On the Importance of Mathematical Models

Last month, our team won the DARPA Chikungunya Challenge. We were asked to predict the number of cases of Chikungunya observed in the Pan American Health Organization (PAHO) countries from the beginning of September 2014 till the end of February 2015. Our predictions were then scored against the actual numbers reported on the PAHO website. Points were also awarded for methodology, presentation, and peak incidence predictions.

None of this could have been achieved without mathematical modeling. Our model was very simple, similar to what we teach in our Mathematical Modeling class. We believe we now understand why the spread of the Chikungunya epidemic in most of the PAHO countries could be described by such a simple approach, but we were nevertheless surprised at first.

It turns out that the best performing models in the competition were the simplest, as confirmed by an analysis of submitted entries conducted by Los Alamos National Laboratories (see the DARPA press release). I believe this is often the case for data-driven models. The simplest models have less parameters to adjust, and as a consequence are typically more robust. There is a lesson to be learned from this experience: one should not dismiss simple models just because they are simple. On the contrary, a good mathematical model should be just as complicated as required, nothing more, nothing less.

Finding the right model is an art, like developing an elegant proof, or doing beautiful mathematics. This art needs to be transmitted to the next generation of applied mathematicians. I designed our mathematical modeling class so that it could contribute to this goal, but all mathematics courses should be taught with this approach in mind.

A multitude of recent reports emphasize the importance of interdisciplinary work to solve the next challenges faced by society. Our team, consisting of Heidi Brown, Assistant Professor of Public Health, and myself, was a good example of cross-college collaboration within a research institution. Mathematical modeling, and more generally mathematics as a discipline, has a lot to contribute to the research enterprise of many units on a research campus. Efforts should be made to support such activities at all levels. They also create wonderful opportunities for students to join exciting projects and develop unique research skills.

Press Releases

 

For More Information About our Work

Please see our Chikungunya Modeling Challenge website