Model.ipynb

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       "<script>\n",
       "    // AUTORUN ALL CELLS ON NOTEBOOK-LOAD!\n",
       "    require(\n",
       "        ['base/js/namespace', 'jquery'], \n",
       "        function(jupyter, $) {\n",
       "            $(jupyter.events).on(\"kernel_ready.Kernel\", function () {\n",
       "                console.log(\"Auto-running all cells-below...\");\n",
       "                jupyter.actions.call('jupyter-notebook:run-all-cells-below');\n",
       "                jupyter.actions.call('jupyter-notebook:save-notebook');\n",
       "            });\n",
       "        }\n",
       "    );\n",
       "</script>\n"
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      "text/plain": [
       "<IPython.core.display.HTML object>"
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     "metadata": {},
     "output_type": "display_data"
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   "source": [
    "%%html\n",
    "<script>\n",
    "    // AUTORUN ALL CELLS ON NOTEBOOK-LOAD!\n",
    "    require(\n",
    "        ['base/js/namespace', 'jquery'], \n",
    "        function(jupyter, $) {\n",
    "            $(jupyter.events).on(\"kernel_ready.Kernel\", function () {\n",
    "                console.log(\"Auto-running all cells-below...\");\n",
    "                jupyter.actions.call('jupyter-notebook:run-all-cells-below');\n",
    "                jupyter.actions.call('jupyter-notebook:save-notebook');\n",
    "            });\n",
    "        }\n",
    "    );\n",
    "</script>"
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  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<script>\n",
       "code_show=true; \n",
       "function code_toggle() {\n",
       " if (code_show){\n",
       " $('div.input').hide();\n",
       " } else {\n",
       " $('div.input').show();\n",
       " }\n",
       " code_show = !code_show\n",
       "} \n",
       "$( document ).ready(code_toggle);\n",
       "</script>\n",
       "<form action=\"javascript:code_toggle()\"><input type=\"submit\" value=\"Click here to toggle on/off the raw code.\"></form>"
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      "text/plain": [
       "<IPython.core.display.HTML object>"
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     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "from IPython.display import HTML\n",
    "\n",
    "HTML('''<script>\n",
    "code_show=true; \n",
    "function code_toggle() {\n",
    " if (code_show){\n",
    " $('div.input').hide();\n",
    " } else {\n",
    " $('div.input').show();\n",
    " }\n",
    " code_show = !code_show\n",
    "} \n",
    "$( document ).ready(code_toggle);\n",
    "</script>\n",
    "<form action=\"javascript:code_toggle()\"><input type=\"submit\" value=\"Click here to toggle on/off the raw code.\"></form>''')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "from tqdm import tqdm\n",
    "import ipywidgets as widgets\n",
    "from ipywidgets import interact, interactive, fixed, interact_manual, interactive_output, Layout\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import odeint\n",
    "from scipy import optimize\n",
    "from IPython.display import display\n",
    "from matplotlib.gridspec import GridSpec\n",
    "\n",
    "\n",
    "import matplotlib\n",
    "matplotlib.rcParams.update({'font.size': 22})\n",
    "\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Basic SIR model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "58d971c6282946e1b39d3b5f9bf194f0",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Button(description='Reset', style=ButtonStyle())"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "cb18660799ea4161bf24844615cc8000",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=1.75, continuous_update=False, description='Transmission Rate', max=2.…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# def get_rate_of_change(SIRvals, t, InitVals):\n",
    "def get_rate_of_change(y, t, beta, gamma):\n",
