├── README.md
└── compartmental_models
    ├── SEIR Simulator in Python.ipynb
    ├── SEIR Simulator with Parameter Estimation in Python.ipynb
    ├── SEIRD Simulator in Python.ipynb
    ├── SEIRD Simulator with Parameter Estimation in Python.ipynb
    └── images
        ├── notations.png
        ├── seir_de_eqns.png
        ├── seir_model.png
        ├── seir_simulation.png
        ├── seird_de_eqns.png
        ├── seird_model.png
        ├── seird_simulation.png
        └── seird_simulator.png


/README.md:
--------------------------------------------------------------------------------
 1 | # Simulators for different purposes
 2 | 
 3 | The repo currently has the following models implemented in jupyter notebooks:
 4 | * [Compartmental models](https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology "Compartmental models in epidemiology") namely [SEIR](https://github.com/silpara/simulators/blob/master/compartmental_models/SEIR%20Simulator%20in%20Python.ipynb "SEIR Simulator in Python") and [SEIRD](https://github.com/silpara/simulators/blob/master/compartmental_models/SEIRD%20Simulator%20in%20Python.ipynb  "SEIRD Simulator in Python") which are elaborations of the basic SIR model. These models are used in epidemiology to predict the spread of a disease. E.g. variations of these basic models are being used in prediction of spread of COVID-19.
 5 | * Estimation of [SEIR](https://github.com/silpara/simulators/blob/master/compartmental_models/SEIR%20Simulator%20with%20Parameter%20Estimation%20in%20Python.ipynb "SEIR Simulator with Parameter Estimation in Python") and [SEIRD](https://github.com/silpara/simulators/blob/master/compartmental_models/SEIRD%20Simulator%20with%20Parameter%20Estimation%20in%20Python.ipynb "SEIRD Simulator with Parameter Estimation in Python") model parameters using nonlinear least squares.
 6 | 
 7 | The simulator is built using IPython Widgets. Here is how SEIRD simulator looks like,<br>
 8 | <img src="compartmental_models/images/seird_simulator.png" width="800">
 9 | <br>
10 | The simulator doesn't render in Jupyter notebooks hosted on GitHub but on your local machine, you will be able to run the notebook and use the simulator for various parameter values of choice.
11 | <br>
12 | ## Compartmental Models
13 | 
14 | ### SEIR Model
15 | <img src="compartmental_models/images/seir_model.png" width="800">
16 | 
17 | ### SEIRD Model
18 | <img src="compartmental_models/images/seird_model.png" width="800">
19 | 
20 | More details on the models are provided in the corresponding notebooks.
21 | 
22 | ## Organization
23 | 
24 | **compartmental_models**
25 | - [SEIR](https://github.com/silpara/simulators/blob/master/compartmental_models/SEIR%20Simulator%20in%20Python.ipynb "SEIR Simulator in Python")
26 | - [SEIR with Parameter Estimation](https://github.com/silpara/simulators/blob/master/compartmental_models/SEIR%20Simulator%20with%20Parameter%20Estimation%20in%20Python.ipynb "SEIR Simulator with Parameter Estimation in Python")
27 | - [SEIRD](https://github.com/silpara/simulators/blob/master/compartmental_models/SEIRD%20Simulator%20in%20Python.ipynb  "SEIRD Simulator in Python")
28 | - [SEIRD with Parameter Estimation](https://github.com/silpara/simulators/blob/master/compartmental_models/SEIRD%20Simulator%20with%20Parameter%20Estimation%20in%20Python.ipynb "SEIRD Simulator with Parameter Estimation in Python")
29 | 
30 | 
31 | 


--------------------------------------------------------------------------------
/compartmental_models/SEIR Simulator in Python.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "markdown",
  5 |    "metadata": {},
  6 |    "source": [
  7 |     "# Simulation of SEIR Model\n",
  8 |     "\n",
  9 |     "SEIR is a type of compartmental models which are used in modelling of infectious disease using differential equations. These types of models divide the population into groups or compartments and the dynamics of these groups are expressed with the help of a system of differential equations.\n",
 10 |     "\n",
 11 |     "These system of equations are parametrized which capture the mechanistic nature of the disease. For simulation, you select values of these parameters and the resulting curves simulate the behaviour by solving the set of equations. Finally the results are plotted in a graph to visually understand the effect of the parameters.\n",
 12 |     "\n",
 13 |     "## SEIR Model\n",
 14 |     "\n",
 15 |     "For completeness the SEIR model is produced below:\n",
 16 |     "\n",
 17 |     "<img src=\"images/seir_model.png\">\n",
 18 |     "\n",
 19 |     "$\\displaystyle \\frac{dS}{dt} = -\\frac{\\beta S I}{N}$<br><br>\n",
 20 |     "$\\displaystyle \\frac{dE}{dt} = \\frac{\\beta S I}{N} - \\sigma E$<br><br>\n",
 21 |     "$\\displaystyle \\frac{dI}{dt} = \\sigma E -  \\gamma I$<br><br>\n",
 22 |     "$\\displaystyle \\frac{dR}{dt} = \\gamma I$<br><br>\n",
 23 |     "$N = S + E + I + R$<br><br>\n",
 24 |     "Where,<br><br>\n",
 25 |     "$\\beta$ is infection rate or the rate of spread<br><br>\n",
 26 |     "$\\sigma$ is the incubation rate or the rate of latent individuals becoming infectious (average duration of incubation is $1/\\sigma$)<br><br>\n",
 27 |     "$\\gamma$ is the recovery rate or mortality rate. If the duration of indection is D then $\\gamma$ = 1/D\n",
 28 |     "\n",
 29 |     "A supplementary post to this notebook can be read at [Simulating Compartmental Models in Epidemiology using Python & Jupyter Widgets](https://dilbertai.com/2020/04/12/simulating-compartmental-models-in-epidemiology-using-python-jupyter-widgets/)"
 30 |    ]
 31 |   },
 32 |   {
 33 |    "cell_type": "code",
 34 |    "execution_count": 22,
 35 |    "metadata": {},
 36 |    "outputs": [],
 37 |    "source": [
 38 |     "import os\n",
 39 |     "import sys\n",
 40 |     "import matplotlib.pyplot as plt\n",
 41 |     "import numpy as np\n",
 42 |     "import pandas as pd\n",
 43 |     "from scipy.integrate import odeint\n",
 44 |     "import plotly.graph_objects as go\n",
 45 |     "import plotly.io as pio\n",
 46 |     "pio.renderers.default = \"notebook\"\n",
 47 |     "%matplotlib inline\n",
 48 |     "plt.style.use('ggplot')"
 49 |    ]
 50 |   },
 51 |   {
 52 |    "cell_type": "code",
 53 |    "execution_count": 23,
 54 |    "metadata": {},
 55 |    "outputs": [],
 56 |    "source": [
 57 |     "# Jupyter Specifics\n",
 58 |     "from IPython.display import HTML\n",
 59 |     "from ipywidgets.widgets import interact, IntSlider, FloatSlider, Layout\n",
 60 |     "\n",
 61 |     "style = {'description_width': '100px'}\n",
 62 |     "slider_layout = Layout(width='99%')"
 63 |    ]
 64 |   },
 65 |   {
 66 |    "cell_type": "code",
 67 |    "execution_count": 24,
 68 |    "metadata": {},
 69 |    "outputs": [],
 70 |    "source": [
 71 |     "def ode_model(z, t, beta, sigma, gamma):\n",
 72 |     "    \"\"\"\n",
 73 |     "    Reference https://www.idmod.org/docs/hiv/model-seir.html\n",
 74 |     "    \"\"\"\n",
 75 |     "    S, E, I, R = z\n",
 76 |     "    N = S + E + I + R\n",
 77 |     "    dSdt = -beta*S*I/N\n",
 78 |     "    dEdt = beta*S*I/N - sigma*E\n",
 79 |     "    dIdt = sigma*E - gamma*I\n",
 80 |     "    dRdt = gamma*I\n",
 81 |     "    return [dSdt, dEdt, dIdt, dRdt]"
 82 |    ]
 83 |   },
 84 |   {
 85 |    "cell_type": "code",
 86 |    "execution_count": 25,
 87 |    "metadata": {},
 88 |    "outputs": [],
 89 |    "source": [
 90 |     "def ode_solver(t, initial_conditions, params):\n",
 91 |     "    initE, initI, initR, initN = initial_conditions\n",
 92 |     "    beta, sigma, gamma = params\n",
 93 |     "    initS = initN - (initE + initI + initR)\n",
 94 |     "    res = odeint(ode_model, [initS, initE, initI, initR], t, args=(beta, sigma, gamma))\n",
 95 |     "    return res"
 96 |    ]
 97 |   },
 98 |   {
 99 |    "cell_type": "code",
100 |    "execution_count": 26,
101 |    "metadata": {},
102 |    "outputs": [],
103 |    "source": [
104 |     "# ref: https://www.medrxiv.org/content/10.1101/2020.04.01.20049825v1.full.pdf\n",
105 |     "initN = 1380000000\n",
106 |     "# S0 = 966000000\n",
107 |     "initE = 1\n",
108 |     "initI = 1\n",
109 |     "initR = 0\n",
110 |     "sigma = 1/5.2\n",
111 |     "gamma = 1/2.9\n",
112 |     "R0 = 4\n",
113 |     "beta = R0 * gamma\n",
114 |     "days = 150"
115 |    ]
116 |   },
117 |   {
118 |    "cell_type": "code",
119 |    "execution_count": 27,
120 |    "metadata": {},
121 |    "outputs": [],
122 |    "source": [
123 |     "def main(initE, initI, initR, initN, beta, sigma, gamma, days):\n",
124 |     "    initial_conditions = [initE, initI, initR, initN]\n",
125 |     "    params = [beta, sigma, gamma]\n",
126 |     "    tspan = np.arange(0, days, 1)\n",
127 |     "    sol = ode_solver(tspan, initial_conditions, params)\n",
128 |     "    S, E, I, R = sol[:, 0], sol[:, 1], sol[:, 2], sol[:, 3]\n",
129 |     "    \n",
130 |     "    # Create traces\n",
131 |     "    fig = go.Figure()\n",
132 |     "    fig.add_trace(go.Scatter(x=tspan, y=S, mode='lines+markers', name='Susceptible'))\n",
133 |     "    fig.add_trace(go.Scatter(x=tspan, y=E, mode='lines+markers', name='Exposed'))\n",
134 |     "    fig.add_trace(go.Scatter(x=tspan, y=I, mode='lines+markers', name='Infected'))\n",
135 |     "    fig.add_trace(go.Scatter(x=tspan, y=R, mode='lines+markers',name='Recovered'))\n",
136 |     "    \n",
137 |     "    if days <= 30:\n",
138 |     "        step = 1\n",
139 |     "    elif days <= 90:\n",
140 |     "        step = 7\n",
141 |     "    else:\n",
142 |     "        step = 30\n",
143 |     "    \n",
144 |     "    # Edit the layout\n",
145 |     "    fig.update_layout(title='Simulation of SEIR Model',\n",
146 |     "                       xaxis_title='Day',\n",
147 |     "                       yaxis_title='Counts',\n",
148 |     "                       title_x=0.5,\n",
149 |     "                      width=900, height=600\n",
150 |     "                     )\n",
151 |     "    fig.update_xaxes(tickangle=-90, tickformat = None, tickmode='array', tickvals=np.arange(0, days + 1, step))\n",
152 |     "    if not os.path.exists(\"images\"):\n",
153 |     "        os.mkdir(\"images\")\n",
154 |     "    fig.write_image(\"images/seir_simulation.png\")\n",
155 |     "    fig.show()"
156 |    ]
157 |   },
158 |   {
159 |    "cell_type": "code",
160 |    "execution_count": 28,
161 |    "metadata": {},
162 |    "outputs": [
163 |     {
164 |      "data": {
165 |       "application/vnd.jupyter.widget-view+json": {
166 |        "model_id": "9035b90a6cea4fcbbd42244fb0a09f80",
167 |        "version_major": 2,
168 |        "version_minor": 0
169 |       },
170 |       "text/plain": [
171 |        "interactive(children=(IntSlider(value=1, description='initE', layout=Layout(width='99%'), max=100000, style=Sl…"
172 |       ]
173 |      },
174 |      "metadata": {},
175 |      "output_type": "display_data"
176 |     }
177 |    ],
178 |    "source": [
179 |     "interact(main, initE=IntSlider(min=0, max=100000, step=1, value=initE, description='initE', style=style, layout=slider_layout),\n",
180 |     "               initI=IntSlider(min=0, max=100000, step=10, value=initI, description='initI', style=style, layout=slider_layout),\n",
181 |     "               initR=IntSlider(min=0, max=100000, step=10, value=initR, description='initR', style=style, layout=slider_layout),\n",
182 |     "               initN=IntSlider(min=0, max=1380000000, step=1000, value=initN, description='initN', style=style, layout=slider_layout),\n",
183 |     "               beta=FloatSlider(min=0, max=4, step=0.01, value=beta, description='Infection rate', style=style, layout=slider_layout),\n",
184 |     "               sigma=FloatSlider(min=0, max=4, step=0.01, value=sigma, description='Incubation rate', style=style, layout=slider_layout),\n",
185 |     "               gamma=FloatSlider(min=0, max=4, step=0.01, value=gamma, description='Recovery rate', style=style, layout=slider_layout),\n",
186 |     "               days=IntSlider(min=1, max=600, step=7, value=days, description='Days', style=style, layout=slider_layout)\n",
187 |     "        );"
188 |    ]
189 |   },
190 |   {
191 |    "cell_type": "markdown",
192 |    "metadata": {},
193 |    "source": [
194 |     "**References:**<br>\n",
195 |     "1. SEIR and SEIRS Model https://www.idmod.org/docs/hiv/model-seir.html<br>\n",
196 |     "2. Compartmental models in epidemiology https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology#The_SEIR_model<br>\n",
197 |     "3. Solve Differential Equations in Python https://www.youtube.com/watch?v=VV3BnroVjZo<br>\n",
198 |     "4. Computational Statistics in Python https://people.duke.edu/~ccc14/sta-663/CalibratingODEs.html<br>\n",
199 |     "5. Ordinary Differential Equations (ODE) with Python and Jupyter https://elc.github.io/posts/ordinary-differential-equations-with-python/<br>\n",
200 |     "6. SEIRS+ Model https://github.com/ryansmcgee/seirsplus<br>\n",
201 |     "7. Stack Overflow https://stackoverflow.com/questions/40753159/why-is-scipy-minimize-ignoring-my-constraints<br>\n",
202 |     "8. Lotka–Volterra equations https://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equations<br>\n",
203 |     "9. SEIR and Regression Model based COVID-19 outbreak predictions in India https://www.medrxiv.org/content/10.1101/2020.04.01.20049825v1.full.pdf<br>\n",
204 |     "\n",
205 |     "A simulator built with RShiny which provides many more parameters https://alhill.shinyapps.io/COVID19seir/"
206 |    ]
207 |   },
208 |   {
209 |    "cell_type": "code",
210 |    "execution_count": null,
211 |    "metadata": {},
212 |    "outputs": [],
213 |    "source": []
214 |   },
215 |   {
216 |    "cell_type": "code",
217 |    "execution_count": null,
218 |    "metadata": {},
219 |    "outputs": [],
220 |    "source": []
221 |   },
222 |   {
223 |    "cell_type": "code",
224 |    "execution_count": null,
225 |    "metadata": {},
226 |    "outputs": [],
227 |    "source": []
228 |   },
229 |   {
230 |    "cell_type": "code",
231 |    "execution_count": null,
232 |    "metadata": {},
233 |    "outputs": [],
234 |    "source": []
235 |   }
236 |  ],
237 |  "metadata": {
238 |   "kernelspec": {
