{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Fitting a model's parameters with run-at-a-time optimization\n",
"\n",
"In this notebook, we'll fit a simple compartmental model to disease propagation data. We'll use a standard optimizer built into the python `scipy` library to set two independent parameters to minimize the sum of squared errors between the model's timeseries output and data from the World Health Organization.\n",
"\n",
"## About this technique\n",
"A run-at-a-time optimization runs the simulation forward from a single starting point, and so only requires an *a-priori* full state estimate for this initial condition. This makes it especially appropriate when we only have partial information about the state of the system. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Ingredients:\n",
"\n",
"We'll use the familiar `pandas` library along with `pysd`, and introduce the optimization functionality provided by `scipy.optimize`."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"source": [
"%pylab inline\n",
"import pandas as pd\n",
"import pysd\n",
"import scipy.optimize"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The model that we'll try to fit is simple 'Susceptible-Infectious' model. This model assumes that everyone is either susceptible, or infectious. It assumes that there is no recovery, or death; and doesn't account for changes in behavior due to the presence of the disease. But it is super simple, and Çso we'll accept those limitations for now, until we've seen it's fit to the data.\n",
"\n",
""
]
},
{
"cell_type": "raw",
"metadata": {},
"source": [
".. image:: ../../../source/models/Epidemic/SI_Model.png\n",
" :width: 600 px"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We'll hold **infectivity** constant, and try to infer values for the **total population** and the **contact frequency**."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"model = pysd.read_vensim('../../models/Epidemic/SI_Model.mdl')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We'll fit our model to data from the WHO patient database for Sierra Leone. We see the standard *S-Shaped* growth in the cumulative infections curve. As our model has no structure for representing recovery or death, we will compare this directly to the **Population Infected with Ebola**. We format this dataset in the notebook [Ebola Data Loader](https://pysd-cookbook.readthedocs.io/en/latest/data/Ebola/Ebola_Data_Loader.html)."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"data": {
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",
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