    "    S, I, R = y\n",
    "    dydt = [-beta*S*I, beta*S*I - gamma*I, gamma*I]\n",
    "    return dydt\n",
    "\n",
    "\n",
    "def plot_func(beta,gamma, N, I0, tmax, data, logscale_y=False):\n",
    "    fig=plt.figure(figsize=[12,6])\n",
    "    gs=GridSpec(3,2) # 2 rows, 3 columns\n",
    "\n",
    "    ax1=fig.add_subplot(gs[0,1]) # First row, first column\n",
    "    ax2=fig.add_subplot(gs[1,1]) # First row, second column\n",
    "    ax3=fig.add_subplot(gs[2,1]) # First row, third column\n",
    "    ax4=fig.add_subplot(gs[:,0]) # Second row, span all columns\n",
    "\n",
    "        \n",
    "    for ax in [ax1,ax2,ax3]:\n",
    "        ax.yaxis.tick_right()\n",
    "        ax.yaxis.set_label_position(\"right\")\n",
    "    \n",
    "    ax4.set_xlabel('t')\n",
    "    ax4.set_ylabel(\"Number of Cases\")\n",
    "    ax4.grid()\n",
    "    \n",
    "    ax1.set_ylabel(\"Surceptible\")\n",
    "    ax2.set_ylabel(\"Infected\")\n",
    "    ax3.set_ylabel(\"Recovered\")\n",
    "\n",
    "    ax4.text(0.5,0.9,\"$R_0={0:.1f}$\".format(beta/gamma),transform=ax4.transAxes)\n",
    "    fig.subplots_adjust(wspace=0, hspace=0.06)\n",
    "    \n",
    "    \n",
    "    t = np.linspace(0, tmax, tmax*100)\n",
    "    S0 = N-I0\n",
    "    R0 = 0\n",
    "    D0 = 0\n",
    "\n",
    "    y0 = [S0/N,I0/N,R0/N]\n",
    "    \n",
    "    sol = odeint(get_rate_of_change, y0, t, args=(beta,gamma))\n",
    "    \n",
    "    \n",
    "    ax1.plot(t, sol[:, 0]*N, 'b', label='Surceptible({0:.2f}%)'.format(sol[:, 0][-1]*100))\n",
    "    ax2.plot(t, sol[:, 1]*N, 'r', label='Infected({0:.2f}%)'.format(sol[:, 1][-1]*100))\n",
    "    ax3.plot(t, sol[:, 2]*N, 'g', label='Recovered ({0:.2f}%)'.format(sol[:, 2][-1]*100))\n",
    "    ax4.plot(t, sol[:, 0]*N, 'b', label='Surceptible({0:.2f}%)'.format(sol[:, 0][-1]*100))\n",
    "    ax4.plot(t, sol[:, 1]*N, 'r', label='Infected({0:.2f}%)'.format(sol[:, 1][-1]*100))\n",
    "    ax4.plot(t, sol[:, 2]*N, 'g', label='Recovered ({0:.2f}%)'.format(sol[:, 2][-1]*100))\n",
    "    \n",
    "    for ax in [ax1,ax2]:\n",
    "        ax.legend(loc='upper right', frameon=True)\n",
    "    ax3.legend(loc='lower right', frameon=True)\n",
    "        \n",
    "    \n",
    "    \n",
    "    \n",
    "    try:\n",
    "        data = pd.read_csv(\"Data/\"+data+\".txt\")\n",
    "        data[\"Infected\"] = data.TotalInfected.diff()\n",
    "        ydata = data.Infected.values[1:]\n",
    "        xdata = data.Day.values[1:] - data.Day.values[1]\n",
    "        ax2.plot(xdata, ydata, 'o')\n",
    "    except:\n",
    "        pass\n",
    "    \n",
    "    if logscale_y: \n",
    "        ax4.set_ylim([1,None])\n",
    "        ax4.set_yscale(\"log\")\n",
    "\n",
    "    \n",
    "\n",
    "dashboard_SIR = interactive(plot_func, \n",
    "         N = widgets.IntText(value=130000, min=10, continuous_update=True,\n",
    "                                    description =\"Population Size\",\n",
    "                                    style={'description_width': 'initial'}),\n",
    "         I0 = widgets.IntText(value=18, min=0,  continuous_update=True,\n",
    "                                    description = \"Initial Infected Population\", \n",
    "                                    style={'description_width': 'initial'}),\n",
    "         beta = widgets.FloatSlider(value=1.75,\n",
    "                                   min=0,\n",
    "                                   max=2.0,\n",
    "                                   step=0.01,continuous_update=False, description=\"Transmission Rate\",\n",
    "                                   style={'description_width': 'initial'}),\n",
    "                    \n",
    "         gamma = widgets.FloatSlider(value=1.55,\n",
    "                                   min=0,\n",
    "                                   max=2.0,\n",
    "                                   step=0.01,continuous_update=False, description=\"Recovery Rate\",\n",