239 |    "display_name": "Python 3",
240 |    "language": "python",
241 |    "name": "python3"
242 |   },
243 |   "language_info": {
244 |    "codemirror_mode": {
245 |     "name": "ipython",
246 |     "version": 3
247 |    },
248 |    "file_extension": ".py",
249 |    "mimetype": "text/x-python",
250 |    "name": "python",
251 |    "nbconvert_exporter": "python",
252 |    "pygments_lexer": "ipython3",
253 |    "version": "3.7.6"
254 |   }
255 |  },
256 |  "nbformat": 4,
257 |  "nbformat_minor": 4
258 | }
259 | 


--------------------------------------------------------------------------------
/compartmental_models/SEIR Simulator with Parameter Estimation in Python.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "markdown",
  5 |    "metadata": {},
  6 |    "source": [
  7 |     "# Simulation & Parameter Estimation of SEIR Model\n",
  8 |     "\n",
  9 |     "SEIR is a type of compartmental models which are used in modelling of infectious disease using differential equations. These types of models divide the population into groups or compartments and the dynamics of these groups are expressed with the help of a system of differential equations.\n",
 10 |     "\n",
 11 |     "These system of equations are parametrized which capture the mechanistic nature of the disease. For simulation, you select values of these parameters and the resulting curves simulate the behaviour by solving the set of equations. Finally the results are plotted in a graph to visually understand the effect of the parameters.\n",
 12 |     "\n",
 13 |     "## SEIR Model\n",
 14 |     "\n",
 15 |     "For completeness the SEIR model is produced below:\n",
 16 |     "\n",
 17 |     "<img src=\"images/seir_model.png\">\n",
 18 |     "\n",
 19 |     "$\\displaystyle \\frac{dS}{dt} = -\\frac{\\beta S I}{N}$<br><br>\n",
 20 |     "$\\displaystyle \\frac{dE}{dt} = \\frac{\\beta S I}{N} - \\sigma E$<br><br>\n",
 21 |     "$\\displaystyle \\frac{dI}{dt} = \\sigma E -  \\gamma I$<br><br>\n",
 22 |     "$\\displaystyle \\frac{dR}{dt} = \\gamma I$<br><br>\n",
 23 |     "$N = S + E + I + R$<br><br>\n",
 24 |     "Where,<br><br>\n",
 25 |     "$\\beta$ is infection rate or the rate of spread<br><br>\n",
 26 |     "$\\sigma$ is the incubation rate or the rate of latent individuals becoming infectious (average duration of incubation is $1/\\sigma$)<br><br>\n",
 27 |     "$\\gamma$ is the recovery rate or mortality rate. If the duration of indection is D then $\\gamma$ = 1/D\n",
 28 |     "\n",
 29 |     "#### A supplementary blogpost to this notebook can be found at [Estimating Parameters of Compartmental Models from Observed Data](https://dilbertai.com/2020/04/27/estimating-parameters-of-compartmental-models-from-observed-data/)"
 30 |    ]
 31 |   },
 32 |   {
 33 |    "cell_type": "code",
 34 |    "execution_count": 1,
 35 |    "metadata": {},
 36 |    "outputs": [],
 37 |    "source": [
 38 |     "import os\n",
 39 |     "import sys\n",
 40 |     "import matplotlib.pyplot as plt\n",
 41 |     "import numpy as np\n",
 42 |     "import pandas as pd\n",
 43 |     "from scipy.integrate import odeint\n",
 44 |     "import plotly.graph_objects as go\n",
 45 |     "import plotly.io as pio\n",
 46 |     "import requests\n",
 47 |     "from lmfit import minimize, Parameters, Parameter, report_fit\n",
 48 |     "pio.renderers.default = \"notebook\"\n",
 49 |     "%matplotlib inline\n",
 50 |     "plt.style.use('ggplot')"
 51 |    ]
 52 |   },
 53 |   {
 54 |    "cell_type": "code",
 55 |    "execution_count": 2,
 56 |    "metadata": {},
 57 |    "outputs": [],
 58 |    "source": [
 59 |     "# Jupyter Specifics\n",
 60 |     "from IPython.display import HTML\n",
 61 |     "from ipywidgets.widgets import interact, IntSlider, FloatSlider, Layout, ToggleButton\n",
 62 |     "\n",
 63 |     "style = {'description_width': '100px'}\n",
 64 |     "slider_layout = Layout(width='99%')"
 65 |    ]
 66 |   },
 67 |   {
 68 |    "cell_type": "code",
 69 |    "execution_count": 3,
 70 |    "metadata": {},
 71 |    "outputs": [],
 72 |    "source": [
 73 |     "def ode_model(z, t, beta, sigma, gamma):\n",
 74 |     "    \"\"\"\n",
 75 |     "    Reference https://www.idmod.org/docs/hiv/model-seir.html\n",
 76 |     "    \"\"\"\n",
 77 |     "    S, E, I, R = z\n",
 78 |     "    N = S + E + I + R\n",
 79 |     "    dSdt = -beta*S*I/N\n",
 80 |     "    dEdt = beta*S*I/N - sigma*E\n",
 81 |     "    dIdt = sigma*E - gamma*I\n",
 82 |     "    dRdt = gamma*I\n",
 83 |     "    return [dSdt, dEdt, dIdt, dRdt]"
 84 |    ]
 85 |   },
 86 |   {
 87 |    "cell_type": "code",
 88 |    "execution_count": 4,
 89 |    "metadata": {},
 90 |    "outputs": [],
 91 |    "source": [
 92 |     "def ode_solver(t, initial_conditions, params):\n",
 93 |     "    initE, initI, initR, initN = initial_conditions\n",
 94 |     "    beta, sigma, gamma = params['beta'].value, params['sigma'].value, params['gamma'].value\n",
 95 |     "    initS = initN - (initE + initI + initR)\n",
 96 |     "    res = odeint(ode_model, [initS, initE, initI, initR], t, args=(beta, sigma, gamma))\n",
 97 |     "    return res"
 98 |    ]
 99 |   },
100 |   {
101 |    "cell_type": "code",
102 |    "execution_count": 5,
103 |    "metadata": {},
104 |    "outputs": [
105 |     {
106 |      "name": "stdout",
107 |      "output_type": "stream",
108 |      "text": [
109 |       "Request Success? True\n"
110 |      ]
111 |     }
112 |    ],
113 |    "source": [
114 |     "response = requests.get('https://api.rootnet.in/covid19-in/stats/history')\n",
115 |     "print('Request Success? {}'.format(response.status_code == 200))\n",
116 |     "covid_history = response.json()['data']"
117 |    ]
118 |   },
119 |   {
120 |    "cell_type": "code",
121 |    "execution_count": 6,
122 |    "metadata": {},
123 |    "outputs": [],
124 |    "source": [
125 |     "keys = ['day', 'total', 'confirmedCasesIndian', 'confirmedCasesForeign', 'confirmedButLocationUnidentified',\n",
126 |     "        'discharged', 'deaths']\n",
127 |     "df_covid_history = pd.DataFrame([[d.get('day'), \n",
128 |     "                                  d['summary'].get('total'), \n",
129 |     "                                  d['summary'].get('confirmedCasesIndian'), \n",
130 |     "                                  d['summary'].get('confirmedCasesForeign'),\n",
131 |     "                                  d['summary'].get('confirmedButLocationUnidentified'),\n",
132 |     "                                  d['summary'].get('discharged'), \n",
133 |     "                                  d['summary'].get('deaths')] \n",
134 |     "                                 for d in covid_history],\n",
135 |     "                    columns=keys)\n",
136 |     "df_covid_history = df_covid_history.sort_values(by='day')\n",
137 |     "df_covid_history['infected'] = df_covid_history['total'] - df_covid_history['discharged'] - df_covid_history['deaths']\n",
138 |     "df_covid_history['total_recovered_or_dead'] = df_covid_history['discharged'] + df_covid_history['deaths']"
139 |    ]
140 |   },
141 |   {
142 |    "cell_type": "code",
143 |    "execution_count": 7,
144 |    "metadata": {},
145 |    "outputs": [],
146 |    "source": [
147 |     "# ref: https://www.medrxiv.org/content/10.1101/2020.04.01.20049825v1.full.pdf\n",
148 |     "initN = 1380000000\n",
149 |     "# S0 = 966000000\n",
150 |     "initE = 1000\n",
151 |     "initI = 47\n",
152 |     "initR = 0\n",
153 |     "sigma = 1/5.2\n",
154 |     "gamma = 1/2.9\n",
155 |     "R0 = 4\n",
156 |     "beta = R0 * gamma\n",
157 |     "days = 112\n",
158 |     "\n",
159 |     "params = Parameters()\n",
160 |     "params.add('beta', value=beta, min=0, max=10)\n",
161 |     "params.add('sigma', value=sigma, min=0, max=10)\n",
162 |     "params.add('gamma', value=gamma, min=0, max=10)"
163 |    ]
164 |   },
165 |   {
166 |    "cell_type": "markdown",
167 |    "metadata": {},
168 |    "source": [
169 |     "## Simulation"
170 |    ]
171 |   },
172 |   {
173 |    "cell_type": "code",
174 |    "execution_count": 23,
175 |    "metadata": {},
176 |    "outputs": [],
177 |    "source": [
178 |     "def main(initE, initI, initR, initN, beta, sigma, gamma, days, param_fitting):\n",
179 |     "    initial_conditions = [initE, initI, initR, initN]\n",
180 |     "    params['beta'].value, params['sigma'].value,params['gamma'].value = [beta, sigma, gamma]\n",
181 |     "    tspan = np.arange(0, days, 1)\n",
182 |     "    sol = ode_solver(tspan, initial_conditions, params)\n",
183 |     "    S, E, I, R = sol[:, 0], sol[:, 1], sol[:, 2], sol[:, 3]\n",
184 |     "    \n",
185 |     "    # Create traces\n",
186 |     "    fig = go.Figure()\n",
187 |     "    if not param_fitting:\n",
188 |     "        fig.add_trace(go.Scatter(x=tspan, y=S, mode='lines+markers', name='Susceptible'))\n",
189 |     "        fig.add_trace(go.Scatter(x=tspan, y=E, mode='lines+markers', name='Exposed'))\n",
190 |     "    fig.add_trace(go.Scatter(x=tspan, y=I, mode='lines+markers', name='Infected'))\n",
191 |     "    fig.add_trace(go.Scatter(x=tspan, y=R, mode='lines+markers',name='Recovered'))\n",
192 |     "    if param_fitting:\n",
193 |     "        fig.add_trace(go.Scatter(x=tspan, y=df_covid_history.infected, mode='lines+markers',\\\n",
194 |     "                             name='Infections Observed', line = dict(dash='dash')))\n",
195 |     "        fig.add_trace(go.Scatter(x=tspan, y=df_covid_history.total_recovered_or_dead, mode='lines+markers',\\\n",
196 |     "                             name='Recovered/Deceased Observed', line = dict(dash='dash')))\n",
197 |     "    \n",
198 |     "    if days <= 30:\n",
199 |     "        step = 1\n",
200 |     "    elif days <= 90:\n",
201 |     "        step = 7\n",
202 |     "    else:\n",
203 |     "        step = 30\n",
204 |     "    \n",
205 |     "    # Edit the layout\n",
206 |     "    fig.update_layout(title='Simulation of SEIR Model',\n",
207 |     "                       xaxis_title='Day',\n",
208 |     "                       yaxis_title='Counts',\n",
209 |     "                       title_x=0.5,\n",
210 |     "                      width=900, height=600\n",
211 |     "                     )\n",
212 |     "    fig.update_xaxes(tickangle=-90, tickformat = None, tickmode='array', tickvals=np.arange(0, days + 1, step))\n",
213 |     "    if not os.path.exists(\"images\"):\n",
214 |     "        os.mkdir(\"images\")\n",
215 |     "    fig.write_image(\"images/seir_simulation.png\")\n",
216 |     "    fig.show()"
217 |    ]
218 |   },
219 |   {
220 |    "cell_type": "code",
221 |    "execution_count": 24,
222 |    "metadata": {},
223 |    "outputs": [
224 |     {
225 |      "data": {
226 |       "application/vnd.jupyter.widget-view+json": {
227 |        "model_id": "a787662501c544789daa0c0b3a4b3c80",
228 |        "version_major": 2,
229 |        "version_minor": 0
230 |       },
231 |       "text/plain": [
232 |        "interactive(children=(IntSlider(value=1000, description='initE', layout=Layout(width='99%'), max=100000, style…"
233 |       ]
234 |      },
235 |      "metadata": {},
236 |      "output_type": "display_data"
237 |     }
238 |    ],
239 |    "source": [
240 |     "interact(main, initE=IntSlider(min=0, max=100000, step=1, value=initE, description='initE', style=style, \\\n",
241 |     "                               layout=slider_layout),\n",
242 |     "               initI=IntSlider(min=0, max=100000, step=10, value=initI, description='initI', style=style, \\\n",
243 |     "                               layout=slider_layout),\n",
244 |     "               initR=IntSlider(min=0, max=100000, step=10, value=initR, description='initR', style=style, \\\n",
245 |     "                               layout=slider_layout),\n",
246 |     "               initN=IntSlider(min=0, max=1380000000, step=1000, value=initN, description='initN', style=style, \\\n",
247 |     "                               layout=slider_layout),\n",
248 |     "               beta=FloatSlider(min=0, max=4, step=0.01, value=beta, description='Infection rate', style=style, \\\n",
249 |     "                                layout=slider_layout),\n",
250 |     "               sigma=FloatSlider(min=0, max=4, step=0.01, value=sigma, description='Incubation rate', style=style, \\\n",
251 |     "                                 layout=slider_layout),\n",
252 |     "               gamma=FloatSlider(min=0, max=4, step=0.01, value=gamma, description='Recovery rate', style=style, \\\n",
253 |     "                                 layout=slider_layout),\n",
254 |     "               days=IntSlider(min=0, max=600, step=7, value=days, description='Days', style=style, \\\n",
255 |     "                              layout=slider_layout),\n",
256 |     "               param_fitting=ToggleButton(value=False, description='Fitting Mode', disabled=False, button_style='', \\\n",
257 |     "             tooltip='Click to show fewer plots', icon='check-circle')\n",
258 |     "        );"
259 |    ]
260 |   },
261 |   {
262 |    "cell_type": "markdown",
263 |    "metadata": {},
264 |    "source": [
265 |     "## Parameter Estimation"
266 |    ]
267 |   },
268 |   {
269 |    "cell_type": "code",
270 |    "execution_count": 25,
271 |    "metadata": {},
272 |    "outputs": [],
273 |    "source": [
274 |     "def error(params, initial_conditions, tspan, data):\n",
275 |     "    sol = ode_solver(tspan, initial_conditions, params)\n",
276 |     "    return (sol[:, 2:4] - data).ravel()"
277 |    ]
278 |   },
279 |   {
280 |    "cell_type": "code",
281 |    "execution_count": 26,
282 |    "metadata": {},
283 |    "outputs": [],
284 |    "source": [
285 |     "initial_conditions = [initE, initI, initR, initN]\n",
286 |     "beta = 1.08\n",
287 |     "sigma = 0.02\n",
288 |     "gamma = 0.02\n",
289 |     "params['beta'].value = beta\n",
290 |     "params['sigma'].value = sigma\n",
291 |     "params['gamma'].value = gamma\n",
292 |     "days = 45\n",
293 |     "tspan = np.arange(0, days, 1)\n",
294 |     "data = df_covid_history.loc[0:(days-1), ['infected', 'total_recovered_or_dead']].values"
295 |    ]
296 |   },
297 |   {
298 |    "cell_type": "code",
299 |    "execution_count": 27,
