Disease Modeling with epispot

To get started with this post, install epispot, one of the largest epidemiological modelers for Python. Fire up a command line and type one of the following:

pip install epispot # pip
pip install epispot-nightly # pip (nightly version)
conda install epispot # Anaconda

Alternatively, you can install epispot from the source via:

git clone https://github.com/epispot/epispot
cd epispot
git checkout master
# git checkout nightly (nightly version)
python setup.py install

Now let's get started! In this tutorial, we will be recreating the SIR model, the most basic of compartmental models in epidemiology. At its core, the SIR model consists of three "classes:"

• Susceptible (not infected yet)
• Infected (infected and actively spreading disease)
• Removed (either dead or recovered --i.e. not spreading the disease)

Parameters

Before we dive into creating the Model, we need to
establish some of the parameters that will be used to
define our model.



Note: if you aren't sure about which parameters are
needed for a specific model, always consult the
compartment docstrings using the built-in Python
help() command.

1. R_0 (basic reproductive number)

This number represents the number of
Susceptibles one Infected will infect,
assuming that everyone else is Susceptible. A
number greater than one means the disease is still
spreading, whereas a number less than one means
the disease is dying out. For reference, most
epidemics have an R_0 value of around 2.

2. gamma (recovery rate)

This variable is set to:

1 / avg time to recover


This acts as a buffer between the time an individual
is infected and when that individual recovers.

3. N (total population)

This is, of course, the total population of the
region in question.

4. p_recovery (probability of recovery)

The probability of recovery determines an individual's
chances of recovering after 1 / gamma days. This can
be used as a proxy measure to increase or decrease
gamma or can just be left as 1.

Before we finish this section, it is important to
understand how parameters are implemented in epi-spot.
All parameters are functions. This is because many
parameters change over the course of a disease. Take
R_0 for example. As social distancing and
quarantining measures are put in place, the disease
spreads more slowly and Infecteds are only able to
spread the disease to a fewer number of people, if at
all. This essentially lowers R_0 during the course
of the disease. In order to do this in epi-spot, we
simply change R_0 as time progresses, as we will be
doing in this example.

Coding

For R_0 we will use a simple logistic model,
something that lowers R_0 as a function of time:
slowly at the beginning, fast as the outbreak emerges,
and then slowly as R_0 creeps to 0 in order to end
the outbreak. We will use the following values:

R_0 start value: 2.0
R_0 end value: 0.0
gamma: 0.2
N: 100,000
p_recovery: 1.0

Each function takes in a parameter t representing
the time in days from the beginning of the outbreak.
This is implemented in lines 1-27.

Next, we create an instance of each layer in the
Model. These are listed in epispot.comps. Each
layer contains a certain category of people, whether
that be Susceptible, Infected, or Recovered. Before
using any of them, be sure to look at which parameters
to include depending on the next and previous layers.
Here, we implement them as:

Susceptible = epi.comps.Susceptible(0, R_0, gamma, N)  # Susceptible layer
Infected = epi.comps.Infected(1, N, R_0=R_0, gamma=gamma, p_recovery=p_recovery, recovery_rate=gamma)  # Infected layer
Recovered = epi.comps.Recovered(2, p_from_inf=p_recovery, from_inf_rate=gamma)  # Recovered layer

Next, we compile the Model class in epispot.models.

Model = epi.models.Model(N(0), 
        layers=[Susceptible, Infected, Recovered], 
        layer_names=['Susceptible', 'Infected', 'Recovered'],
        layer_map=[[Infected], [Recovered], []])

The layer_map parameter here contains an array with
an instance of the class of the next layer to each of
the layers in the Model. It will be more useful later
in complex models where we want to create different
paths through each of the layers.


Lastly, we call

epi.plots.plot_comp_nums(Model, range(0, 150, 1))

passing in our Model as one parameter and a time
range that we would like to plot. This will return a
matplotlib plot showing the values of each of those
compartments over the timerange specified.


There you have it! You've completed the basic tutorial
and understand the three main modules of epi-spot
(comps, models, and plots) and how to use them! To see the exact source code for this model, check out the GitHub source!