_deaths    = np.array(covid19_deaths[   covid19_deaths[   'Country/Region']=='Russia'].iloc[0,4:], dtype=float)\n",
    "Russia_recovered = np.array(covid19_recovered[covid19_recovered['Country/Region']=='Russia'].iloc[0,4:], dtype=float)   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Следующие заклинания переводят дату из американского формата (месяц/число/год) в более привычный: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "dates = covid19_confirmed.columns[4:]\n",
    "dates = np.array([datetime.datetime.strptime(x, '%m/%d/%y').strftime('%d/%m') for x in dates])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Визуализируем и анализируем данные"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "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": [
    "T = len(Russia_confirmed)\n",
    "t = np.arange(T)\n",
    "plt.plot(t, Russia_confirmed, 'o')\n",
    "plt.xticks(t[0::10], dates[0::10])\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Наблюдается экспоненциальный рост. Удобнее использовать полулогарифмический масштаб: обычный линейный по горизонтальной оси и логарифмический по вертикальной."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "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": [
    "plt.semilogy(t, Russia_confirmed, 'o')\n",
    "plt.xticks(t[0::10], dates[0::10])\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Начиная примерно с 6 марта данные расположились вдоль прямой, что говорит об экспоненциальном росте. Это закономерное развитие эпидемии.\n",
    "\n",
    "Выделим эти данные. Вначале найдем индекс, соответствующий дате 6 марта:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([44], dtype=int64),)"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.where(dates=='06/03')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Выделяем данные с 44 позиции:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "C = Russia_confirmed[44:]\n",
    "D = Russia_deaths[44:]\n",
    "R = Russia_recovered[44:]\n",
    "I = Russia_confirmed[44:] - Russia_deaths[43:-1] - Russia_recovered[43:-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`C`, `D`, `R` - это массивы, содержащие количества подтвержденных случаев, смертей и количество выздоровевших на каждый день.\n",
    "\n",
    "`I` - количество зарегистрированных инфицированных.\n",
    "\n",
    "Теперь можем изобразить эти данные:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "T = len(C)\n",
    "t = np.arange(T)\n",
    "dates = dates[44:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "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": [
    "plt.semilogy(C, label='Confirmed')\n",
    "plt.semilogy(I, label='Infected')\n",
    "plt.semilogy(R, label='Recovered')\n",
    "plt.semilogy(D, label='Deaths')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.xticks(t[0::5], dates[0::5])\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Графики `C` и `I` практически совпадают (особенно в логарифмическом масштабе), так как в начале эпидемии еще мало выздоровевших"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Настройка параметров модели\n",
    "\n",
    "Как уже отмечалось, количество зараженных `I` (и количество новых случаев `С`) в начале эпидемии растет экспоненциально: \n",
    "\n",
    "$$\n",
    "I = I_0 e^{\\alpha t}. \\tag{$*$}\n",
    "$$\n",
    "\n",
    "Параметры $I_0$ и $\\alpha$ это *модели экспоненциального роста* подберем по данным.\n",
    "\n",
    "Рассмотрим два подхода.\n",
    "\n",
    "### 4.1. Сведение к линейной задаче наименьших квадратов\n",
    "\n",
    "Параметр $\\alpha$ входит в модель нелинейно, поэтому напрямую метод наименьших квадратов в данном случае применить нельзя. Однако, прологарифмировав уравнение ($*$), получаем\n",
    "$$\n",
    "\\ln I = \\ln I_0 + \\alpha t.\n",
    "$$\n",
    "Обозначим\n",
    "$$\n",
    "y = \\ln I, \\qquad y_0 = \\ln I_0.\n",
    "$$\n",
    "Теперь зависимость выглядит так:\n",
    "$$\n",
    "y = y_0 + \\alpha t.\n",
    "$$\n",
    "Теперь неизвестные параметры входят линейно.\n",
    "Найдем из методом наименьших квадратов с помощью функции `polyfit`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.22691027342592582, 2.118752495738248)"
      ]
     },
     "execution_count": 85,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "alpha, y0 = np.polyfit(t, np.log(I), 1)\n",
    "alpha, y0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "8.320750838208339"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "I0 = np.exp(y0)\n",
    "I0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Изобразим график построенной линейной зависимости:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "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": [