300 |    "metadata": {},
301 |    "outputs": [
302 |     {
303 |      "data": {
304 |       "text/html": [
305 |        "<table><tr><th> name </th><th> value </th><th> initial value </th><th> min </th><th> max </th><th> vary </th></tr><tr><td> beta </td><td>  1.08000000 </td><td> 1.3793103448275863 </td><td>  0.00000000 </td><td>  10.0000000 </td><td> True </td></tr><tr><td> sigma </td><td>  0.02000000 </td><td> 0.1923076923076923 </td><td>  0.00000000 </td><td>  10.0000000 </td><td> True </td></tr><tr><td> gamma </td><td>  0.02000000 </td><td> 0.3448275862068966 </td><td>  0.00000000 </td><td>  10.0000000 </td><td> True </td></tr></table>"
306 |       ],
307 |       "text/plain": [
308 |        "Parameters([('beta', <Parameter 'beta', value=1.08, bounds=[0:10]>),\n",
309 |        "            ('sigma', <Parameter 'sigma', value=0.02, bounds=[0:10]>),\n",
310 |        "            ('gamma', <Parameter 'gamma', value=0.02, bounds=[0:10]>)])"
311 |       ]
312 |      },
313 |      "execution_count": 27,
314 |      "metadata": {},
315 |      "output_type": "execute_result"
316 |     }
317 |    ],
318 |    "source": [
319 |     "params"
320 |    ]
321 |   },
322 |   {
323 |    "cell_type": "code",
324 |    "execution_count": 28,
325 |    "metadata": {},
326 |    "outputs": [],
327 |    "source": [
328 |     "# fit model and find predicted values\n",
329 |     "result = minimize(error, params, args=(initial_conditions, tspan, data), method='leastsq')"
330 |    ]
331 |   },
332 |   {
333 |    "cell_type": "code",
334 |    "execution_count": 29,
335 |    "metadata": {},
336 |    "outputs": [
337 |     {
338 |      "data": {
339 |       "text/html": [
340 |        "<table><tr><th> name </th><th> value </th><th> standard error </th><th> relative error </th><th> initial value </th><th> min </th><th> max </th><th> vary </th></tr><tr><td> beta </td><td>  0.25240521 </td><td>  0.02426587 </td><td> (9.61%) </td><td> 1.08 </td><td>  0.00000000 </td><td>  10.0000000 </td><td> True </td></tr><tr><td> sigma </td><td>  0.07915451 </td><td>  0.00865739 </td><td> (10.94%) </td><td> 0.02 </td><td>  0.00000000 </td><td>  10.0000000 </td><td> True </td></tr><tr><td> gamma </td><td>  0.02201161 </td><td>  0.00129203 </td><td> (5.87%) </td><td> 0.02 </td><td>  0.00000000 </td><td>  10.0000000 </td><td> True </td></tr></table>"
341 |       ],
342 |       "text/plain": [
343 |        "Parameters([('beta',\n",
344 |        "             <Parameter 'beta', value=0.25240520565167124 +/- 0.0243, bounds=[0:10]>),\n",
345 |        "            ('sigma',\n",
346 |        "             <Parameter 'sigma', value=0.07915450950986003 +/- 0.00866, bounds=[0:10]>),\n",
347 |        "            ('gamma',\n",
348 |        "             <Parameter 'gamma', value=0.022011605792732203 +/- 0.00129, bounds=[0:10]>)])"
349 |       ]
350 |      },
351 |      "execution_count": 29,
352 |      "metadata": {},
353 |      "output_type": "execute_result"
354 |     }
355 |    ],
356 |    "source": [
357 |     "result.params"
358 |    ]
359 |   },
360 |   {
361 |    "cell_type": "code",
362 |    "execution_count": 30,
363 |    "metadata": {},
364 |    "outputs": [
365 |     {
366 |      "name": "stdout",
367 |      "output_type": "stream",
368 |      "text": [
369 |       "[[Fit Statistics]]\n",
370 |       "    # fitting method   = leastsq\n",
371 |       "    # function evals   = 64\n",
372 |       "    # data points      = 90\n",
373 |       "    # variables        = 3\n",
374 |       "    chi-square         = 25843295.5\n",
375 |       "    reduced chi-square = 297049.373\n",
376 |       "    Akaike info crit   = 1137.09769\n",
377 |       "    Bayesian info crit = 1144.59712\n",
378 |       "[[Variables]]\n",
379 |       "    beta:   0.25240521 +/- 0.02426587 (9.61%) (init = 1.08)\n",
380 |       "    sigma:  0.07915451 +/- 0.00865739 (10.94%) (init = 0.02)\n",
381 |       "    gamma:  0.02201161 +/- 0.00129203 (5.87%) (init = 0.02)\n",
382 |       "[[Correlations]] (unreported correlations are < 0.100)\n",
383 |       "    C(beta, sigma)  = -0.991\n",
384 |       "    C(beta, gamma)  =  0.437\n",
385 |       "    C(sigma, gamma) = -0.327\n"
386 |      ]
387 |     }
388 |    ],
389 |    "source": [
390 |     "# display fitted statistics\n",
391 |     "report_fit(result)"
392 |    ]
393 |   },
394 |   {
395 |    "cell_type": "code",
396 |    "execution_count": 31,
397 |    "metadata": {},
398 |    "outputs": [
399 |     {
400 |      "data": {
401 |       "text/html": [
402 |        "<div>\n",
403 |        "        \n",
404 |        "        \n",
405 |        "            <div id=\"8dabc243-3547-47fc-b346-22f5a83e4c41\" class=\"plotly-graph-div\" style=\"height:600px; width:1000px;\"></div>\n",
406 |        "            <script type=\"text/javascript\">\n",
407 |        "                require([\"plotly\"], function(Plotly) {\n",
408 |        "                    window.PLOTLYENV=window.PLOTLYENV || {};\n",
409 |        "                    \n",
410 |        "                if (document.getElementById(\"8dabc243-3547-47fc-b346-22f5a83e4c41\")) {\n",
411 |        "                    Plotly.newPlot(\n",
412 |        "                        '8dabc243-3547-47fc-b346-22f5a83e4c41',\n",
413 |        "                        [{\"line\": {\"dash\": \"dot\"}, \"mode\": \"markers\", \"name\": \"Observed Infections\", \"type\": \"scatter\", \"x\": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44], \"y\": [47, 60, 73, 70, 72, 95, 99, 120, 134, 149, 196, 256, 329, 424, 469, 553, 634, 640, 810, 901, 1118, 1238, 1649, 1860, 2322, 2784, 3219, 3851, 4312, 4714, 5218, 6039, 6634, 7409, 8048, 9272, 10197, 10824, 11616, 12289, 13295, 14255, 15122, 15859, 16689]}, {\"line\": {\"dash\": \"dot\"}, \"mode\": \"markers\", \"name\": \"Observed Recovered/Deceased\", \"type\": \"scatter\", \"x\": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44], \"y\": [0, 0, 0, 12, 12, 15, 15, 17, 17, 24, 27, 27, 31, 43, 50, 53, 60, 84, 99, 123, 133, 159, 185, 209, 225, 288, 358, 430, 477, 560, 647, 722, 895, 1038, 1304, 1543, 1736, 1935, 2219, 2503, 2821, 3401, 3863, 4612, 5011]}, {\"mode\": \"lines+markers\", \"name\": \"Fitted Infections\", \"type\": \"scatter\", \"x\": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44], \"y\": [47.0, 121.93945599912564, 191.78665420458944, 258.2448665323269, 322.7946114892799, 386.7408035519474, 451.25231885706546, 517.3953867147102, 586.1619882130099, 658.4942314388144, 735.3055166080162, 817.4991632130607, 905.9850715342029, 1001.6948955335492, 1105.5961330646087, 1218.7054833713573, 1342.1017733786975, 1476.9387208887902, 1624.4577682189138, 1786.001206670372, 1963.0257897031563, 2157.1170236610033, 2370.004320661652, 2603.577192918343, 2859.9026694397153, 3141.2441209246235, 3450.0816830673652, 3789.1344799591507, 4161.384860741957, 4570.1048757543, 5018.8852368285125, 5511.667026114684, 6052.776439046636, 6646.962872967847, 7299.440710038885, 8015.935120587657, 8802.732392127722, 9666.735075937857, 10615.522645805648, 11657.417941202446, 12801.560232392845, 14057.985398098288, 15437.713894108158, 16952.84751221901, 18616.675394705802]}, {\"mode\": \"lines+markers\", \"name\": \"Fitted Recovered/Deceased\", \"type\": \"scatter\", \"x\": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44], \"y\": [0.0, 1.870368893590941, 5.330871494492761, 10.288621864948826, 16.68567978708348, 24.494682056501006, 33.71542489863358, 44.37224745082952, 56.512093004353055, 70.20314957284408, 85.53399010944248, 102.61314988787299, 121.56909110905595, 142.5505170287964, 165.7270075382864, 191.28995618656197, 219.4537960485481, 250.45750762764698, 284.566408430343, 322.07422757749725, 363.30547435651334, 408.61811365039114, 458.4065649870086, 513.1050462817893, 573.1912872214667, 639.1906411253515, 711.6806281883144, 791.295948272033, 878.7340039987671, 974.760981958488, 1080.218543424491, 1196.0311822480396, 1323.2143136053699, 1462.8831637593842, 1616.2625402634815, 1784.697556624641, 1969.6654304405097, 2172.78841975851, 2395.8480622648176, 2640.8007779352192, 2909.795033756946, 3205.190184086683, 3529.577145951644, 3885.8011437747773, 4276.986632913569]}],\n",
414 |        "                        {\"height\": 600, \"template\": {\"data\": {\"bar\": [{\"error_x\": {\"color\": \"#2a3f5f\"}, \"error_y\": {\"color\": \"#2a3f5f\"}, \"marker\": {\"line\": {\"color\": \"#E5ECF6\", \"width\": 0.5}}, \"type\": \"bar\"}], \"barpolar\": [{\"marker\": {\"line\": {\"color\": \"#E5ECF6\", \"width\": 0.5}}, \"type\": \"barpolar\"}], \"carpet\": [{\"aaxis\": {\"endlinecolor\": \"#2a3f5f\", \"gridcolor\": \"white\", \"linecolor\": \"white\", \"minorgridcolor\": \"white\", \"startlinecolor\": \"#2a3f5f\"}, \"baxis\": {\"endlinecolor\": \"#2a3f5f\", \"gridcolor\": \"white\", \"linecolor\": \"white\", \"minorgridcolor\": \"white\", \"startlinecolor\": \"#2a3f5f\"}, \"type\": \"carpet\"}], \"choropleth\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"choropleth\"}], \"contour\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"contour\"}], \"contourcarpet\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"contourcarpet\"}], \"heatmap\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"heatmap\"}], \"heatmapgl\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"heatmapgl\"}], \"histogram\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"histogram\"}], \"histogram2d\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"histogram2d\"}], \"histogram2dcontour\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"histogram2dcontour\"}], \"mesh3d\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"mesh3d\"}], \"parcoords\": [{\"line\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"parcoords\"}], \"pie\": [{\"automargin\": true, \"type\": \"pie\"}], \"scatter\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatter\"}], \"scatter3d\": [{\"line\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatter3d\"}], \"scattercarpet\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattercarpet\"}], \"scattergeo\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattergeo\"}], \"scattergl\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattergl\"}], \"scattermapbox\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattermapbox\"}], \"scatterpolar\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterpolar\"}], \"scatterpolargl\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterpolargl\"}], \"scatterternary\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterternary\"}], \"surface\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"surface\"}], \"table\": [{\"cells\": {\"fill\": {\"color\": \"#EBF0F8\"}, \"line\": {\"color\": \"white\"}}, \"header\": {\"fill\": {\"color\": \"#C8D4E3\"}, \"line\": {\"color\": \"white\"}}, \"type\": \"table\"}]}, \"layout\": {\"annotationdefaults\": {\"arrowcolor\": \"#2a3f5f\", \"arrowhead\": 0, \"arrowwidth\": 1}, \"coloraxis\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"colorscale\": {\"diverging\": [[0, \"#8e0152\"], [0.1, \"#c51b7d\"], [0.2, \"#de77ae\"], [0.3, \"#f1b6da\"], [0.4, \"#fde0ef\"], [0.5, \"#f7f7f7\"], [0.6, \"#e6f5d0\"], [0.7, \"#b8e186\"], [0.8, \"#7fbc41\"], [0.9, \"#4d9221\"], [1, \"#276419\"]], \"sequential\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"sequentialminus\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]]}, \"colorway\": [\"#636efa\", \"#EF553B\", \"#00cc96\", \"#ab63fa\", \"#FFA15A\", \"#19d3f3\", \"#FF6692\", \"#B6E880\", \"#FF97FF\", \"#FECB52\"], \"font\": {\"color\": \"#2a3f5f\"}, \"geo\": {\"bgcolor\": \"white\", \"lakecolor\": \"white\", \"landcolor\": \"#E5ECF6\", \"showlakes\": true, \"showland\": true, \"subunitcolor\": \"white\"}, \"hoverlabel\": {\"align\": \"left\"}, \"hovermode\": \"closest\", \"mapbox\": {\"style\": \"light\"}, \"paper_bgcolor\": \"white\", \"plot_bgcolor\": \"#E5ECF6\", \"polar\": {\"angularaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"radialaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"scene\": {\"xaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"yaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"zaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}}, \"shapedefaults\": {\"line\": {\"color\": \"#2a3f5f\"}}, \"ternary\": {\"aaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"baxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"caxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"title\": {\"x\": 0.05}, \"xaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}, \"yaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}}}, \"title\": {\"text\": \"Observed vs Fitted\", \"x\": 0.5}, \"width\": 1000, \"xaxis\": {\"title\": {\"text\": \"Day\"}}, \"yaxis\": {\"title\": {\"text\": \"Counts\"}}},\n",
415 |        "                        {\"responsive\": true}\n",
416 |        "                    ).then(function(){\n",
417 |        "                            \n",
418 |        "var gd = document.getElementById('8dabc243-3547-47fc-b346-22f5a83e4c41');\n",
419 |        "var x = new MutationObserver(function (mutations, observer) {{\n",
420 |        "        var display = window.getComputedStyle(gd).display;\n",
421 |        "        if (!display || display === 'none') {{\n",
422 |        "            console.log([gd, 'removed!']);\n",
423 |        "            Plotly.purge(gd);\n",
424 |        "            observer.disconnect();\n",
425 |        "        }}\n",
426 |        "}});\n",
427 |        "\n",
428 |        "// Listen for the removal of the full notebook cells\n",
429 |        "var notebookContainer = gd.closest('#notebook-container');\n",
430 |        "if (notebookContainer) {{\n",
431 |        "    x.observe(notebookContainer, {childList: true});\n",
432 |        "}}\n",
433 |        "\n",
434 |        "// Listen for the clearing of the current output cell\n",
435 |        "var outputEl = gd.closest('.output');\n",
436 |        "if (outputEl) {{\n",
437 |        "    x.observe(outputEl, {childList: true});\n",
438 |        "}}\n",
439 |        "\n",
440 |        "                        })\n",
441 |        "                };\n",
442 |        "                });\n",
443 |        "            </script>\n",
444 |        "        </div>"
