Popdynamics

Popdynamics is a library for building epidemiological models, or for that matter, any kind of compartmental model. It provides an easy way to switch between different integration methods

• direct integration of ODE
• integration of ODE using the Scipy library
• stochastic discrete-time
• stochastic continuous-time

Installation

Popdynamics has been written to be compatible with Python 2 and Python 3. There are two main approaches to install the dependencies.

1) Anaconda Python

Install the Anaconda Python environment. This package already contains most of the dependencies required.

2) Local Python

If you have your own Python environment, you will have to install the dependencies. In the main Popdynamics directory, to install the dependencies:

> python setup.py develop

Requirements: python 2/3; numpy, scipy, matplotlib, graphviz (python), graphviz (binary)

Optional Graphviz

If you want to generate flow-charts of your models. You will need Graphviz. However, Popydnamics will work fine if Graphviz is not installed.

1) Anacaonda Python

To install graphviz for flow diagrams:

> conda install graphviz

Then:

> conda install python-graphviz

2) Local Python

Follow the Graphviz download instructions.

In Windows you will also have to set the PATH environment variable to point to the Graphviz.

Quick start

Once the modules are installed, go the examples directory, and run:

> python sir_model.py

Then try the other examples.

• sir_model.py - a simple model showing a basic SIR model
• seir_model.py - basic SEIR model with a demography variation
• stochastic_strains_model.py - an SIR model using stochastic models to average over many runs
• tb_model.py - a basic TB model that represents the approach used by AuTuMN
• rmit_tb_model.py - a reproduction of a TB model in the literature

Why?

Epidemiological models are typically modeled as compartmental models where populations evolve through linear ordinary differential equations (ODE), or through stochastic models with probability transition matrices.

Approaches to modelling involve writing out the complete ODE for each compartment and typing these equations in matrix based programming enviromnents such as Fortran, Matlab and R.

In this approach, the management of these equations involve the use of poor mnemonics (single or two letter variables) and large chains of equation. This is an error-prone process.

The marjority of the terms in the ODE's is to connect coupled changes between compartments, with a smaller number of single entry/exit terms. Since the coupling is between different equations, it is exceedingly easy to lose track of the coupling.

A more modern approach is to track the coupling between compartments, and use meaningful descriptive variable names. The resultant ODE is then constructed from these couplings. This is essentially automating the double-entry book-keeping between coupled changes between compartments.

By approaching compartmental models in terms of coupling between compartments, it is then very easy to apply stochastic approaches to the integration, as well as to use the information to auto-generate flow-charts of the model.

The model has been carefully considered to use an underlying data structure that is as simple as possible, and allows the results to be easily exported for graphing.