    "                                   style={'description_width': 'initial'}),\n",
    "         tmax = widgets.IntSlider(value=60, min = 1 , max= 150, continuous_update=False, description = \"Time\"),\n",
    "         data = widgets.Dropdown(options=[\"None\",\"SouthKorea\"], value=\"SouthKorea\",description=\"Select Country\",\n",
    "                                style={'description_width': 'initial'})\n",
    "        )\n",
    "\n",
    "init_state  = [i.value for i in dashboard_SIR.children[:-1]].copy()\n",
    "\n",
    "\n",
    "def reset_values(a):\n",
    "    for i, item in enumerate(dashboard_SIR.children[:-1]): \n",
    "        item.value = init_state[i]\n",
    "    \n",
    "reset_button = widgets.Button(description= \"Reset\")\n",
    "\n",
    "reset_button.on_click(reset_values)\n",
    "display(reset_button)\n",
    "display(dashboard_SIR)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# SIR model with deaths"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(VBox(children=(FloatSlider(value=10.0, continuous_update=False, description='Contact Number', m…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Button(description='Reset', style=ButtonStyle())"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "Output()"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# def get_rate_of_change(SIRvals, t, InitVals):\n",
    "def get_rate_of_change_with_deaths(y, t, beta, gamma, omega):\n",
    "    \n",
    "    X, Y, Z, D = y\n",
    "    N = X + Y + Z \n",
    "    \n",
    "    m = omega/float(1-omega)*gamma\n",
    "    dydt = [-beta*X*Y/N, beta*X*Y/N - gamma*Y - m*Y, gamma*Y, m*Y]\n",
    "    return dydt\n",
    "\n",
    "\n",
    "\n",
    "def plot_func(tmax,beta,gamma,omega, N, I0, logscale_x,logscale_y):\n",
    "    N = float(N)\n",
    "    X0 = N-I0\n",
    "    Y0 = I0\n",
    "    Z0 = 0\n",
    "    D0 = 0\n",
    "\n",
    "    y0 = [X0,Y0,Z0,D0]\n",
    "\n",
    "    t = np.linspace(0, tmax, tmax*1000)\n",
    "    omega = omega/100.0\n",
    "    m = omega/float(1-omega)*gamma\n",
    "    \n",
    "    sol = odeint(get_rate_of_change_with_deaths, y0, t, args=(beta,gamma,omega))\n",
    "    \n",
    "    \n",
    "    fig=plt.figure(figsize=[12,6])\n",
    "    gs=GridSpec(4,2) # 2 rows, 3 columns\n",
    "\n",
    "    \n",
    "    ax1=fig.add_subplot(gs[0,1]) # First row, first column\n",
    "    ax2=fig.add_subplot(gs[1,1]) # First row, second column\n",
    "    ax3=fig.add_subplot(gs[2,1]) # First row, third column\n",
    "    ax4=fig.add_subplot(gs[3,1])\n",
    "    ax5=fig.add_subplot(gs[:,0]) # Second row, span all columns\n",
    "\n",
    "\n",
    "        \n",
    "    for ax in [ax1,ax2,ax3,ax4]:\n",
    "        ax.yaxis.tick_right()\n",
    "        ax.yaxis.set_label_position(\"right\")\n",
    "    \n",
    "    ax5.set_xlabel('t')\n",
    "    ax5.set_ylabel(\"Number of Cases\")\n",
    "    ax5.grid()\n",
    "    \n",
    "    ax1.set_ylabel(\"Surceptible\")\n",
    "    ax2.set_ylabel(\"Infected\")\n",
    "    ax3.set_ylabel(\"Recovered\")\n",
    "    ax4.set_ylabel(\"Dead\")\n",
    "    ax4.set_xlabel(\"t\")\n",
    "\n",
    "    ax5.text(0.5,0.9,\"$R_0={0:.1f}$\".format(beta/gamma),transform=ax5.transAxes)\n",
    "    fig.subplots_adjust(wspace=0, hspace=0.06)\n",
    "    \n",
    "    ax5.plot(t, sol[:, 0], 'b', label='Surceptible({})'.format(int(sol[:, 0][-1])))\n",
    "    ax5.plot(t, sol[:, 1], 'r', label='Infected({})'.format(int(sol[:, 1][-1])))\n",
    "    ax5.plot(t, sol[:, 2], 'g', label='Recovered ({})'.format(int(sol[:, 2][-1])))\n",
    "    ax5.plot(t, sol[:, 3], 'k', \\\n",
    "             label='Dead ({0:.2f}%'.format(sol[:, 3][-1]/N*100)+\", {} People\".format(int(sol[:, 3][-1])))\n",
    "\n",
    "    ax1.plot(t, sol[:, 0], 'b', label='Surceptible({})'.format(int(sol[:, 0][-1])))\n",
    "    ax2.plot(t, sol[:, 1], 'r', label='Infected({})'.format(int(sol[:, 1][-1])))\n",
    "    ax3.plot(t, sol[:, 2], 'g', label='Recovered ({})'.format(int(sol[:, 2][-1])))\n",