445 |       ]
446 |      },
447 |      "metadata": {},
448 |      "output_type": "display_data"
449 |     }
450 |    ],
451 |    "source": [
452 |     "final = data + result.residual.reshape(data.shape)\n",
453 |     "fig = go.Figure()\n",
454 |     "fig.add_trace(go.Scatter(x=tspan, y=data[:, 0], mode='markers', name='Observed Infections', line = dict(dash='dot')))\n",
455 |     "fig.add_trace(go.Scatter(x=tspan, y=data[:, 1], mode='markers', name='Observed Recovered/Deceased', line = dict(dash='dot')))\n",
456 |     "fig.add_trace(go.Scatter(x=tspan, y=final[:, 0], mode='lines+markers', name='Fitted Infections'))\n",
457 |     "fig.add_trace(go.Scatter(x=tspan, y=final[:, 1], mode='lines+markers', name='Fitted Recovered/Deceased'))\n",
458 |     "fig.update_layout(title='Observed vs Fitted',\n",
459 |     "                       xaxis_title='Day',\n",
460 |     "                       yaxis_title='Counts',\n",
461 |     "                       title_x=0.5,\n",
462 |     "                      width=1000, height=600\n",
463 |     "                     )"
464 |    ]
465 |   },
466 |   {
467 |    "cell_type": "code",
468 |    "execution_count": 32,
469 |    "metadata": {},
470 |    "outputs": [
471 |     {
472 |      "name": "stdout",
473 |      "output_type": "stream",
474 |      "text": [
475 |       "(48, 2)\n"
476 |      ]
477 |     }
478 |    ],
479 |    "source": [
480 |     "observed_IR = df_covid_history.loc[:, ['infected', 'total_recovered_or_dead']].values\n",
481 |     "print(observed_IR.shape)"
482 |    ]
483 |   },
484 |   {
485 |    "cell_type": "code",
486 |    "execution_count": 33,
487 |    "metadata": {},
488 |    "outputs": [],
489 |    "source": [
490 |     "tspan_fit_pred = np.arange(0, observed_IR.shape[0], 1)\n",
491 |     "params['beta'].value = result.params['beta'].value\n",
492 |     "params['sigma'].value = result.params['sigma'].value\n",
493 |     "params['gamma'].value = result.params['gamma'].value\n",
494 |     "fitted_predicted = ode_solver(tspan_fit_pred, initial_conditions, params)"
495 |    ]
496 |   },
497 |   {
498 |    "cell_type": "code",
499 |    "execution_count": 34,
500 |    "metadata": {},
501 |    "outputs": [
502 |     {
503 |      "name": "stdout",
504 |      "output_type": "stream",
505 |      "text": [
506 |       "(48, 2)\n"
507 |      ]
508 |     }
509 |    ],
510 |    "source": [
511 |     "fitted_predicted_IR = fitted_predicted[:, 2:4]\n",
512 |     "print(fitted_predicted_IR.shape)"
513 |    ]
514 |   },
515 |   {
516 |    "cell_type": "code",
517 |    "execution_count": 35,
518 |    "metadata": {},
519 |    "outputs": [
520 |     {
521 |      "name": "stdout",
522 |      "output_type": "stream",
523 |      "text": [
524 |       "Fitted MAE\n",
525 |       "Infected:  587.1564520730407\n",
526 |       "Recovered/Deceased:  220.23711453849532\n",
527 |       "\n",
528 |       "Fitted RMSE\n",
529 |       "Infected:  702.6622222460597\n",
530 |       "Recovered/Deceased:  283.8331485287845\n"
531 |      ]
532 |     }
533 |    ],
534 |    "source": [
535 |     "print(\"Fitted MAE\")\n",
536 |     "print('Infected: ', np.mean(np.abs(fitted_predicted_IR[:days, 0] - observed_IR[:days, 0])))\n",
537 |     "print('Recovered/Deceased: ', np.mean(np.abs(fitted_predicted_IR[:days, 1] - observed_IR[:days, 1])))\n",
538 |     "\n",
539 |     "print(\"\\nFitted RMSE\")\n",
540 |     "print('Infected: ', np.sqrt(np.mean((fitted_predicted_IR[:days, 0] - observed_IR[:days, 0])**2)))\n",
541 |     "print('Recovered/Deceased: ', np.sqrt(np.mean((fitted_predicted_IR[:days, 1] - observed_IR[:days, 1])**2)))"
542 |    ]
543 |   },
544 |   {
545 |    "cell_type": "code",
546 |    "execution_count": 36,
547 |    "metadata": {},
548 |    "outputs": [
549 |     {
550 |      "name": "stdout",
551 |      "output_type": "stream",
552 |      "text": [
553 |       "Predicted MAE\n",
554 |       "Infected:  3500.8548519859637\n",
555 |       "Recovered/Deceased:  894.9307531861135\n",
556 |       "\n",
557 |       "Predicted RMSE\n",
558 |       "Infected:  3590.026376405217\n",
559 |       "Recovered/Deceased:  901.1249714019484\n"
560 |      ]
561 |     }
562 |    ],
563 |    "source": [
564 |     "print(\"Predicted MAE\")\n",
565 |     "print('Infected: ', np.mean(np.abs(fitted_predicted_IR[days:observed_IR.shape[0], 0] - observed_IR[days:, 0])))\n",
566 |     "print('Recovered/Deceased: ', np.mean(np.abs(fitted_predicted_IR[days:observed_IR.shape[0], 1] - observed_IR[days:, 1])))\n",
567 |     "\n",
568 |     "print(\"\\nPredicted RMSE\")\n",
569 |     "print('Infected: ', np.sqrt(np.mean((fitted_predicted_IR[days:observed_IR.shape[0], 0] - observed_IR[days:, 0])**2)))\n",
570 |     "print('Recovered/Deceased: ', np.sqrt(np.mean((fitted_predicted_IR[days:observed_IR.shape[0], 1] - observed_IR[days:, 1])**2)))"
571 |    ]
572 |   },
573 |   {
574 |    "cell_type": "code",
575 |    "execution_count": 37,
576 |    "metadata": {},
577 |    "outputs": [
578 |     {
579 |      "data": {
580 |       "application/vnd.jupyter.widget-view+json": {
581 |        "model_id": "6c4e20b45f724cec829aa0bba02c0ca2",
582 |        "version_major": 2,
583 |        "version_minor": 0
584 |       },
585 |       "text/plain": [
586 |        "interactive(children=(IntSlider(value=1000, description='initE', layout=Layout(width='99%'), max=100000, style…"
587 |       ]
588 |      },
589 |      "metadata": {},
590 |      "output_type": "display_data"
591 |     }
592 |    ],
593 |    "source": [
594 |     "interact(main, initE=IntSlider(min=0, max=100000, step=1, value=initE, description='initE', style=style, \\\n",
595 |     "                               layout=slider_layout),\n",
596 |     "               initI=IntSlider(min=0, max=100000, step=10, value=initI, description='initI', style=style, \\\n",
597 |     "                               layout=slider_layout),\n",
598 |     "               initR=IntSlider(min=0, max=100000, step=10, value=initR, description='initR', style=style, \\\n",
599 |     "                               layout=slider_layout),\n",
600 |     "               initN=IntSlider(min=0, max=1380000000, step=1000, value=initN, description='initN', style=style, \\\n",
601 |     "                               layout=slider_layout),\n",
602 |     "               beta=FloatSlider(min=0, max=4, step=0.01, value=result.params['beta'].value, description='Infection rate', style=style, \\\n",
603 |     "                                layout=slider_layout),\n",
604 |     "               sigma=FloatSlider(min=0, max=4, step=0.01, value=result.params['sigma'].value, description='Incubation rate', style=style, \\\n",
605 |     "                                 layout=slider_layout),\n",
606 |     "               gamma=FloatSlider(min=0, max=4, step=0.01, value=result.params['gamma'].value, description='Recovery rate', style=style, \\\n",
607 |     "                                 layout=slider_layout),\n",
608 |     "               days=IntSlider(min=0, max=600, step=7, value=240, description='Days', style=style, \\\n",
609 |     "                              layout=slider_layout),\n",
610 |     "               param_fitting=ToggleButton(value=False, description='Fitting Mode', disabled=True, button_style='', \\\n",
611 |     "             tooltip='Click to show fewer plots', icon='check-circle')\n",
612 |     "        );"
613 |    ]
614 |   },
615 |   {
616 |    "cell_type": "markdown",
617 |    "metadata": {},
618 |    "source": [
619 |     "**References:**<br>\n",
620 |     "1. SEIR and SEIRS Model https://www.idmod.org/docs/hiv/model-seir.html<br>\n",
621 |     "2. Compartmental models in epidemiology https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology#The_SEIR_model<br>\n",
622 |     "3. Solve Differential Equations in Python https://www.youtube.com/watch?v=VV3BnroVjZo<br>\n",
623 |     "4. Computational Statistics in Python https://people.duke.edu/~ccc14/sta-663/CalibratingODEs.html<br>\n",
624 |     "5. Ordinary Differential Equations (ODE) with Python and Jupyter https://elc.github.io/posts/ordinary-differential-equations-with-python/<br>\n",
625 |     "6. SEIRS+ Model https://github.com/ryansmcgee/seirsplus<br>\n",
626 |     "7. Stack Overflow https://stackoverflow.com/questions/40753159/why-is-scipy-minimize-ignoring-my-constraints<br>\n",
627 |     "8. Lotka–Volterra equations https://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equations<br>\n",
628 |     "9. SEIR and Regression Model based COVID-19 outbreak predictions in India https://www.medrxiv.org/content/10.1101/2020.04.01.20049825v1.full.pdf<br>\n",
629 |     "\n",
630 |     "A simulator built with RShiny which provides many more parameters https://alhill.shinyapps.io/COVID19seir/"
631 |    ]
632 |   },
633 |   {
634 |    "cell_type": "code",
635 |    "execution_count": null,
636 |    "metadata": {},
637 |    "outputs": [],
638 |    "source": []
639 |   }
640 |  ],
641 |  "metadata": {
642 |   "kernelspec": {
643 |    "display_name": "Python 3",
644 |    "language": "python",
645 |    "name": "python3"
646 |   },
647 |   "language_info": {
648 |    "codemirror_mode": {
649 |     "name": "ipython",
650 |     "version": 3
651 |    },
652 |    "file_extension": ".py",
653 |    "mimetype": "text/x-python",
654 |    "name": "python",
655 |    "nbconvert_exporter": "python",
656 |    "pygments_lexer": "ipython3",
657 |    "version": "3.7.6"
658 |   }
659 |  },
660 |  "nbformat": 4,
661 |  "nbformat_minor": 4
662 | }
663 | 


--------------------------------------------------------------------------------
/compartmental_models/SEIRD Simulator in Python.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "markdown",
  5 |    "metadata": {},
  6 |    "source": [
  7 |     "# Simulation of SEIRD Model\n",
  8 |     "\n",
  9 |     "SEIRD is a type of compartmental models which are used in modelling of infectious disease using differential equations. These types of models divide the population into groups or compartments and the dynamics of these groups are expressed with the help of a system of differential equations.\n",
 10 |     "\n",
 11 |     "These system of equations are parametrized which capture the mechanistic nature of the disease. For simulation, you select values of these parameters and the resulting curves simulate the behaviour by solving the set of equations. Finally the results are plotted in a graph to visually understand the effect of the parameters.\n",
 12 |     "\n",
 13 |     "## SEIRD Model\n",
 14 |     "\n",
 15 |     "For completeness the SEIR model is produced below:\n",
 16 |     "\n",
 17 |     "<img src=\"images/seird_model.png\">\n",
 18 |     "\n",
 19 |     "$\\displaystyle \\frac{dS}{dt} = -\\frac{\\beta S I}{N}$<br><br>\n",
 20 |     "$\\displaystyle \\frac{dE}{dt} = \\frac{\\beta S I}{N} - \\sigma E$<br><br>\n",
 21 |     "$\\displaystyle \\frac{dI}{dt} = \\sigma E -  \\gamma I - \\mu I$<br><br>\n",
 22 |     "$\\displaystyle \\frac{dR}{dt} = \\gamma I$<br><br>\n",
 23 |     "$\\displaystyle \\frac{dD}{dt} = \\mu I$<br><br>\n",
 24 |     "$N = S + E + I + R + D$<br><br>\n",
 25 |     "Where,<br><br>\n",
 26 |     "$\\beta$ is infection rate or the rate of spread<br><br>\n",
 27 |     "$\\sigma$ is the incubation rate or the rate of latent individuals becoming infectious (average duration of incubation is $1/\\sigma$)<br><br>\n",
 28 |     "$\\gamma$ is the recovery rate or mortality rate. If the duration of indection is D then $\\gamma$ = 1/D<br><br>\n",
 29 |     "$\\mu$ is the mortality rate due to the disease\n",
 30 |     "\n",
 31 |     "#### A supplementary post to this notebook can be read at [Simulating Compartmental Models in Epidemiology using Python & Jupyter Widgets](https://dilbertai.com/2020/04/12/simulating-compartmental-models-in-epidemiology-using-python-jupyter-widgets/)"
 32 |    ]
 33 |   },
 34 |   {
 35 |    "cell_type": "code",
 36 |    "execution_count": 1,
 37 |    "metadata": {},
 38 |    "outputs": [],
 39 |    "source": [
 40 |     "import os\n",
 41 |     "import sys\n",
 42 |     "import matplotlib.pyplot as plt\n",
 43 |     "import numpy as np\n",
 44 |     "import pandas as pd\n",
 45 |     "from scipy.integrate import odeint\n",
 46 |     "import plotly.graph_objects as go\n",
 47 |     "import plotly.io as pio\n",
 48 |     "pio.renderers.default = \"notebook\"\n",
 49 |     "%matplotlib inline\n",
 50 |     "plt.style.use('ggplot')"
 51 |    ]
 52 |   },
 53 |   {
 54 |    "cell_type": "code",
 55 |    "execution_count": 3,
 56 |    "metadata": {},
 57 |    "outputs": [],
 58 |    "source": [
 59 |     "# Jupyter Specifics\n",
 60 |     "from IPython.display import HTML\n",
 61 |     "from ipywidgets.widgets import interact, IntSlider, FloatSlider, Layout\n",
 62 |     "\n",
 63 |     "style = {'description_width': '100px'}\n",
 64 |     "slider_layout = Layout(width='99%')"
 65 |    ]
 66 |   },
 67 |   {
 68 |    "cell_type": "code",
 69 |    "execution_count": 4,
 70 |    "metadata": {},
 71 |    "outputs": [],
 72 |    "source": [
 73 |     "def ode_model(z, t, beta, sigma, gamma, mu):\n",
 74 |     "    \"\"\"\n",
 75 |     "    Reference https://www.idmod.org/docs/hiv/model-seir.html\n",
 76 |     "    \"\"\"\n",
 77 |     "    S, E, I, R, D = z\n",
 78 |     "    N = S + E + I + R + D\n",
 79 |     "    dSdt = -beta*S*I/N\n",
 80 |     "    dEdt = beta*S*I/N - sigma*E\n",
 81 |     "    dIdt = sigma*E - gamma*I - mu*I\n",
 82 |     "    dRdt = gamma*I\n",
 83 |     "    dDdt = mu*I\n",
 84 |     "    return [dSdt, dEdt, dIdt, dRdt, dDdt]"
 85 |    ]
 86 |   },
 87 |   {
 88 |    "cell_type": "code",
 89 |    "execution_count": 5,
 90 |    "metadata": {},
 91 |    "outputs": [],
 92 |    "source": [
 93 |     "def ode_solver(t, initial_conditions, params):\n",
 94 |     "    initE, initI, initR, initN, initD = initial_conditions\n",
 95 |     "    beta, sigma, gamma, mu = params\n",
 96 |     "    initS = initN - (initE + initI + initR + initD)\n",
 97 |     "    res = odeint(ode_model, [initS, initE, initI, initR, initD], t, args=(beta, sigma, gamma, mu))\n",
 98 |     "    return res"
 99 |    ]
100 |   },
101 |   {
102 |    "cell_type": "code",
103 |    "execution_count": 6,
