Influenza models with Wolfram Mathematica

Finding optimal policies to minimize the mortality and morbidity of epidemic outbreaks is a top public health priority. The previous influenza pandemic and other emerging / reemerging diseases demonstrate the importance of mathematical modeling, and calls for a synergistic cooperation of epidemiologists, mathematical modelers and public health experts. The purpose of this paper is to provide an introduction to the basic principles of compartmental models and their implementation in Wolfram’s Mathematica. Motivated by the 2009 A/H1N1 influenza pandemic, here we focus on how to develop advanced models for an influenza outbreak from simple building blocks using this computer algebra system. The content of this paper spans from the most basic SIR model to research level problems. Given the flexibility of the software, the models presented here are easy to modify or extend to include various intervention strategies, population structure or other features. The Manipulate tool is especially useful when someone wants to have a quick overview of the possible scenarios by changing various parameters. This way we can construct interactive and spectacular simulation tools. We hope that this work will be useful for those who are interested in infectious disease modelling, to help them to create and study their own models using Mathematica.