Covid19_Loglet_knime_Tableau_github.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy.optimize import curve_fit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "path = 'https://raw.githubusercontent.com/deganza/Loglet-analysis-revisiting-covid19-projections/main/covid_daten_knime.csv'\n",
    "df_country = pd.read_csv(path)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_country_exp = pd.DataFrame()\n",
    "\n",
    "df_country_list = df_country.groupby(['Country']).last().reset_index()\n",
    "country_list = df_country_list['Country'].to_list()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "#df_country_period = df_country[df_country['df_days'] <= 360]\n",
    "df_country_period = df_country\n",
    "zeilen = df_country_period['cases'].count()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Continent</th>\n",
       "      <th>Country</th>\n",
       "      <th>Lat</th>\n",
       "      <th>Long</th>\n",
       "      <th>Date</th>\n",
       "      <th>cases</th>\n",
       "      <th>deaths</th>\n",
       "      <th>cases_lastday</th>\n",
       "      <th>deaths_lastday</th>\n",
       "      <th>increase_cases</th>\n",
       "      <th>increase_deaths</th>\n",
       "      <th>increase_cases_lastday</th>\n",
       "      <th>increase_cases_proz</th>\n",
       "      <th>Max_Date</th>\n",
       "      <th>actual_day</th>\n",
       "      <th>df_days</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Asia</td>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>33.939110</td>\n",
       "      <td>67.709953</td>\n",
       "      <td>2020-01-22</td>\n",
       "      <td>0</td>\n",
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       "      <td>2021-01-02</td>\n",
       "      <td>0</td>\n",
       "      <td>346</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Asia</td>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>33.939110</td>\n",
       "      <td>67.709953</td>\n",
       "      <td>2020-01-23</td>\n",
       "      <td>0</td>\n",
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       "      <td>2021-01-02</td>\n",
       "      <td>0</td>\n",
       "      <td>345</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Asia</td>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>33.939110</td>\n",
       "      <td>67.709953</td>\n",
       "      <td>2020-01-24</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>2021-01-02</td>\n",
       "      <td>0</td>\n",
       "      <td>344</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Asia</td>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>33.939110</td>\n",
       "      <td>67.709953</td>\n",
       "      <td>2020-01-25</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>0.000000</td>\n",
       "      <td>2021-01-02</td>\n",
       "      <td>0</td>\n",
       "      <td>343</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Asia</td>\n",
       "      <td>Afghanistan</td>\n",
       "      <td>33.939110</td>\n",
       "      <td>67.709953</td>\n",
       "      <td>2020-01-26</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>0.000000</td>\n",
       "      <td>2021-01-02</td>\n",
       "      <td>0</td>\n",
       "      <td>342</td>\n",
       "    </tr>\n",
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       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74600</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Zimbabwe</td>\n",
       "      <td>-19.015438</td>\n",
       "      <td>29.154857</td>\n",
       "      <td>2020-12-29</td>\n",
       "      <td>13325</td>\n",
       "      <td>359</td>\n",
       "      <td>13148</td>\n",
       "      <td>354</td>\n",
       "      <td>177</td>\n",
       "      <td>5</td>\n",
       "      <td>71</td>\n",
       "      <td>1.492958</td>\n",
       "      <td>2021-01-02</td>\n",
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       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74601</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Zimbabwe</td>\n",
       "      <td>-19.015438</td>\n",
       "      <td>29.154857</td>\n",
       "      <td>2020-12-30</td>\n",
       "      <td>13625</td>\n",
       "      <td>360</td>\n",
       "      <td>13325</td>\n",
       "      <td>359</td>\n",
       "      <td>300</td>\n",
       "      <td>1</td>\n",
       "      <td>177</td>\n",
       "      <td>0.694915</td>\n",
       "      <td>2021-01-02</td>\n",
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       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74602</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Zimbabwe</td>\n",
       "      <td>-19.015438</td>\n",
       "      <td>29.154857</td>\n",
       "      <td>2020-12-31</td>\n",
       "      <td>13867</td>\n",
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       "      <td>2021-01-02</td>\n",
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       "    <tr>\n",
       "      <th>74603</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Zimbabwe</td>\n",
       "      <td>-19.015438</td>\n",