104 |    "metadata": {},
105 |    "outputs": [],
106 |    "source": [
107 |     "# ref: https://www.medrxiv.org/content/10.1101/2020.04.01.20049825v1.full.pdf\n",
108 |     "initN = 1380000000\n",
109 |     "# S0 = 966000000\n",
110 |     "initE = 1\n",
111 |     "initI = 1\n",
112 |     "initR = 0\n",
113 |     "initD = 0\n",
114 |     "sigma = 1/5.2\n",
115 |     "gamma = 1/2.9\n",
116 |     "mu = 0.034\n",
117 |     "R0 = 4\n",
118 |     "beta = R0 * gamma\n",
119 |     "days = 180"
120 |    ]
121 |   },
122 |   {
123 |    "cell_type": "code",
124 |    "execution_count": 29,
125 |    "metadata": {},
126 |    "outputs": [],
127 |    "source": [
128 |     "def main(initE, initI, initR, initD, initN, beta, sigma, gamma, mu, days):\n",
129 |     "    initial_conditions = [initE, initI, initR, initN, initD]\n",
130 |     "    params = [beta, sigma, gamma, mu]\n",
131 |     "    tspan = np.arange(0, days, 1)\n",
132 |     "    sol = ode_solver(tspan, initial_conditions, params)\n",
133 |     "    S, E, I, R, D = sol[:, 0], sol[:, 1], sol[:, 2], sol[:, 3], sol[:, 4]\n",
134 |     "    \n",
135 |     "    # Create traces\n",
136 |     "    fig = go.Figure()\n",
137 |     "    fig.add_trace(go.Scatter(x=tspan, y=S, mode='lines+markers', name='Susceptible'))\n",
138 |     "    fig.add_trace(go.Scatter(x=tspan, y=E, mode='lines+markers', name='Exposed'))\n",
139 |     "    fig.add_trace(go.Scatter(x=tspan, y=I, mode='lines+markers', name='Infected'))\n",
140 |     "    fig.add_trace(go.Scatter(x=tspan, y=R, mode='lines+markers',name='Recovered'))\n",
141 |     "    fig.add_trace(go.Scatter(x=tspan, y=D, mode='lines+markers',name='Death'))\n",
142 |     "    \n",
143 |     "    if days <= 30:\n",
144 |     "        step = 1\n",
145 |     "    elif days <= 90:\n",
146 |     "        step = 7\n",
147 |     "    else:\n",
148 |     "        step = 30\n",
149 |     "    \n",
150 |     "    # Edit the layout\n",
151 |     "    fig.update_layout(title='Simulation of SEIRD Model',\n",
152 |     "                       xaxis_title='Day',\n",
153 |     "                       yaxis_title='Counts',\n",
154 |     "                       title_x=0.5,\n",
155 |     "                      width=900, height=600\n",
156 |     "                     )\n",
157 |     "    fig.update_xaxes(tickangle=-90, tickformat = None, tickmode='array', tickvals=np.arange(0, days + 1, step))\n",
158 |     "    if not os.path.exists(\"images\"):\n",
159 |     "        os.mkdir(\"images\")\n",
160 |     "    fig.write_image(\"images/seird_simulation.png\")\n",
161 |     "    fig.show()"
162 |    ]
163 |   },
164 |   {
165 |    "cell_type": "code",
166 |    "execution_count": 8,
167 |    "metadata": {},
168 |    "outputs": [
169 |     {
170 |      "data": {
171 |       "application/vnd.jupyter.widget-view+json": {
172 |        "model_id": "ed764ea271e643938faad7a3d9421b66",
173 |        "version_major": 2,
174 |        "version_minor": 0
175 |       },
176 |       "text/plain": [
177 |        "interactive(children=(IntSlider(value=1, description='initE', layout=Layout(width='99%'), max=100000, style=Sl…"
178 |       ]
179 |      },
180 |      "metadata": {},
181 |      "output_type": "display_data"
182 |     }
183 |    ],
184 |    "source": [
185 |     "interact(main, \n",
186 |     "         initE=IntSlider(min=0, max=100000, step=1, value=initE, description='initE', style=style, layout=slider_layout),\n",
187 |     "         initI=IntSlider(min=0, max=100000, step=10, value=initI, description='initI', style=style, layout=slider_layout),\n",
188 |     "         initR=IntSlider(min=0, max=100000, step=10, value=initR, description='initR', style=style, layout=slider_layout),\n",
189 |     "         initD=IntSlider(min=0, max=100000, step=10, value=initD, description='initD', style=style, layout=slider_layout),\n",
190 |     "         initN=IntSlider(min=0, max=1380000000, step=1000, value=initN, description='initN', style=style, layout=slider_layout),\n",
191 |     "         beta=FloatSlider(min=0, max=4, step=0.01, value=beta, description='Infection rate', style=style, layout=slider_layout),\n",
192 |     "         sigma=FloatSlider(min=0, max=4, step=0.01, value=sigma, description='Incubation rate', style=style, layout=slider_layout),\n",
193 |     "         gamma=FloatSlider(min=0, max=4, step=0.01, value=gamma, description='Recovery rate', style=style, layout=slider_layout),\n",
194 |     "         mu=FloatSlider(min=0, max=1, step=0.01, value=mu, description='Mortality rate', style=style, layout=slider_layout),\n",
195 |     "         days=IntSlider(min=1, max=600, step=7, value=days, description='Days', style=style, layout=slider_layout)\n",
196 |     "        );"
197 |    ]
198 |   },
199 |   {
200 |    "cell_type": "markdown",
201 |    "metadata": {},
202 |    "source": [
203 |     "**References:**<br>\n",
204 |     "1. SEIR and SEIRS Model https://www.idmod.org/docs/hiv/model-seir.html<br>\n",
205 |     "2. Compartmental models in epidemiology https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology#The_SEIR_model<br>\n",
206 |     "3. Solve Differential Equations in Python https://www.youtube.com/watch?v=VV3BnroVjZo<br>\n",
207 |     "4. Computational Statistics in Python https://people.duke.edu/~ccc14/sta-663/CalibratingODEs.html<br>\n",
208 |     "5. Ordinary Differential Equations (ODE) with Python and Jupyter https://elc.github.io/posts/ordinary-differential-equations-with-python/<br>\n",
209 |     "6. SEIRS+ Model https://github.com/ryansmcgee/seirsplus<br>\n",
210 |     "7. Stack Overflow https://stackoverflow.com/questions/40753159/why-is-scipy-minimize-ignoring-my-constraints<br>\n",
211 |     "8. Lotka–Volterra equations https://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equations<br>\n",
212 |     "9. SEIR and Regression Model based COVID-19 outbreak predictions in India https://www.medrxiv.org/content/10.1101/2020.04.01.20049825v1.full.pdf<br>\n",
213 |     "\n",
214 |     "A simulator built with RShiny which provides many more parameters https://alhill.shinyapps.io/COVID19seir/"
215 |    ]
216 |   },
217 |   {
218 |    "cell_type": "code",
219 |    "execution_count": null,
220 |    "metadata": {},
221 |    "outputs": [],
222 |    "source": []
223 |   },
224 |   {
225 |    "cell_type": "code",
226 |    "execution_count": null,
227 |    "metadata": {},
228 |    "outputs": [],
229 |    "source": []
230 |   }
231 |  ],
232 |  "metadata": {
233 |   "kernelspec": {
234 |    "display_name": "Python 3",
235 |    "language": "python",
236 |    "name": "python3"
237 |   },
238 |   "language_info": {
239 |    "codemirror_mode": {
240 |     "name": "ipython",
241 |     "version": 3
242 |    },
243 |    "file_extension": ".py",
244 |    "mimetype": "text/x-python",
245 |    "name": "python",
246 |    "nbconvert_exporter": "python",
247 |    "pygments_lexer": "ipython3",
248 |    "version": "3.7.6"
249 |   }
250 |  },
251 |  "nbformat": 4,
252 |  "nbformat_minor": 4
253 | }
254 | 


--------------------------------------------------------------------------------
/compartmental_models/SEIRD Simulator with Parameter Estimation in Python.ipynb:
--------------------------------------------------------------------------------
  1 | {
  2 |  "cells": [
  3 |   {
  4 |    "cell_type": "markdown",
  5 |    "metadata": {},
  6 |    "source": [
  7 |     "# Simulation & Parameter Estimation of SEIRD Model\n",
  8 |     "\n",
  9 |     "SEIRD is a type of compartmental models which are used in modelling of infectious disease using differential equations. These types of models divide the population into groups or compartments and the dynamics of these groups are expressed with the help of a system of differential equations.\n",
 10 |     "\n",
 11 |     "These system of equations are parametrized which capture the mechanistic nature of the disease. For simulation, you select values of these parameters and the resulting curves simulate the behaviour by solving the set of equations. Finally the results are plotted in a graph to visually understand the effect of the parameters.\n",
 12 |     "\n",
 13 |     "## SEIRD Model\n",
 14 |     "\n",
 15 |     "For completeness the SEIR model is produced below:\n",
 16 |     "\n",
 17 |     "<img src=\"images/seird_model.png\">\n",
 18 |     "\n",
 19 |     "$\\displaystyle \\frac{dS}{dt} = -\\frac{\\beta S I}{N}$<br><br>\n",
 20 |     "$\\displaystyle \\frac{dE}{dt} = \\frac{\\beta S I}{N} - \\sigma E$<br><br>\n",
 21 |     "$\\displaystyle \\frac{dI}{dt} = \\sigma E -  \\gamma I - \\mu I$<br><br>\n",
 22 |     "$\\displaystyle \\frac{dR}{dt} = \\gamma I$<br><br>\n",
 23 |     "$\\displaystyle \\frac{dD}{dt} = \\mu I$<br><br>\n",
 24 |     "$N = S + E + I + R + D$<br><br>\n",
 25 |     "Where,<br><br>\n",
 26 |     "$\\beta$ is infection rate or the rate of spread<br><br>\n",
 27 |     "$\\sigma$ is the incubation rate or the rate of latent individuals becoming infectious (average duration of incubation is $1/\\sigma$)<br><br>\n",
 28 |     "$\\gamma$ is the recovery rate or mortality rate. If the duration of indection is D then $\\gamma$ = 1/D<br><br>\n",
 29 |     "$\\mu$ is the mortality rate due to the disease\n",
 30 |     "\n",
 31 |     "#### A supplementary blogpost to this notebook can be found at [Estimating Parameters of Compartmental Models from Observed Data](https://dilbertai.com/2020/04/27/estimating-parameters-of-compartmental-models-from-observed-data/)"
 32 |    ]
 33 |   },
 34 |   {
 35 |    "cell_type": "code",
 36 |    "execution_count": 1,
 37 |    "metadata": {},
 38 |    "outputs": [],
 39 |    "source": [
 40 |     "import os\n",
 41 |     "import sys\n",
 42 |     "import matplotlib.pyplot as plt\n",
 43 |     "import numpy as np\n",
 44 |     "import pandas as pd\n",
 45 |     "from scipy.integrate import odeint\n",
 46 |     "import plotly.graph_objects as go\n",
 47 |     "import plotly.io as pio\n",
 48 |     "import requests\n",
 49 |     "from lmfit import minimize, Parameters, Parameter, report_fit\n",
 50 |     "pio.renderers.default = \"notebook\"\n",
 51 |     "%matplotlib inline\n",
 52 |     "plt.style.use('ggplot')"
 53 |    ]
 54 |   },
 55 |   {
 56 |    "cell_type": "code",
 57 |    "execution_count": 2,
 58 |    "metadata": {},
 59 |    "outputs": [],
 60 |    "source": [
 61 |     "# Jupyter Specifics\n",
 62 |     "from IPython.display import HTML\n",
 63 |     "from ipywidgets.widgets import interact, IntSlider, FloatSlider, Layout, ToggleButton, ToggleButtons\n",
 64 |     "\n",
 65 |     "style = {'description_width': '100px'}\n",
 66 |     "slider_layout = Layout(width='99%')"
 67 |    ]
 68 |   },
 69 |   {
 70 |    "cell_type": "code",
 71 |    "execution_count": 3,
 72 |    "metadata": {},
 73 |    "outputs": [],
 74 |    "source": [
 75 |     "def ode_model(z, t, beta, sigma, gamma, mu):\n",
 76 |     "    \"\"\"\n",
 77 |     "    Reference https://www.idmod.org/docs/hiv/model-seir.html\n",
 78 |     "    \"\"\"\n",
 79 |     "    S, E, I, R, D = z\n",
 80 |     "    N = S + E + I + R + D\n",
 81 |     "    dSdt = -beta*S*I/N\n",
 82 |     "    dEdt = beta*S*I/N - sigma*E\n",
 83 |     "    dIdt = sigma*E - gamma*I - mu*I\n",
 84 |     "    dRdt = gamma*I\n",
 85 |     "    dDdt = mu*I\n",
 86 |     "    return [dSdt, dEdt, dIdt, dRdt, dDdt]"
 87 |    ]
 88 |   },
 89 |   {
 90 |    "cell_type": "code",
 91 |    "execution_count": 4,
 92 |    "metadata": {},
 93 |    "outputs": [],
 94 |    "source": [
 95 |     "def ode_solver(t, initial_conditions, params):\n",
 96 |     "    initE, initI, initR, initN, initD = initial_conditions\n",
 97 |     "    beta, sigma, gamma, mu = params['beta'].value, params['sigma'].value, params['gamma'].value, params['mu'].value\n",
 98 |     "    initS = initN - (initE + initI + initR + initD)\n",
 99 |     "    res = odeint(ode_model, [initS, initE, initI, initR, initD], t, args=(beta, sigma, gamma, mu))\n",
100 |     "    return res"
101 |    ]
102 |   },
103 |   {
104 |    "cell_type": "code",
105 |    "execution_count": 5,
106 |    "metadata": {},
107 |    "outputs": [
108 |     {
109 |      "name": "stdout",
110 |      "output_type": "stream",
111 |      "text": [
112 |       "Request Success? True\n"
113 |      ]
114 |     }
115 |    ],
116 |    "source": [
117 |     "response = requests.get('https://api.rootnet.in/covid19-in/stats/history')\n",
118 |     "print('Request Success? {}'.format(response.status_code == 200))\n",
119 |     "covid_history = response.json()['data']"
120 |    ]
121 |   },
122 |   {
123 |    "cell_type": "code",
124 |    "execution_count": 6,
125 |    "metadata": {},
126 |    "outputs": [],
127 |    "source": [
128 |     "keys = ['day', 'total', 'confirmedCasesIndian', 'confirmedCasesForeign', 'confirmedButLocationUnidentified',\n",
129 |     "        'discharged', 'deaths']\n",
130 |     "df_covid_history = pd.DataFrame([[d.get('day'), \n",
131 |     "                                  d['summary'].get('total'), \n",
132 |     "                                  d['summary'].get('confirmedCasesIndian'), \n",
133 |     "                                  d['summary'].get('confirmedCasesForeign'),\n",
134 |     "                                  d['summary'].get('confirmedButLocationUnidentified'),\n",
135 |     "                                  d['summary'].get('discharged'), \n",
136 |     "                                  d['summary'].get('deaths')] \n",
137 |     "                                 for d in covid_history],\n",
138 |     "                    columns=keys)\n",
139 |     "df_covid_history = df_covid_history.sort_values(by='day')\n",
140 |     "df_covid_history['infected'] = df_covid_history['total'] - df_covid_history['discharged'] - df_covid_history['deaths']\n",
141 |     "df_covid_history['total_recovered_or_dead'] = df_covid_history['discharged'] + df_covid_history['deaths']"
142 |    ]
143 |   },
144 |   {
145 |    "cell_type": "code",
146 |    "execution_count": 41,
147 |    "metadata": {},
148 |    "outputs": [
149 |     {
150 |      "data": {
151 |       "text/html": [
152 |        "<div>\n",
153 |        "<style scoped>\n",
154 |        "    .dataframe tbody tr th:only-of-type {\n",
