epidemic_model.ipynb

{
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  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Model the spread of disease:\n",
    "\n",
    "1. Susceptible: those who have never had the illness and can catch it;\n",
    "2. Infected: those who currently have the illness and are contagious;\n",
    "3. Recovered: those who have already had the illness and are immune\n",
    "\n",
    "a: transmission coefficient; depends on the general health for all populations and the level of social interaction\n",
    "b: depends on the illness involved(I->R)\n",
    "\n",
    "1. S'=-aSI\n",
    "2. I'=aSI-bI\n",
    "3. R'=bI"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "#intial condition\n",
    "S=45400\n",
    "I=2100\n",
    "R=2500\n",
    "a=0.00001\n",
    "b=1/14\n",
    "def S_change(a,S,I):\n",
    "    return -a*S*I\n",
    "\n",
    "def I_change(a,b,S,I):\n",
    "    return a*S*I-b*I\n",
    "\n",
    "def R_change(b,I):\n",
    "    return b*I"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>S</th>\n",
       "      <th>I</th>\n",
       "      <th>R</th>\n",
       "      <th>S'</th>\n",
       "      <th>I'</th>\n",
       "      <th>R'</th>\n",
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       "      <th>0</th>\n",
       "      <td>45400.0</td>\n",
       "      <td>2100.0</td>\n",
       "      <td>2500.0</td>\n",
       "      <td>-953.4</td>\n",
       "      <td>803.4</td>\n",
       "      <td>150.0</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
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      "text/plain": [
       "         S       I       R     S'     I'     R'\n",
       "0  45400.0  2100.0  2500.0 -953.4  803.4  150.0\n",
       "1      0.0     0.0     0.0    0.0    0.0    0.0\n",
       "2      0.0     0.0     0.0    0.0    0.0    0.0\n",
       "3      0.0     0.0     0.0    0.0    0.0    0.0"
      ]
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     "execution_count": 18,
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   "source": [
    "df_future=pd.DataFrame(np.zeros((4,6)),columns=['S','I','R',\"S'\",\"I'\",\"R'\"])\n",
    "df_future.iloc[0]=S,I,R,S_change(a,S,I),I_change(a,b,S,I),R_change(b,I)\n",
    "df_future"
   ]
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  {
   "cell_type": "code",
   "execution_count": 19,
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   "outputs": [
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       "      <th></th>\n",
       "      <th>S</th>\n",
       "      <th>I</th>\n",
       "      <th>R</th>\n",
       "      <th>S'</th>\n",
       "      <th>I'</th>\n",
       "      <th>R'</th>\n",
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       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>45400.000000</td>\n",
       "      <td>2100.000000</td>\n",
       "      <td>2500.000000</td>\n",
       "      <td>-953.400000</td>\n",
       "      <td>803.400000</td>\n",
       "      <td>150.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>44446.600000</td>\n",
       "      <td>2903.400000</td>\n",
       "      <td>2650.000000</td>\n",
       "      <td>-1290.462584</td>\n",
       "      <td>1083.076870</td>\n",
       "      <td>207.385714</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>43156.137416</td>\n",
       "      <td>3986.476870</td>\n",
       "      <td>2857.385714</td>\n",
       "      <td>-1720.409436</td>\n",
       "      <td>1435.661088</td>\n",
       "      <td>284.748348</td>\n",
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       "      <td>5422.137958</td>\n",
       "      <td>3142.134062</td>\n",
       "      <td>-2246.702335</td>\n",
       "      <td>1859.406767</td>\n",
       "      <td>387.295568</td>\n",
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       "              S            I            R           S'           I'  \\\n",
       "0  45400.000000  2100.000000  2500.000000  -953.400000   803.400000   \n",
       "1  44446.600000  2903.400000  2650.000000 -1290.462584  1083.076870   \n",
       "2  43156.137416  3986.476870  2857.385714 -1720.409436  1435.661088   \n",
       "3  41435.727979  5422.137958  3142.134062 -2246.702335  1859.406767   \n",
       "\n",
       "           R'  \n",
       "0  150.000000  \n",
       "1  207.385714  \n",
       "2  284.748348  \n",
       "3  387.295568  "
      ]
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     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "for i in range(1,4):\n",
    "    S_updated=df_future.iloc[i-1]['S']+df_future.iloc[i-1][\"S'\"]*1\n",
    "    I_updated=df_future.iloc[i-1]['I']+df_future.iloc[i-1][\"I'\"]*1\n",
    "    R_updated=df_future.iloc[i-1]['R']+df_future.iloc[i-1][\"R'\"]*1\n",
    "    Sp_updated=S_change(a,S_updated,I_updated)\n",
    "    Ip_updated=I_change(a,b,S_updated,I_updated)\n",
    "    Rp_updated=R_change(b,I_updated)\n",
    "    df_future.iloc[i]=S_updated,I_updated,R_updated,Sp_updated,Ip_updated,Rp_updated\n",
    "\n",
    "df_future"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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