       "      <td>29.154857</td>\n",
       "      <td>2021-01-01</td>\n",
       "      <td>14084</td>\n",
       "      <td>369</td>\n",
       "      <td>13867</td>\n",
       "      <td>363</td>\n",
       "      <td>217</td>\n",
       "      <td>6</td>\n",
       "      <td>242</td>\n",
       "      <td>-0.103306</td>\n",
       "      <td>2021-01-02</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>74604</th>\n",
       "      <td>Africa</td>\n",
       "      <td>Zimbabwe</td>\n",
       "      <td>-19.015438</td>\n",
       "      <td>29.154857</td>\n",
       "      <td>2021-01-02</td>\n",
       "      <td>14491</td>\n",
       "      <td>377</td>\n",
       "      <td>14084</td>\n",
       "      <td>369</td>\n",
       "      <td>407</td>\n",
       "      <td>8</td>\n",
       "      <td>217</td>\n",
       "      <td>0.875576</td>\n",
       "      <td>2021-01-02</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>74605 rows × 16 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "      Continent      Country        Lat       Long        Date  cases  deaths  \\\n",
       "0          Asia  Afghanistan  33.939110  67.709953  2020-01-22      0       0   \n",
       "1          Asia  Afghanistan  33.939110  67.709953  2020-01-23      0       0   \n",
       "2          Asia  Afghanistan  33.939110  67.709953  2020-01-24      0       0   \n",
       "3          Asia  Afghanistan  33.939110  67.709953  2020-01-25      0       0   \n",
       "4          Asia  Afghanistan  33.939110  67.709953  2020-01-26      0       0   \n",
       "...         ...          ...        ...        ...         ...    ...     ...   \n",
       "74600    Africa     Zimbabwe -19.015438  29.154857  2020-12-29  13325     359   \n",
       "74601    Africa     Zimbabwe -19.015438  29.154857  2020-12-30  13625     360   \n",
       "74602    Africa     Zimbabwe -19.015438  29.154857  2020-12-31  13867     363   \n",
       "74603    Africa     Zimbabwe -19.015438  29.154857  2021-01-01  14084     369   \n",
       "74604    Africa     Zimbabwe -19.015438  29.154857  2021-01-02  14491     377   \n",
       "\n",
       "       cases_lastday  deaths_lastday  increase_cases  increase_deaths  \\\n",
       "0                  0               0               0                0   \n",
       "1                  0               0               0                0   \n",
       "2                  0               0               0                0   \n",
       "3                  0               0               0                0   \n",
       "4                  0               0               0                0   \n",
       "...              ...             ...             ...              ...   \n",
       "74600          13148             354             177                5   \n",
       "74601          13325             359             300                1   \n",
       "74602          13625             360             242                3   \n",
       "74603          13867             363             217                6   \n",
       "74604          14084             369             407                8   \n",
       "\n",
       "       increase_cases_lastday  increase_cases_proz    Max_Date  actual_day  \\\n",
       "0                           0             0.000000  2021-01-02           0   \n",
       "1                           0             0.000000  2021-01-02           0   \n",
       "2                           0             0.000000  2021-01-02           0   \n",
       "3                           0             0.000000  2021-01-02           0   \n",
       "4                           0             0.000000  2021-01-02           0   \n",
       "...                       ...                  ...         ...         ...   \n",
       "74600                      71             1.492958  2021-01-02           0   \n",
       "74601                     177             0.694915  2021-01-02           0   \n",
       "74602                     300            -0.193333  2021-01-02           0   \n",
       "74603                     242            -0.103306  2021-01-02           0   \n",
       "74604                     217             0.875576  2021-01-02           1   \n",
       "\n",
       "       df_days  \n",
       "0          346  \n",
       "1          345  \n",
       "2          344  \n",
       "3          343  \n",
       "4          342  \n",
       "...        ...  \n",
       "74600        4  \n",
       "74601        3  \n",
       "74602        2  \n",
       "74603        1  \n",
       "74604        0  \n",
       "\n",
       "[74605 rows x 16 columns]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_country_period"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Switzerland 4\n",
      "finished\n",
      "347\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# Select country or for evaluation of every country remark the variable country_list\n",
    "\n",
    "\n",
    "#country_list =['Austria','Switzerland','Germany','United Kingdom','Spain']\n",