    "    ax4.plot(t, sol[:, 3], 'k', \\\n",
    "             label='Dead ({0:.2f}%'.format(sol[:, 3][-1]/N*100)+\", {} People\".format(int(sol[:, 3][-1])))\n",
    "    \n",
    "    for ax in [ax1,ax2,ax3,ax4]:\n",
    "        ax.legend(loc=\"center right\", frameon=True)\n",
    "        \n",
    "    ax5.set_ylim([0,None])\n",
    "    if logscale_x: \n",
    "        ax5.set_xscale(\"log\")\n",
    "    if logscale_y: \n",
    "        ax5.set_yscale(\"log\")\n",
    "        ax5.set_ylim([1,None])\n",
    "\n",
    "    ax5.legend(loc='center right', ncol = 1, frameon=True)\n",
    "\n",
    "        \n",
    "\n",
    "ContactNumber = widgets.FloatSlider(value=10, min=0, max=15,step=0.1, continuous_update=False, \n",
    "                                    description=\"Contact Number\",\n",
    "                                    style={'description_width': 'auto'})\n",
    "InfectionProbability = widgets.FloatSlider(value=0.5, min=0, max=1, step=0.01,continuous_update=False,\n",
    "                                    description=\"Infection Probabity\",\n",
    "                                    style={'description_width': 'initial'})\n",
    "\n",
    "def on_value_chage(change):\n",
    "    beta.value = -ContactNumber.value*np.log(1-InfectionProbability.value)\n",
    "    \n",
    "    \n",
    "ContactNumber.observe(on_value_chage, names='value')\n",
    "InfectionProbability.observe(on_value_chage, names='value')\n",
    "\n",
    "beta = widgets.FloatSlider(value=7,\n",
    "                        min=0,\n",
    "                        max=10.0,\n",
    "                        step=0.01,continuous_update=False, description=\"Transmission Rate\",\n",
    "                        style={'description_width': 'initial'})\n",
    "\n",
    "gamma = widgets.FloatSlider(value=1.3,\n",
    "                        min=0,\n",
    "                        max=2.0,\n",
    "                        step=0.01,continuous_update=False, description=\"Recovery Rate\",\n",
    "                        style={'description_width': 'initial'})\n",
    "\n",
    "omega = widgets.FloatSlider(value=5,\n",
    "                        min=0,\n",
    "                        max=99.99,\n",
    "                        step = 0.1,\n",
    "                        continuous_update=False, description=\"Death Rate (%)\",\n",
    "                        style={'description_width': 'initial'})\n",
    "\n",
    "tmax = widgets.IntSlider(value=8, min = 1, max=150, step = 1, \n",
    "                        description=\"Max Time\",continuous_update=False,\n",
    "                        style={'description_width': 'initial'})\n",
    "    \n",
    "N = widgets.IntText(value=1000, min=10, continuous_update=True,\n",
    "                        description =\"Population Size\",\n",
    "                        style={'description_width': 'initial'})\n",
    "    \n",
    "I0 = widgets.IntText(value=1, min=0, continuous_update=True,\n",
    "                        description = \"Initial Infected Population\", \n",
    "                        style={'description_width': 'initial'})\n",
    "    \n",
    "logscale_x  = widgets.Checkbox(value=False, \n",
    "                        description = \"Logscale X axis\", \n",
    "                        style={'description_width': 'initial'})\n",
    "    \n",
    "logscale_y  = widgets.Checkbox(value=False, \n",
    "                        description = \"Logscale Y axis\", \n",
    "                        style={'description_width': 'initial'})\n",
    "            \n",
    "dashboard_elements = {\n",
    "         'beta' : beta,\n",
    "         'gamma' : gamma,\n",
    "         'omega' :omega,\n",
    "         'tmax' : tmax,\n",
    "         'N' : N,\n",
    "         'I0' : I0,\n",
    "         'logscale_x'  : logscale_x,\n",
    "         'logscale_y'  : logscale_y\n",
    "        }\n",
    "dashboard = interactive_output(plot_func, dashboard_elements)\n",