155 |        "        vertical-align: middle;\n",
156 |        "    }\n",
157 |        "\n",
158 |        "    .dataframe tbody tr th {\n",
159 |        "        vertical-align: top;\n",
160 |        "    }\n",
161 |        "\n",
162 |        "    .dataframe thead th {\n",
163 |        "        text-align: right;\n",
164 |        "    }\n",
165 |        "</style>\n",
166 |        "<table border=\"1\" class=\"dataframe\">\n",
167 |        "  <thead>\n",
168 |        "    <tr style=\"text-align: right;\">\n",
169 |        "      <th></th>\n",
170 |        "      <th>day</th>\n",
171 |        "      <th>total</th>\n",
172 |        "      <th>confirmedCasesIndian</th>\n",
173 |        "      <th>confirmedCasesForeign</th>\n",
174 |        "      <th>confirmedButLocationUnidentified</th>\n",
175 |        "      <th>discharged</th>\n",
176 |        "      <th>deaths</th>\n",
177 |        "      <th>infected</th>\n",
178 |        "      <th>total_recovered_or_dead</th>\n",
179 |        "    </tr>\n",
180 |        "  </thead>\n",
181 |        "  <tbody>\n",
182 |        "    <tr>\n",
183 |        "      <th>0</th>\n",
184 |        "      <td>2020-03-10</td>\n",
185 |        "      <td>47</td>\n",
186 |        "      <td>31</td>\n",
187 |        "      <td>16</td>\n",
188 |        "      <td>0</td>\n",
189 |        "      <td>0</td>\n",
190 |        "      <td>0</td>\n",
191 |        "      <td>47</td>\n",
192 |        "      <td>0</td>\n",
193 |        "    </tr>\n",
194 |        "    <tr>\n",
195 |        "      <th>1</th>\n",
196 |        "      <td>2020-03-11</td>\n",
197 |        "      <td>60</td>\n",
198 |        "      <td>44</td>\n",
199 |        "      <td>16</td>\n",
200 |        "      <td>0</td>\n",
201 |        "      <td>0</td>\n",
202 |        "      <td>0</td>\n",
203 |        "      <td>60</td>\n",
204 |        "      <td>0</td>\n",
205 |        "    </tr>\n",
206 |        "    <tr>\n",
207 |        "      <th>2</th>\n",
208 |        "      <td>2020-03-12</td>\n",
209 |        "      <td>73</td>\n",
210 |        "      <td>56</td>\n",
211 |        "      <td>17</td>\n",
212 |        "      <td>0</td>\n",
213 |        "      <td>0</td>\n",
214 |        "      <td>0</td>\n",
215 |        "      <td>73</td>\n",
216 |        "      <td>0</td>\n",
217 |        "    </tr>\n",
218 |        "    <tr>\n",
219 |        "      <th>3</th>\n",
220 |        "      <td>2020-03-13</td>\n",
221 |        "      <td>82</td>\n",
222 |        "      <td>65</td>\n",
223 |        "      <td>17</td>\n",
224 |        "      <td>0</td>\n",
225 |        "      <td>10</td>\n",
226 |        "      <td>2</td>\n",
227 |        "      <td>70</td>\n",
228 |        "      <td>12</td>\n",
229 |        "    </tr>\n",
230 |        "    <tr>\n",
231 |        "      <th>4</th>\n",
232 |        "      <td>2020-03-14</td>\n",
233 |        "      <td>84</td>\n",
234 |        "      <td>67</td>\n",
235 |        "      <td>17</td>\n",
236 |        "      <td>0</td>\n",
237 |        "      <td>10</td>\n",
238 |        "      <td>2</td>\n",
239 |        "      <td>72</td>\n",
240 |        "      <td>12</td>\n",
241 |        "    </tr>\n",
242 |        "  </tbody>\n",
243 |        "</table>\n",
244 |        "</div>"
245 |       ],
246 |       "text/plain": [
247 |        "          day  total  confirmedCasesIndian  confirmedCasesForeign  \\\n",
248 |        "0  2020-03-10     47                    31                     16   \n",
249 |        "1  2020-03-11     60                    44                     16   \n",
250 |        "2  2020-03-12     73                    56                     17   \n",
251 |        "3  2020-03-13     82                    65                     17   \n",
252 |        "4  2020-03-14     84                    67                     17   \n",
253 |        "\n",
254 |        "   confirmedButLocationUnidentified  discharged  deaths  infected  \\\n",
255 |        "0                                 0           0       0        47   \n",
256 |        "1                                 0           0       0        60   \n",
257 |        "2                                 0           0       0        73   \n",
258 |        "3                                 0          10       2        70   \n",
259 |        "4                                 0          10       2        72   \n",
260 |        "\n",
261 |        "   total_recovered_or_dead  \n",
262 |        "0                        0  \n",
263 |        "1                        0  \n",
264 |        "2                        0  \n",
265 |        "3                       12  \n",
266 |        "4                       12  "
267 |       ]
268 |      },
269 |      "execution_count": 41,
270 |      "metadata": {},
271 |      "output_type": "execute_result"
272 |     }
273 |    ],
274 |    "source": [
275 |     "df_covid_history.head()"
276 |    ]
277 |   },
278 |   {
279 |    "cell_type": "code",
280 |    "execution_count": 7,
281 |    "metadata": {},
282 |    "outputs": [],
283 |    "source": [
284 |     "# ref: https://www.medrxiv.org/content/10.1101/2020.04.01.20049825v1.full.pdf\n",
285 |     "initN = 1380000000\n",
286 |     "# S0 = 966000000\n",
287 |     "initE = 1000\n",
288 |     "initI = 47\n",
289 |     "initR = 0\n",
290 |     "initD = 0\n",
291 |     "sigma = 1/5.2\n",
292 |     "gamma = 1/2.9\n",
293 |     "mu = 0.034\n",
294 |     "R0 = 4\n",
295 |     "beta = R0 * gamma\n",
296 |     "days = 112\n",
297 |     "\n",
298 |     "params = Parameters()\n",
299 |     "params.add('beta', value=beta, min=0, max=10)\n",
300 |     "params.add('sigma', value=sigma, min=0, max=10)\n",
301 |     "params.add('gamma', value=gamma, min=0, max=10)\n",
302 |     "params.add('mu', value=mu, min=0, max=10)"
303 |    ]
304 |   },
305 |   {
306 |    "cell_type": "markdown",
307 |    "metadata": {},
308 |    "source": [
309 |     "## Simulation"
310 |    ]
311 |   },
312 |   {
313 |    "cell_type": "code",
314 |    "execution_count": 8,
315 |    "metadata": {},
316 |    "outputs": [],
317 |    "source": [
318 |     "def main(initE, initI, initR, initD, initN, beta, sigma, gamma, mu, days, param_fitting):\n",
319 |     "    initial_conditions = [initE, initI, initR, initN, initD]\n",
320 |     "    params['beta'].value, params['sigma'].value,params['gamma'].value, params['mu'].value = [beta, sigma, gamma, mu]\n",
321 |     "    tspan = np.arange(0, days, 1)\n",
322 |     "    sol = ode_solver(tspan, initial_conditions, params)\n",
323 |     "    S, E, I, R, D = sol[:, 0], sol[:, 1], sol[:, 2], sol[:, 3], sol[:, 4]\n",
324 |     "    \n",
325 |     "    # Create traces\n",
326 |     "    fig = go.Figure()\n",
327 |     "    if not param_fitting:\n",
328 |     "        fig.add_trace(go.Scatter(x=tspan, y=S, mode='lines+markers', name='Susceptible'))\n",
329 |     "        fig.add_trace(go.Scatter(x=tspan, y=E, mode='lines+markers', name='Exposed'))\n",
330 |     "    fig.add_trace(go.Scatter(x=tspan, y=I, mode='lines+markers', name='Infected'))\n",
331 |     "    fig.add_trace(go.Scatter(x=tspan, y=R, mode='lines+markers',name='Recovered'))\n",
332 |     "    fig.add_trace(go.Scatter(x=tspan, y=D, mode='lines+markers',name='Death'))\n",
333 |     "    if param_fitting:\n",
334 |     "        fig.add_trace(go.Scatter(x=tspan, y=df_covid_history.infected, mode='lines+markers',\\\n",
335 |     "                             name='Infections Observed', line = dict(dash='dash')))\n",
336 |     "        fig.add_trace(go.Scatter(x=tspan, y=df_covid_history.discharged, mode='lines+markers',\\\n",
337 |     "                             name='Recovered Observed', line = dict(dash='dash')))\n",
338 |     "        fig.add_trace(go.Scatter(x=tspan, y=df_covid_history.deaths, mode='lines+markers',\\\n",
339 |     "                             name='Deaths Observed', line = dict(dash='dash')))\n",
340 |     "    \n",
341 |     "    if days <= 30:\n",
342 |     "        step = 1\n",
343 |     "    elif days <= 90:\n",
344 |     "        step = 7\n",
345 |     "    else:\n",
346 |     "        step = 30\n",
347 |     "    \n",
348 |     "    # Edit the layout\n",
349 |     "    fig.update_layout(title='Simulation of SEIRD Model',\n",
350 |     "                       xaxis_title='Day',\n",
351 |     "                       yaxis_title='Counts',\n",
352 |     "                       title_x=0.5,\n",
353 |     "                      width=900, height=600\n",
354 |     "                     )\n",
355 |     "    fig.update_xaxes(tickangle=-90, tickformat = None, tickmode='array', tickvals=np.arange(0, days + 1, step))\n",
356 |     "    if not os.path.exists(\"images\"):\n",
357 |     "        os.mkdir(\"images\")\n",
358 |     "    fig.write_image(\"images/seird_simulation.png\")\n",
359 |     "    fig.show()"
360 |    ]
361 |   },
362 |   {
363 |    "cell_type": "code",
364 |    "execution_count": 9,
365 |    "metadata": {
366 |     "scrolled": false
367 |    },
368 |    "outputs": [
369 |     {
370 |      "data": {
371 |       "application/vnd.jupyter.widget-view+json": {
372 |        "model_id": "37f85c2d12ab4759938835c16d282fda",
373 |        "version_major": 2,
374 |        "version_minor": 0
375 |       },
376 |       "text/plain": [
377 |        "interactive(children=(IntSlider(value=1000, description='initE', layout=Layout(width='99%'), max=100000, style…"
378 |       ]
379 |      },
380 |      "metadata": {},
381 |      "output_type": "display_data"
382 |     }
383 |    ],
384 |    "source": [
385 |     "interact(main, \n",
386 |     "         initE=IntSlider(min=0, max=100000, step=1, value=initE, description='initE', style=style, layout=slider_layout),\n",
387 |     "         initI=IntSlider(min=0, max=100000, step=10, value=initI, description='initI', style=style, layout=slider_layout),\n",
388 |     "         initR=IntSlider(min=0, max=100000, step=10, value=initR, description='initR', style=style, layout=slider_layout),\n",
389 |     "         initD=IntSlider(min=0, max=100000, step=10, value=initD, description='initD', style=style, layout=slider_layout),\n",
390 |     "         initN=IntSlider(min=0, max=1380000000, step=1000, value=initN, description='initN', style=style, layout=slider_layout),\n",
391 |     "         beta=FloatSlider(min=0, max=4, step=0.01, value=beta, description='Infection rate', style=style, layout=slider_layout),\n",
392 |     "         sigma=FloatSlider(min=0, max=4, step=0.01, value=sigma, description='Incubation rate', style=style, layout=slider_layout),\n",
393 |     "         gamma=FloatSlider(min=0, max=4, step=0.01, value=gamma, description='Recovery rate', style=style, layout=slider_layout),\n",
394 |     "         mu=FloatSlider(min=0, max=1, step=0.001, value=mu, description='Mortality rate', style=style, layout=slider_layout),\n",
395 |     "         days=IntSlider(min=0, max=600, step=7, value=days, description='Days', style=style, layout=slider_layout),\n",
396 |     "         param_fitting=ToggleButton(value=False, description='Fitting Mode', disabled=False, button_style='', \\\n",
397 |     "             tooltip='Click to show fewer plots', icon='check-circle')\n",
398 |     "        );"
399 |    ]
400 |   },
401 |   {
402 |    "cell_type": "markdown",
403 |    "metadata": {},
404 |    "source": [
405 |     "## Parameter Estimation"
406 |    ]
407 |   },
408 |   {
409 |    "cell_type": "code",
410 |    "execution_count": 24,
411 |    "metadata": {},
412 |    "outputs": [],
413 |    "source": [
414 |     "def error(params, initial_conditions, tspan, data):\n",
415 |     "    sol = ode_solver(tspan, initial_conditions, params)\n",
416 |     "    return (sol[:, 2:5] - data).ravel()"
417 |    ]
418 |   },
419 |   {
420 |    "cell_type": "code",
421 |    "execution_count": 25,
422 |    "metadata": {},
423 |    "outputs": [],
424 |    "source": [
425 |     "initial_conditions = [initE, initI, initR, initN, initD]\n",
426 |     "beta = 1.14\n",
427 |     "sigma = 0.02\n",
428 |     "gamma = 0.02\n",
429 |     "mu = 0.01\n",
430 |     "params['beta'].value = beta\n",
431 |     "params['sigma'].value = sigma\n",
432 |     "params['gamma'].value = gamma\n",
433 |     "params['mu'].value = mu\n",
434 |     "days = 45\n",
435 |     "tspan = np.arange(0, days, 1)\n",
436 |     "data = df_covid_history.loc[0:(days-1), ['infected', 'discharged', 'deaths']].values"
437 |    ]
438 |   },
439 |   {
440 |    "cell_type": "code",
441 |    "execution_count": 26,
442 |    "metadata": {},
443 |    "outputs": [
444 |     {
445 |      "data": {
446 |       "text/plain": [
447 |        "(45, 3)"
448 |       ]
449 |      },
450 |      "execution_count": 26,
451 |      "metadata": {},
452 |      "output_type": "execute_result"
453 |     }
454 |    ],
455 |    "source": [
456 |     "data.shape"
457 |    ]
458 |   },
459 |   {
460 |    "cell_type": "code",
461 |    "execution_count": 27,
462 |    "metadata": {},
463 |    "outputs": [
464 |     {
465 |      "data": {
466 |       "text/html": [
467 |        "<table><tr><th> name </th><th> value </th><th> initial value </th><th> min </th><th> max </th><th> vary </th></tr><tr><td> beta </td><td>  1.14000000 </td><td> 1.3793103448275863 </td><td>  0.00000000 </td><td>  10.0000000 </td><td> True </td></tr><tr><td> sigma </td><td>  0.02000000 </td><td> 0.1923076923076923 </td><td>  0.00000000 </td><td>  10.0000000 </td><td> True </td></tr><tr><td> gamma </td><td>  0.02000000 </td><td> 0.3448275862068966 </td><td>  0.00000000 </td><td>  10.0000000 </td><td> True </td></tr><tr><td> mu </td><td>  0.01000000 </td><td> 0.034 </td><td>  0.00000000 </td><td>  10.0000000 </td><td> True </td></tr></table>"
468 |       ],
469 |       "text/plain": [
470 |        "Parameters([('beta', <Parameter 'beta', value=1.14, bounds=[0:10]>),\n",
471 |        "            ('sigma', <Parameter 'sigma', value=0.02, bounds=[0:10]>),\n",
472 |        "            ('gamma', <Parameter 'gamma', value=0.02, bounds=[0:10]>),\n",
473 |        "            ('mu', <Parameter 'mu', value=0.01, bounds=[0:10]>)])"
474 |       ]
475 |      },
476 |      "execution_count": 27,
477 |      "metadata": {},
478 |      "output_type": "execute_result"
479 |     }
480 |    ],
481 |    "source": [
482 |     "params"
483 |    ]
484 |   },
485 |   {