    "#country_list =['United Kingdom']\n",
    "#country_list =['Germany']\n",
    "#country_list =['Spain']\n",
    "country_list =['Switzerland']\n",
    "#country_list =['Poland']\n",
    "#country_list =['Turkey']\n",
    "#country_list =['US']\n",
    "\n",
    "\n",
    "df_country_exp = pd.DataFrame()\n",
    "\n",
    "#logistic functions\n",
    "\n",
    "def logistic_function1(x,b1,dt1,K1,b2,dt2,K2,b3,dt3,K3,b4,dt4,K4):\n",
    "    return K1/(1+np.exp(-np.log2(81)/dt1*(x-b1)))\n",
    "\n",
    "def logistic_function2(x,b1,dt1,K1,b2,dt2,K2,b3,dt3,K3,b4,dt4,K4):\n",
    "    return  K1/(1+np.exp(-np.log2(81)/dt1*(x-b1))) + K2/(1+np.exp(-np.log2(81)/dt2*(x-b2)))\n",
    "\n",
    "def logistic_function3(x,b1,dt1,K1,b2,dt2,K2,b3,dt3,K3,b4,dt4,K4):\n",
    "    return  K1/(1+np.exp(-np.log2(81)/dt1*(x-b1))) + K2/(1+np.exp(-np.log2(81)/dt2*(x-b2))) + K3/(1+np.exp(-np.log2(81)/dt3*(x-b3)))\n",
    "\n",
    "def logistic_function4(x,b1,dt1,K1,b2,dt2,K2,b3,dt3,K3,b4,dt4,K4):\n",
    "    return  K1/(1+np.exp(-np.log2(81)/dt1*(x-b1))) + K2/(1+np.exp(-np.log2(81)/dt2*(x-b2))) + K3/(1+np.exp(-np.log2(81)/dt3*(x-b3))) + K4/(1+np.exp(-np.log2(81)/dt4*(x-b4)))\n",
    "\n",
    "\n",
    "for country in country_list:\n",
    "\n",
    "        df_country_modell = df_country_period[df_country['Country'] == country]\n",
    "     \n",
    "        expdays = 30\n",
    "        wave = 0\n",
    "\n",
    "        datum = pd.date_range(start=df_country_modell['Date'].max(), periods=expdays)\n",
    "        datum = pd.date_range(start=df_country_modell['Date'].min(),end=datum.max())\n",
    "        datum = datum.strftime(\"%Y-%m-%d\")\n",
    "                   \n",
    "        zeilen= df_country_modell['cases'].count()\n",
    "        x = np.arange(1,zeilen+1)\n",
    "        x_exp = np.arange(1, x.max() + expdays  )\n",
    "        y = df_country_modell['cases'] \n",
    "        \n",
    "        y_min = y.min()\n",
    "        y = y - y_min\n",
    "        \n",
    "              \n",
    "        try:   \n",
    "            popt, pcov = curve_fit(logistic_function4, x, y  )\n",
    "            y_exp = (logistic_function4(x_exp, *popt))    \n",
    "            \n",
    "            df = pd.DataFrame({'day':x_exp, 'expected':y_exp,'datum':datum, 'Country' : country})\n",
    "            df_country_exp = df_country_exp.append(df)\n",
    "            \n",
    "            wave=4\n",
    "            print(country,wave)\n",
    "    \n",
    "        except RuntimeError:\n",
    "            try:\n",
    "                popt, pcov = curve_fit(logistic_function3, x, y  )\n",
    "                y_exp = (logistic_function3(x_exp, *popt)) \n",
    "    \n",
    "                df = pd.DataFrame({'day':x_exp, 'expected':y_exp,'datum':datum, 'Country' : country})\n",
    "                df_country_exp = df_country_exp.append(df)\n",
    "                \n",
    "                wave=3\n",
    "                print(country,wave)\n",
    "                \n",
    "            except RuntimeError:\n",
    "                try:\n",
    "                    popt, pcov = curve_fit(logistic_function2, x, y  )\n",
    "                    y_exp = (logistic_function2(x_exp, *popt)) \n",
    "    \n",
    "                    df = pd.DataFrame({'day':x_exp, 'expected':y_exp,'datum':datum, 'Country' : country})\n",
    "                    df_country_exp = df_country_exp.append(df)\n",
    "                \n",
    "                    wave=2\n",
    "                    print(country,wave)\n",
    "                  \n",
    "                except RuntimeError:\n",
    "                    try:\n",
    "                        popt, pcov = curve_fit(logistic_function1, x, y  )\n",
    "                        y_exp = (logistic_function2(x_exp, *popt)) \n",
    "    \n",
    "                        df = pd.DataFrame({'day':x_exp, 'expected':y_exp,'datum':datum, 'Country' : country})\n",
    "                        df_country_exp = df_country_exp.append(df)\n",
    "                \n",
    "                        wave=1\n",
    "                        print(country,wave)    \n",
    "                                   \n",
    "                    except RuntimeError:\n",
    "                        print(''.join(country) +  \": Error - curve_fit Log failed\")\n",
    " \n",
    "            \n",
    "df_country_exp.reset_index(drop=True, inplace=True)\n",
    "print('finished')\n",
    "print(zeilen)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x,y)\n",
    "plt.plot(x_exp,y_exp)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\degan\\anaconda3\\lib\\site-packages\\pandas\\core\\series.py:679: RuntimeWarning: divide by zero encountered in log2\n",
      "  result = getattr(ufunc, method)(*inputs, **kwargs)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1ac30fcedc0>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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.plot(x,np.log2(y))\n",
    "plt.plot((x_exp), np.log2(y_exp))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}