    "\n",
    "init_values  = {key:dashboard_elements[key].value for key in dashboard_elements.keys()}\n",
    "\n",
    "\n",
    "def reset_values(a):\n",
    "    for key in init_values.keys(): \n",
    "        dashboard_elements[key].value = init_values[key] \n",
    "    \n",
    "reset_button = widgets.Button(description= \"Reset\")\n",
    "reset_button.on_click(reset_values)\n",
    "\n",
    "display(widgets.HBox([\n",
    "    widgets.VBox([ContactNumber,InfectionProbability,beta, gamma,omega,tmax]),\n",
    "    widgets.VBox([N,I0,logscale_x,logscale_y])\n",
    "]), reset_button, dashboard)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Agent Based Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(IntText(value=1000, description='Population', style=DescriptionStyle(description_width='…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# def calc_instantaneous_mortality_risk(infected_duration, mortality_risk):\n",
    "#     if infected_duration < 6:\n",
    "#         risk = 0\n",
    "#     elif (infected_duration >=6) and (infected_duration<12):\n",
    "#         risk = (mortality_risk/6.0)*(infected_duration-6)/6.0\n",
    "#     elif (infected_duration >=12) and (infected_duration<18):\n",
    "#         risk = (mortality_risk/6.0)*(18-infected_duration)/6.0\n",
    "#     else:\n",
    "#         risk = 0\n",
    "#     return risk\n",
    "\n",
    "\n",
    "def calc_instantaneous_mortality_risk(infected_duration, mortality_risk,recovery_time):\n",
    "    n = recovery_time/3.0\n",
    "    if infected_duration < n:\n",
    "        risk = 0\n",
    "    elif (infected_duration >=n) and (infected_duration<2*n):\n",
    "        risk = (mortality_risk/n)*(infected_duration-n)/n\n",
    "    elif (infected_duration >=2*n) and (infected_duration<3*n):\n",
    "        risk = (mortality_risk/n)*(3*n-infected_duration)/n\n",
    "    else:\n",
    "        risk = 0\n",
    "    return risk\n",
    "\n",
    "    \n",
    "def prob_toss(p):\n",
    "    return np.random.binomial(1, p)\n",
    "\n",
    "def generate_mean_with_probability(n, var=2):\n",
    "    return max(0,round(np.random.normal(n,var)))\n",
    "\n",
    "\n",
    "def run(N,I0,tmax,average_contact_number,transmission_probability,recovery_time,mortality_risk):\n",
    "    recovery_rate = 1/float(recovery_time)\n",
    "    class citizen:\n",
    "        def __init__(self, infected=False, age=30, infected_duration=0):\n",
    "            self.infected  =  infected\n",
    "            self.recovered = False\n",
    "            self.age = age\n",
    "            self.infected_duration = infected_duration\n",
    "            self.mortality_risk = mortality_risk\n",
    "            self.instantaneous_risk = self.mortality_risk/12\n",
    "            self.dead = False\n",
    "        \n",
    "    #Generate population\n",
    "    population = np.array([citizen() for i in range(N)])\n",
    "\n",
    "    #Infect some people\n",
    "    for i in range(I0):\n",
    "        population[np.random.randint(N)].infected = True\n",
    "\n",
    "    \n",
    "    \n",
    "    \n",
    "    fig=plt.figure(figsize=[18,9])\n",
    "\n",
    "    gs=GridSpec(3,2) # 2 rows, 3 columns\n",
    "\n",
    "    ax1=fig.add_subplot(gs[0,1]) # First row, first column\n",
    "    ax2=fig.add_subplot(gs[1,1]) # First row, second column\n",
    "    ax3=fig.add_subplot(gs[2,1]) # First row, third column\n",
    "    ax4=fig.add_subplot(gs[:,0]) # Second row, span all columns\n",
    "\n",
    "\n",
    "        \n",
    "    for ax in [ax1,ax2,ax3]:\n",
    "        ax.yaxis.tick_right()\n",
    "        ax.yaxis.set_label_position(\"right\")\n",
    "    \n",
    "    fig.subplots_adjust(wspace=0, hspace=0.06)\n",
    "    \n",
    "    D_vals, I_vals, R_vals = [] ,[],[]\n",
    "    tlist = range(tmax)\n",
    "    for t in tqdm(tlist):\n",
    "        for p in population:\n",
    "            if ((not p.infected) or (p.dead)):\n",
    "                pass\n",