486 |    "cell_type": "code",
487 |    "execution_count": 28,
488 |    "metadata": {},
489 |    "outputs": [],
490 |    "source": [
491 |     "# fit model and find predicted values\n",
492 |     "result = minimize(error, params, args=(initial_conditions, tspan, data), method='leastsq')\n",
493 |     "# result = minimize(error, params, args=(initial_conditions, tspan, data), method='leastsq', \\\n",
494 |     "# **{'xtol':1.e-15, 'ftol':1.e-15})"
495 |    ]
496 |   },
497 |   {
498 |    "cell_type": "code",
499 |    "execution_count": 29,
500 |    "metadata": {},
501 |    "outputs": [
502 |     {
503 |      "data": {
504 |       "text/html": [
505 |        "<table><tr><th> name </th><th> value </th><th> standard error </th><th> relative error </th><th> initial value </th><th> min </th><th> max </th><th> vary </th></tr><tr><td> beta </td><td>  0.25012193 </td><td>  0.01967139 </td><td> (7.86%) </td><td> 1.14 </td><td>  0.00000000 </td><td>  10.0000000 </td><td> True </td></tr><tr><td> sigma </td><td>  0.07995170 </td><td>  0.00717541 </td><td> (8.97%) </td><td> 0.02 </td><td>  0.00000000 </td><td>  10.0000000 </td><td> True </td></tr><tr><td> gamma </td><td>  0.01816017 </td><td>  0.00102423 </td><td> (5.64%) </td><td> 0.02 </td><td>  0.00000000 </td><td>  10.0000000 </td><td> True </td></tr><tr><td> mu </td><td>  0.00378277 </td><td>  9.6475e-04 </td><td> (25.50%) </td><td> 0.01 </td><td>  0.00000000 </td><td>  10.0000000 </td><td> True </td></tr></table>"
506 |       ],
507 |       "text/plain": [
508 |        "Parameters([('beta',\n",
509 |        "             <Parameter 'beta', value=0.2501219283004641 +/- 0.0197, bounds=[0:10]>),\n",
510 |        "            ('sigma',\n",
511 |        "             <Parameter 'sigma', value=0.07995170066026125 +/- 0.00718, bounds=[0:10]>),\n",
512 |        "            ('gamma',\n",
513 |        "             <Parameter 'gamma', value=0.01816016664950515 +/- 0.00102, bounds=[0:10]>),\n",
514 |        "            ('mu',\n",
515 |        "             <Parameter 'mu', value=0.003782771947826724 +/- 0.000965, bounds=[0:10]>)])"
516 |       ]
517 |      },
518 |      "execution_count": 29,
519 |      "metadata": {},
520 |      "output_type": "execute_result"
521 |     }
522 |    ],
523 |    "source": [
524 |     "result.params"
525 |    ]
526 |   },
527 |   {
528 |    "cell_type": "code",
529 |    "execution_count": 30,
530 |    "metadata": {},
531 |    "outputs": [
532 |     {
533 |      "name": "stdout",
534 |      "output_type": "stream",
535 |      "text": [
536 |       "[[Fit Statistics]]\n",
537 |       "    # fitting method   = leastsq\n",
538 |       "    # function evals   = 67\n",
539 |       "    # data points      = 135\n",
540 |       "    # variables        = 4\n",
541 |       "    chi-square         = 25872760.4\n",
542 |       "    reduced chi-square = 197501.988\n",
543 |       "    Akaike info crit   = 1650.06257\n",
544 |       "    Bayesian info crit = 1661.68367\n",
545 |       "[[Variables]]\n",
546 |       "    beta:   0.25012193 +/- 0.01967139 (7.86%) (init = 1.14)\n",
547 |       "    sigma:  0.07995170 +/- 0.00717541 (8.97%) (init = 0.02)\n",
548 |       "    gamma:  0.01816017 +/- 0.00102423 (5.64%) (init = 0.02)\n",
549 |       "    mu:     0.00378277 +/- 9.6475e-04 (25.50%) (init = 0.01)\n",
550 |       "[[Correlations]] (unreported correlations are < 0.100)\n",
551 |       "    C(beta, sigma)  = -0.983\n",
552 |       "    C(beta, gamma)  =  0.383\n",
553 |       "    C(sigma, gamma) = -0.270\n",
554 |       "    C(beta, mu)     =  0.143\n"
555 |      ]
556 |     }
557 |    ],
558 |    "source": [
559 |     "# display fitted statistics\n",
560 |     "report_fit(result)"
561 |    ]
562 |   },
563 |   {
564 |    "cell_type": "code",
565 |    "execution_count": 43,
566 |    "metadata": {},
567 |    "outputs": [
568 |     {
569 |      "data": {
570 |       "text/html": [
571 |        "<div>\n",
572 |        "        \n",
573 |        "        \n",
574 |        "            <div id=\"8af69475-1372-4975-b63e-1f438adb2dab\" class=\"plotly-graph-div\" style=\"height:600px; width:1000px;\"></div>\n",
575 |        "            <script type=\"text/javascript\">\n",
576 |        "                require([\"plotly\"], function(Plotly) {\n",
577 |        "                    window.PLOTLYENV=window.PLOTLYENV || {};\n",
578 |        "                    \n",
579 |        "                if (document.getElementById(\"8af69475-1372-4975-b63e-1f438adb2dab\")) {\n",
580 |        "                    Plotly.newPlot(\n",
581 |        "                        '8af69475-1372-4975-b63e-1f438adb2dab',\n",
582 |        "                        [{\"line\": {\"dash\": \"dot\"}, \"mode\": \"markers\", \"name\": \"Observed Infections\", \"type\": \"scatter\", \"x\": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44], \"y\": [47, 60, 73, 70, 72, 95, 99, 120, 134, 149, 196, 256, 329, 424, 469, 553, 634, 640, 810, 901, 1118, 1238, 1649, 1860, 2322, 2784, 3219, 3851, 4312, 4714, 5218, 6039, 6634, 7409, 8048, 9272, 10197, 10824, 11616, 12289, 13295, 14255, 15122, 15859, 16689]}, {\"line\": {\"dash\": \"dot\"}, \"mode\": \"markers\", \"name\": \"Observed Recovered\", \"type\": \"scatter\", \"x\": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44], \"y\": [0, 0, 0, 10, 10, 13, 13, 14, 14, 20, 23, 23, 24, 35, 40, 43, 45, 67, 80, 96, 102, 124, 144, 156, 163, 213, 275, 319, 353, 411, 478, 516, 653, 765, 980, 1190, 1344, 1515, 1767, 2015, 2302, 2842, 3260, 3960, 4325]}, {\"line\": {\"dash\": \"dot\"}, \"mode\": \"markers\", \"name\": \"Observed Deaths\", \"type\": \"scatter\", \"x\": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44], \"y\": [0, 0, 0, 2, 2, 2, 2, 3, 3, 4, 4, 4, 7, 8, 10, 10, 15, 17, 19, 27, 31, 35, 41, 53, 62, 75, 83, 111, 124, 149, 169, 206, 242, 273, 324, 353, 392, 420, 452, 488, 519, 559, 603, 652, 686]}, {\"mode\": \"lines+markers\", \"name\": \"Fitted Infections\", \"type\": \"scatter\", \"x\": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44], \"y\": [47.0, 122.67621183705414, 193.15227611860044, 260.156197951526, 325.1882671146835, 389.56917819639307, 454.48037308680557, 520.9980514310201, 590.1220617249678, 662.8006656391196, 739.952009230301, 822.48298786722, 911.3060896583893, 1007.3547049934117, 1111.5973150226505, 1225.0509157355514, 1348.7939837057254, 1483.9792546783572, 1631.846552868499, 1793.7358906078045, 1971.1010400413732, 2165.5237648561274, 2378.7288971584976, 2612.6004389535565, 2869.1988679051187, 3150.7798326728657, 3459.8144264580033, 3799.0112387236663, 4171.340396460519, 4580.059818424939, 5028.743924566521, 5521.315061676363, 6062.077927438665, 6655.757300075071, 7307.539417072618, 8023.117329714681, 8808.740715878057, 9671.270465196692, 10618.238694309752, 11657.91446972302, 12799.376088674502, 14052.590335338544, 15428.499469063707, 16939.116847885947, 18597.63168165079]}, {\"mode\": \"lines+markers\", \"name\": \"Fitted Recovered\", \"type\": \"scatter\", \"x\": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44], \"y\": [0.0, 1.5499791886320489, 4.424219679321204, 8.544361707350548, 13.861279134883812, 20.351394194118033, 28.013792692144392, 36.868012807154614, 46.95240305135948, 58.32296621066019, 71.05262174509117, 85.23083380242119, 100.96356252418816, 118.37350654720943, 137.60061287014312, 158.80283688927133, 182.1571416873315, 207.86073057254637, 236.13251194764237, 267.2147992595719, 301.37525272375797, 338.9090733643629, 380.1414628347932, 425.4303660545156, 475.16951698366586, 529.7918109868741, 589.7730304973967, 655.6359552260182, 727.9548900600471, 807.3606495533545, 894.5460410520512, 990.2718934176565, 1095.3736832372776, 1210.7688157521975, 1337.4646250956441, 1476.5671552366675, 1629.2908153380383, 1796.9689678416153, 1981.0655777231075, 2183.187974372634, 2405.100892803995, 2648.741873589293, 2916.23816893769, 3209.9253296688357, 3532.3675694000326]}, {\"mode\": \"lines+markers\", \"name\": \"Fitted Deaths\", \"type\": \"scatter\", \"x\": [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44], \"y\": [0.0, 0.322861453181226, 0.9215672089889747, 1.779794888585517, 2.887311492478131, 4.239205759643789, 5.835287263234703, 7.679625815703682, 9.78020943164507, 12.148703519840385, 14.800297240895521, 17.753626022284653, 21.03076141537256, 24.657261608602507, 28.662277632960258, 33.078711677814226, 37.94342524328717, 43.29749587876292, 49.18652231584781, 55.66097856876228, 62.77661839648846, 70.59493232247375, 79.18366001649302, 88.61736158729187, 98.97805201898655, 110.35590363616376, 122.85002216161378, 136.56930287493486, 151.63337377619655, 168.1736338577495, 186.33439524209217, 206.2741389679727, 228.16689523333858, 252.20376001646446, 278.59456152954704, 307.5696892937806, 339.38210535531664, 374.30954978883045, 412.6569672432119, 454.75916524777534, 500.98373900329136, 551.7342791961993, 607.453893543409, 668.6290784683188, 735.7939609713561]}],\n",
583 |        "                        {\"height\": 600, \"template\": {\"data\": {\"bar\": [{\"error_x\": {\"color\": \"#2a3f5f\"}, \"error_y\": {\"color\": \"#2a3f5f\"}, \"marker\": {\"line\": {\"color\": \"#E5ECF6\", \"width\": 0.5}}, \"type\": \"bar\"}], \"barpolar\": [{\"marker\": {\"line\": {\"color\": \"#E5ECF6\", \"width\": 0.5}}, \"type\": \"barpolar\"}], \"carpet\": [{\"aaxis\": {\"endlinecolor\": \"#2a3f5f\", \"gridcolor\": \"white\", \"linecolor\": \"white\", \"minorgridcolor\": \"white\", \"startlinecolor\": \"#2a3f5f\"}, \"baxis\": {\"endlinecolor\": \"#2a3f5f\", \"gridcolor\": \"white\", \"linecolor\": \"white\", \"minorgridcolor\": \"white\", \"startlinecolor\": \"#2a3f5f\"}, \"type\": \"carpet\"}], \"choropleth\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"choropleth\"}], \"contour\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"contour\"}], \"contourcarpet\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"contourcarpet\"}], \"heatmap\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"heatmap\"}], \"heatmapgl\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"heatmapgl\"}], \"histogram\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"histogram\"}], \"histogram2d\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"histogram2d\"}], \"histogram2dcontour\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"histogram2dcontour\"}], \"mesh3d\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"type\": \"mesh3d\"}], \"parcoords\": [{\"line\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"parcoords\"}], \"pie\": [{\"automargin\": true, \"type\": \"pie\"}], \"scatter\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatter\"}], \"scatter3d\": [{\"line\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatter3d\"}], \"scattercarpet\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattercarpet\"}], \"scattergeo\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattergeo\"}], \"scattergl\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattergl\"}], \"scattermapbox\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scattermapbox\"}], \"scatterpolar\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterpolar\"}], \"scatterpolargl\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterpolargl\"}], \"scatterternary\": [{\"marker\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"type\": \"scatterternary\"}], \"surface\": [{\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}, \"colorscale\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"type\": \"surface\"}], \"table\": [{\"cells\": {\"fill\": {\"color\": \"#EBF0F8\"}, \"line\": {\"color\": \"white\"}}, \"header\": {\"fill\": {\"color\": \"#C8D4E3\"}, \"line\": {\"color\": \"white\"}}, \"type\": \"table\"}]}, \"layout\": {\"annotationdefaults\": {\"arrowcolor\": \"#2a3f5f\", \"arrowhead\": 0, \"arrowwidth\": 1}, \"coloraxis\": {\"colorbar\": {\"outlinewidth\": 0, \"ticks\": \"\"}}, \"colorscale\": {\"diverging\": [[0, \"#8e0152\"], [0.1, \"#c51b7d\"], [0.2, \"#de77ae\"], [0.3, \"#f1b6da\"], [0.4, \"#fde0ef\"], [0.5, \"#f7f7f7\"], [0.6, \"#e6f5d0\"], [0.7, \"#b8e186\"], [0.8, \"#7fbc41\"], [0.9, \"#4d9221\"], [1, \"#276419\"]], \"sequential\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]], \"sequentialminus\": [[0.0, \"#0d0887\"], [0.1111111111111111, \"#46039f\"], [0.2222222222222222, \"#7201a8\"], [0.3333333333333333, \"#9c179e\"], [0.4444444444444444, \"#bd3786\"], [0.5555555555555556, \"#d8576b\"], [0.6666666666666666, \"#ed7953\"], [0.7777777777777778, \"#fb9f3a\"], [0.8888888888888888, \"#fdca26\"], [1.0, \"#f0f921\"]]}, \"colorway\": [\"#636efa\", \"#EF553B\", \"#00cc96\", \"#ab63fa\", \"#FFA15A\", \"#19d3f3\", \"#FF6692\", \"#B6E880\", \"#FF97FF\", \"#FECB52\"], \"font\": {\"color\": \"#2a3f5f\"}, \"geo\": {\"bgcolor\": \"white\", \"lakecolor\": \"white\", \"landcolor\": \"#E5ECF6\", \"showlakes\": true, \"showland\": true, \"subunitcolor\": \"white\"}, \"hoverlabel\": {\"align\": \"left\"}, \"hovermode\": \"closest\", \"mapbox\": {\"style\": \"light\"}, \"paper_bgcolor\": \"white\", \"plot_bgcolor\": \"#E5ECF6\", \"polar\": {\"angularaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"radialaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"scene\": {\"xaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"yaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}, \"zaxis\": {\"backgroundcolor\": \"#E5ECF6\", \"gridcolor\": \"white\", \"gridwidth\": 2, \"linecolor\": \"white\", \"showbackground\": true, \"ticks\": \"\", \"zerolinecolor\": \"white\"}}, \"shapedefaults\": {\"line\": {\"color\": \"#2a3f5f\"}}, \"ternary\": {\"aaxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"baxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}, \"bgcolor\": \"#E5ECF6\", \"caxis\": {\"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\"}}, \"title\": {\"x\": 0.05}, \"xaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}, \"yaxis\": {\"automargin\": true, \"gridcolor\": \"white\", \"linecolor\": \"white\", \"ticks\": \"\", \"title\": {\"standoff\": 15}, \"zerolinecolor\": \"white\", \"zerolinewidth\": 2}}}, \"title\": {\"text\": \"SEIRD: Observed vs Fitted\", \"x\": 0.5}, \"width\": 1000, \"xaxis\": {\"title\": {\"text\": \"Day\"}}, \"yaxis\": {\"title\": {\"text\": \"Counts\"}}},\n",