    "tt = np.linspace(0, T, 500)\n",
    "II = I0*np.exp(alpha*tt)\n",
    "plt.semilogy(tt, II)\n",
    "plt.semilogy(t, I, 'o')\n",
    "plt.grid()\n",
    "plt.xticks(t[0::5], dates[0::5])\n",
    "\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2 Нейлинейный метод наименьших квадратов\n",
    "\n",
    "Другой способ подобрать значения параметров в зависимости ($*$) - использовать *нелинейный метод наименьших квадратов*.\n",
    "\n",
    "Как и в линейном методе наименьших квадратов, будем минимизировать сумму квадратов невязок - отклонений предсказанного значения от истинного:\n",
    "$$\n",
    "\\sum_{t=0}^{N-1} \\left(I_0 e^{\\alpha t} - I[t]\\right)^2 \\to \\min\n",
    "$$\n",
    "где $I[t]$ - количество инфицированных в $t$-й день. Теперь, к сожалению, полученная задача минимизации не сводится к решению системы линейных уравнений (как в линейном методе наименьших квадратов), а решается численными методами.\n",
    "\n",
    "Нелинейный метод найименьших квадратов реализован в функции `curve_fit` модуля `numpy.optimize`.\n",
    "\n",
    "Вначале нужно создать функцию, реализующую искому зависимость:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "def exponential_growth(t, I0, alpha):\n",
    "    return I0 * np.exp(alpha*t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Теперь вызываем модуль `curve_fit`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "params, _ = optimize.curve_fit(exponential_growth, t, I)\n",
    "I0, alpha = params"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(13.387593297973238, 0.20400995150564402)"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "I0, alpha"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Значения параметров $\\alpha$, найденные двумя способами, близки друг к другу.\n",
    "Значения параметров $I_0$ отличаются заметнее.\n",
    "\n",
    "Изобразим график зависимости, построенной вторым способом:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "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": [
    "tt = np.linspace(0, T, 500)\n",
    "II = exponential_growth(tt, I0, alpha)\n",
    "plt.semilogy(tt, II)\n",
    "plt.semilogy(t, I, 'o')\n",
    "plt.grid()\n",
    "plt.xticks(t[0::5], dates[0::5])\n",
    "\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Конечно же, для больш*и*х значений $I$ второй метод аппроксимирует данные лучше, чем первый метод.\n",
    "\n",
    "Построенную зависимость можно использовать для предсказания развития эпидемии на ее начальном этапе.\n",
    "\n",
    "В частности, делаем вывод, что сейчас каждые сутки количество зарегистрированных инфицированных увеличивается примерно на 23%: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.22631035702992786"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(alpha) - 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Это примерно такое же (или даже меньшее) значение, как было в начале эпидемии в Италии, США и некоторых других странах. Введение карантина должно снизить эту скорость. Заметим, что если карантин не вводить, то экспоненциальный рост все равно прекратится и эпидемия закончится. Но карантин и другие меры сгладит эпидемиологическую кривую и уменьшит общее количество переболевших и количество больных в пик эпидемии, что очень важно. Карантин в России введен на более ранней стадии, чем в других странах.\n",
    "\n",
    "По найденному параметру $\\alpha$ можно оценить *интенсивность заражения* $\\beta$ и *базовое репродуктивное число* $R_0$, если известна интенсивность выздоравливания $\\gamma$.\n",
    "\n",
    "$R0$ – среднее количество людей, инфицированных одним больным, если все контактные были восприимчивы;\n",
    "$\\beta$ – количество людей, инфицированных одним инфицированным человеком за единицу времени (за день)\n",
    "$\\gamma$ – доля от общего числа инфицированных, выздоровевших или умерших за сутки.\n",
    "\n",
    "Например, если болезнь длится $8$ дней, то $\\gamma = 1/8$.\n",
    "\n",
    "$$\n",
    "R_0 = \\frac{\\beta}{\\gamma} = 1+ \\frac{\\alpha}{\\gamma}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.6320796120451524"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gamma = 1/8\n",
    "R0 = 1 + alpha/gamma\n",
    "R0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Зная найденный параметры, можно смоделировать дальнеший ход эпидемии, используя модель SIR и различные ее уточнения."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
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  "language_info": {
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    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
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