    "            else:\n",
    "                contact_number = generate_mean_with_probability(average_contact_number) \n",
    "                contacts = population[[np.random.randint(N) for i in range(contact_number)]]\n",
    "                for contact in contacts:\n",
    "                    if (contact.infected==False) and (contact.recovered==False) and (contact.dead==False):\n",
    "                        if prob_toss(transmission_probability)==1:\n",
    "                            contact.infected = True\n",
    "\n",
    "                p.instantaneous_risk = calc_instantaneous_mortality_risk(p.infected_duration, p.mortality_risk, recovery_time)\n",
    "                \n",
    "                if prob_toss(p.instantaneous_risk)==1:\n",
    "                    p.dead = True\n",
    "\n",
    "                if not p.dead:\n",
    "                    p.infected_duration += 1\n",
    "                    if prob_toss(recovery_rate)==1: \n",
    "                        p.recovered = True\n",
    "                        p.infected  = False\n",
    "\n",
    "\n",
    "        I_t = len([i.infected for i in population if i.infected])\n",
    "        R_t = len([i.recovered for i in population if i.recovered])\n",
    "        D_t = len([i.dead for i in population if i.dead])\n",
    "        \n",
    "        I_vals.append(I_t)\n",
    "        R_vals.append(R_t)\n",
    "        D_vals.append(D_t)\n",
    "        \n",
    "        ax1.plot(t,I_t,'yo')\n",
    "        ax2.plot(t,R_t,'go')\n",
    "        ax3.plot(t,D_t,'ro')\n",
    "        \n",
    "        \n",
    "        ax4.plot(t,I_t,'yo')\n",
    "        ax4.plot(t,D_t,'ro')\n",
    "        ax4.plot(t,R_t,'go')\n",
    "        \n",
    "        ax3.set_xlabel(\"t\")\n",
    "        \n",
    "\n",
    "        ax1.set_ylabel(\"Infected\")\n",
    "        ax2.set_ylabel(\"Recovered\")\n",
    "        ax3.set_ylabel(\"Dead\")\n",
    "    \n",
    "    ax1.plot(tlist,I_vals,'y-')\n",
    "    ax2.plot(tlist,R_vals,'g-')\n",
    "    ax3.plot(tlist,D_vals,'r-')\n",
    "\n",
    "\n",
    "    ax4.plot(tlist,I_vals,'y-')\n",
    "    ax4.plot(tlist,D_vals,'r-')\n",
    "    ax4.plot(tlist,R_vals,'g-')\n",
    "        \n",
    "N = widgets.IntText(value=1000, description = \"Population\", \n",
    "                        style={'description_width': 'initial'})\n",
    "\n",
    "I0 = widgets.IntSlider(value=1,min=0,max=100,step=1,description = \"Infected\", \n",
    "                        style={'description_width': 'initial'})\n",
    "tmax = widgets.IntSlider(value=40,min=0,max=200,step=1,description = \"Time\", \n",
    "                        style={'description_width': 'initial'})\n",
    "average_contact_number = widgets.FloatSlider(value=2.5, min = 0, max=10,step=0.1, \n",
    "                                description = \"Averge Number of Contacts\", \n",
    "                        style={'description_width': 'initial'})\n",
    "transmission_probability = widgets.FloatSlider(value=0.5, min = 0, max=1,step=0.01, \n",
    "                        description = \"Transmission Probability\", \n",
    "                        style={'description_width': 'initial'})\n",
    "mortality_risk = widgets.FloatSlider(value=0.5, min = 0, max=1,step=0.01, \n",
    "                        description = \"Mortality Risk\", \n",
    "                        style={'description_width': 'initial'})\n",
    "recovery_time = widgets.IntSlider(value=18, min = 1, max=30,step=1, description = \"Recovery Time\", \n",
    "                        style={'description_width': 'initial'})\n",
    "\n",
    "dashboard = interact_manual(run, N=N, I0=I0,tmax=tmax,\n",
    "                            average_contact_number=average_contact_number,\n",
    "                           transmission_probability=transmission_probability,\n",
    "                           recovery_time=recovery_time, mortality_risk=mortality_risk)\n"
   ]
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