584 |        "                        {\"responsive\": true}\n",
585 |        "                    ).then(function(){\n",
586 |        "                            \n",
587 |        "var gd = document.getElementById('8af69475-1372-4975-b63e-1f438adb2dab');\n",
588 |        "var x = new MutationObserver(function (mutations, observer) {{\n",
589 |        "        var display = window.getComputedStyle(gd).display;\n",
590 |        "        if (!display || display === 'none') {{\n",
591 |        "            console.log([gd, 'removed!']);\n",
592 |        "            Plotly.purge(gd);\n",
593 |        "            observer.disconnect();\n",
594 |        "        }}\n",
595 |        "}});\n",
596 |        "\n",
597 |        "// Listen for the removal of the full notebook cells\n",
598 |        "var notebookContainer = gd.closest('#notebook-container');\n",
599 |        "if (notebookContainer) {{\n",
600 |        "    x.observe(notebookContainer, {childList: true});\n",
601 |        "}}\n",
602 |        "\n",
603 |        "// Listen for the clearing of the current output cell\n",
604 |        "var outputEl = gd.closest('.output');\n",
605 |        "if (outputEl) {{\n",
606 |        "    x.observe(outputEl, {childList: true});\n",
607 |        "}}\n",
608 |        "\n",
609 |        "                        })\n",
610 |        "                };\n",
611 |        "                });\n",
612 |        "            </script>\n",
613 |        "        </div>"
614 |       ]
615 |      },
616 |      "metadata": {},
617 |      "output_type": "display_data"
618 |     }
619 |    ],
620 |    "source": [
621 |     "final = data + result.residual.reshape(data.shape)\n",
622 |     "\n",
623 |     "fig = go.Figure()\n",
624 |     "fig.add_trace(go.Scatter(x=tspan, y=data[:, 0], mode='markers', name='Observed Infections', line = dict(dash='dot')))\n",
625 |     "fig.add_trace(go.Scatter(x=tspan, y=data[:, 1], mode='markers', name='Observed Recovered', line = dict(dash='dot')))\n",
626 |     "fig.add_trace(go.Scatter(x=tspan, y=data[:, 2], mode='markers', name='Observed Deaths', line = dict(dash='dot')))\n",
627 |     "fig.add_trace(go.Scatter(x=tspan, y=final[:, 0], mode='lines+markers', name='Fitted Infections'))\n",
628 |     "fig.add_trace(go.Scatter(x=tspan, y=final[:, 1], mode='lines+markers', name='Fitted Recovered'))\n",
629 |     "fig.add_trace(go.Scatter(x=tspan, y=final[:, 2], mode='lines+markers', name='Fitted Deaths'))\n",
630 |     "fig.update_layout(title='SEIRD: Observed vs Fitted',\n",
631 |     "                       xaxis_title='Day',\n",
632 |     "                       yaxis_title='Counts',\n",
633 |     "                       title_x=0.5,\n",
634 |     "                      width=1000, height=600\n",
635 |     "                     )"
636 |    ]
637 |   },
638 |   {
639 |    "cell_type": "code",
640 |    "execution_count": 35,
641 |    "metadata": {},
642 |    "outputs": [
643 |     {
644 |      "name": "stdout",
645 |      "output_type": "stream",
646 |      "text": [
647 |       "(48, 3)\n"
648 |      ]
649 |     }
650 |    ],
651 |    "source": [
652 |     "observed_IRD = df_covid_history.loc[:, ['infected', 'discharged', 'deaths']].values\n",
653 |     "print(observed_IRD.shape)"
654 |    ]
655 |   },
656 |   {
657 |    "cell_type": "code",
658 |    "execution_count": 36,
659 |    "metadata": {},
660 |    "outputs": [],
661 |    "source": [
662 |     "tspan_fit_pred = np.arange(0, observed_IRD.shape[0], 1)\n",
663 |     "params['beta'].value = result.params['beta'].value\n",
664 |     "params['sigma'].value = result.params['sigma'].value\n",
665 |     "params['gamma'].value = result.params['gamma'].value\n",
666 |     "params['mu'].value = result.params['mu'].value\n",
667 |     "fitted_predicted = ode_solver(tspan_fit_pred, initial_conditions, params)"
668 |    ]
669 |   },
670 |   {
671 |    "cell_type": "code",
672 |    "execution_count": 37,
673 |    "metadata": {},
674 |    "outputs": [
675 |     {
676 |      "name": "stdout",
677 |      "output_type": "stream",
678 |      "text": [
679 |       "(48, 3)\n"
680 |      ]
681 |     }
682 |    ],
683 |    "source": [
684 |     "fitted_predicted_IRD = fitted_predicted[:, 2:5]\n",
685 |     "print(fitted_predicted_IRD.shape)"
686 |    ]
687 |   },
688 |   {
689 |    "cell_type": "code",
690 |    "execution_count": 38,
691 |    "metadata": {},
692 |    "outputs": [
693 |     {
694 |      "name": "stdout",
695 |      "output_type": "stream",
696 |      "text": [
697 |       "Fitted MAE\n",
698 |       "Infected:  587.5587793520101\n",
699 |       "Recovered:  216.5347633701369\n",
700 |       "Dead:  21.532532235433454\n",
701 |       "\n",
702 |       "Fitted RMSE\n",
703 |       "Infected:  702.1643902204037\n",
704 |       "Recovered:  284.9841911847741\n",
705 |       "Dead:  26.4463792416788\n"
706 |      ]
707 |     }
708 |    ],
709 |    "source": [
710 |     "print(\"Fitted MAE\")\n",
711 |     "print('Infected: ', np.mean(np.abs(fitted_predicted_IRD[:days, 0] - observed_IRD[:days, 0])))\n",
712 |     "print('Recovered: ', np.mean(np.abs(fitted_predicted_IRD[:days, 1] - observed_IRD[:days, 1])))\n",
713 |     "print('Dead: ', np.mean(np.abs(fitted_predicted_IRD[:days, 2] - observed_IRD[:days, 2])))\n",
714 |     "\n",
715 |     "print(\"\\nFitted RMSE\")\n",
716 |     "print('Infected: ', np.sqrt(np.mean((fitted_predicted_IRD[:days, 0] - observed_IRD[:days, 0])**2)))\n",
717 |     "print('Recovered: ', np.sqrt(np.mean((fitted_predicted_IRD[:days, 1] - observed_IRD[:days, 1])**2)))\n",
718 |     "print('Dead: ', np.sqrt(np.mean((fitted_predicted_IRD[:days, 2] - observed_IRD[:days, 2])**2)))"
719 |    ]
720 |   },
721 |   {
722 |    "cell_type": "code",
723 |    "execution_count": 39,
724 |    "metadata": {},
725 |    "outputs": [
726 |     {
727 |      "name": "stdout",
728 |      "output_type": "stream",
729 |      "text": [
730 |       "Predicted MAE\n",
731 |       "Infected:  3467.935464895652\n",
732 |       "Recovered:  1024.9276874384093\n",
733 |       "Dead:  117.13820975700246\n",
734 |       "\n",
735 |       "Predicted RMSE\n",
736 |       "Infected:  3556.5050027558914\n",
737 |       "Recovered:  1033.452662364444\n",
738 |       "Dead:  120.34147562618548\n"
739 |      ]
740 |     }
741 |    ],
742 |    "source": [
743 |     "print(\"Predicted MAE\")\n",
744 |     "print('Infected: ', np.mean(np.abs(fitted_predicted_IRD[days:observed_IRD.shape[0], 0] - observed_IRD[days:, 0])))\n",
745 |     "print('Recovered: ', np.mean(np.abs(fitted_predicted_IRD[days:observed_IRD.shape[0], 1] - observed_IRD[days:, 1])))\n",
746 |     "print('Dead: ', np.mean(np.abs(fitted_predicted_IRD[days:observed_IRD.shape[0], 2] - observed_IRD[days:, 2])))\n",
747 |     "\n",
748 |     "print(\"\\nPredicted RMSE\")\n",
749 |     "print('Infected: ', np.sqrt(np.mean((fitted_predicted_IRD[days:observed_IRD.shape[0], 0] - observed_IRD[days:, 0])**2)))\n",
750 |     "print('Recovered: ', np.sqrt(np.mean((fitted_predicted_IRD[days:observed_IRD.shape[0], 1] - observed_IRD[days:, 1])**2)))\n",
751 |     "print('Dead: ', np.sqrt(np.mean((fitted_predicted_IRD[days:observed_IRD.shape[0], 2] - observed_IRD[days:, 2])**2)))"
752 |    ]
753 |   },
754 |   {
755 |    "cell_type": "code",
756 |    "execution_count": 40,
757 |    "metadata": {},
758 |    "outputs": [
759 |     {
760 |      "data": {
761 |       "application/vnd.jupyter.widget-view+json": {
762 |        "model_id": "d0841add0f994906a4d0e84d0a4d7506",
763 |        "version_major": 2,
764 |        "version_minor": 0
765 |       },
766 |       "text/plain": [
767 |        "interactive(children=(IntSlider(value=1000, description='initE', layout=Layout(width='99%'), max=100000, style…"
768 |       ]
769 |      },
770 |      "metadata": {},
771 |      "output_type": "display_data"
772 |     }
773 |    ],
774 |    "source": [
775 |     "interact(main, \n",
776 |     "         initE=IntSlider(min=0, max=100000, step=1, value=initE, description='initE', style=style, layout=slider_layout),\n",
777 |     "         initI=IntSlider(min=0, max=100000, step=10, value=initI, description='initI', style=style, layout=slider_layout),\n",
778 |     "         initR=IntSlider(min=0, max=100000, step=10, value=initR, description='initR', style=style, layout=slider_layout),\n",
779 |     "         initD=IntSlider(min=0, max=100000, step=10, value=initD, description='initD', style=style, layout=slider_layout),\n",
780 |     "         initN=IntSlider(min=0, max=1380000000, step=1000, value=initN, description='initN', style=style, layout=slider_layout),\n",
781 |     "         beta=FloatSlider(min=0, max=4, step=0.01, value=result.params['beta'].value, description='Infection rate', style=style, layout=slider_layout),\n",
782 |     "         sigma=FloatSlider(min=0, max=4, step=0.01, value=result.params['sigma'].value, description='Incubation rate', style=style, layout=slider_layout),\n",
783 |     "         gamma=FloatSlider(min=0, max=4, step=0.01, value=result.params['gamma'].value, description='Recovery rate', style=style, layout=slider_layout),\n",
784 |     "         mu=FloatSlider(min=0, max=1, step=0.01, value=result.params['mu'].value, description='Mortality rate', style=style, layout=slider_layout),\n",
785 |     "         days=IntSlider(min=1, max=600, step=7, value=240, description='Days', style=style, layout=slider_layout),\n",
786 |     "         param_fitting=ToggleButton(value=False, description='Fitting Mode', disabled=True, button_style='', \\\n",
787 |     "             tooltip='Click to show fewer plots', icon='check-circle')\n",
788 |     "        );"
789 |    ]
790 |   },
791 |   {
792 |    "cell_type": "markdown",
793 |    "metadata": {},
794 |    "source": [
795 |     "**References:**<br>\n",
796 |     "1. SEIR and SEIRS Model https://www.idmod.org/docs/hiv/model-seir.html<br>\n",
797 |     "2. Compartmental models in epidemiology https://en.wikipedia.org/wiki/Compartmental_models_in_epidemiology#The_SEIR_model<br>\n",
798 |     "3. Solve Differential Equations in Python https://www.youtube.com/watch?v=VV3BnroVjZo<br>\n",
799 |     "4. Computational Statistics in Python https://people.duke.edu/~ccc14/sta-663/CalibratingODEs.html<br>\n",
800 |     "5. Ordinary Differential Equations (ODE) with Python and Jupyter https://elc.github.io/posts/ordinary-differential-equations-with-python/<br>\n",
801 |     "6. SEIRS+ Model https://github.com/ryansmcgee/seirsplus<br>\n",
802 |     "7. Stack Overflow https://stackoverflow.com/questions/40753159/why-is-scipy-minimize-ignoring-my-constraints<br>\n",
803 |     "8. Lotka–Volterra equations https://en.wikipedia.org/wiki/Lotka%E2%80%93Volterra_equations<br>\n",
804 |     "9. SEIR and Regression Model based COVID-19 outbreak predictions in India https://www.medrxiv.org/content/10.1101/2020.04.01.20049825v1.full.pdf<br>\n",
805 |     "\n",
806 |     "A simulator built with RShiny which provides many more parameters https://alhill.shinyapps.io/COVID19seir/"
807 |    ]
808 |   },
809 |   {
810 |    "cell_type": "code",
811 |    "execution_count": null,
812 |    "metadata": {},
813 |    "outputs": [],
814 |    "source": []
815 |   }
816 |  ],
817 |  "metadata": {
818 |   "kernelspec": {
819 |    "display_name": "Python 3",
820 |    "language": "python",
821 |    "name": "python3"
822 |   },
823 |   "language_info": {
824 |    "codemirror_mode": {
825 |     "name": "ipython",
826 |     "version": 3
827 |    },
828 |    "file_extension": ".py",
829 |    "mimetype": "text/x-python",
830 |    "name": "python",
831 |    "nbconvert_exporter": "python",
832 |    "pygments_lexer": "ipython3",
833 |    "version": "3.7.6"
834 |   }
835 |  },
836 |  "nbformat": 4,
837 |  "nbformat_minor": 4
838 | }
839 | 


--------------------------------------------------------------------------------
/compartmental_models/images/notations.png:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/silpara/simulators/8737465a08d48eec6763098f98c7772d2a21d2f8/compartmental_models/images/notations.png


--------------------------------------------------------------------------------
/compartmental_models/images/seir_de_eqns.png:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/silpara/simulators/8737465a08d48eec6763098f98c7772d2a21d2f8/compartmental_models/images/seir_de_eqns.png


--------------------------------------------------------------------------------
/compartmental_models/images/seir_model.png:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/silpara/simulators/8737465a08d48eec6763098f98c7772d2a21d2f8/compartmental_models/images/seir_model.png


--------------------------------------------------------------------------------
/compartmental_models/images/seir_simulation.png:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/silpara/simulators/8737465a08d48eec6763098f98c7772d2a21d2f8/compartmental_models/images/seir_simulation.png


--------------------------------------------------------------------------------
/compartmental_models/images/seird_de_eqns.png:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/silpara/simulators/8737465a08d48eec6763098f98c7772d2a21d2f8/compartmental_models/images/seird_de_eqns.png


--------------------------------------------------------------------------------
/compartmental_models/images/seird_model.png:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/silpara/simulators/8737465a08d48eec6763098f98c7772d2a21d2f8/compartmental_models/images/seird_model.png


--------------------------------------------------------------------------------
/compartmental_models/images/seird_simulation.png:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/silpara/simulators/8737465a08d48eec6763098f98c7772d2a21d2f8/compartmental_models/images/seird_simulation.png


--------------------------------------------------------------------------------
/compartmental_models/images/seird_simulator.png:
--------------------------------------------------------------------------------
https://raw.githubusercontent.com/silpara/simulators/8737465a08d48eec6763098f98c7772d2a21d2f8/compartmental_models/images/seird_simulator.png


--------------------------------------------------------------------------------