Reproduced from the Fall 2015 School of Mathematical Sciences newsletter (PDF)
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Chikungunya fever in the Americas
In August 2014, DARPA (the federal Defense Advanced Research Projects Agency) launched a challenge, asking the public to predict the number of cases of chikungunya fever in each of the PAHO (Pan American Health Organization) countries, many of which were for the first time facing a huge outbreak of this disease. The framework was simple: predictions would be compared to numbers of reported cases, and teams would be scored on the accuracy of their approach. When a colleague in the College of Public Health, Dr. Heidi Brown, forwarded the announcement to me, I found the format both appealing and intriguing. First, this provided a unique opportunity (at least for a mathematician) to observe the unfolding of an epidemic in an area where it had never been reported before. Second, the funding approach was different.
Grants versus challenges
Academic research is typically supported by grants or contracts: funds are allocated based on proposals, which are evaluated for their intellectual merit. About 6 years ago, “President Obama called on [federal] agencies to increase their ability to promote innovation by using tools such as prizes and challenges to solve tough problems,”  which led to the development of the Challenge.gov platform. This site explains that
“With a challenge competition, you are defining the problem and framing the end-result you seek. Solvers enter the competition and have free reign and creativity to go about getting you the result you’ve described as the best possible outcome. If a solver meets your criteria and is judged a winner, you award them a prize (whether financial, incentive, or a combination) and your contractual relationship is complete.”
A quick survey of the literature reveals that post-invention reward systems used to be the norm; they were progressively replaced by patents and procurement in the 19th century, only to come back to life “as a legitimate innovation incentive mechanism” in the past 15-20 years.  There is in fact a lot of current debate  on the efficacy of various models (prizes, grants, contracts) to promote innovation. For a researcher, participating in a challenge can be quite exciting and energizing. Moreover, supporting research with both grants and prizes seems preferable, especially since, at least in theory, “reward systems engender incentives to innovate without creating the monopoly power of intellectual property rights.” 
Ironically, the renewed popularity of prize incentives is raising a challenge of its own: in order to compete, universities need to adapt to this new paradigm and find ways to support promising ideas and innovations before external funding is received to develop them.
Chikungunya, which causes joint pain and fever, is a viral disease transmitted to humans by infected mosquitoes. According to the WHO site, the name means “to become contorted” and the first outbreak was reported in Tanzania in 1952. In 2013, chikungunya arrived in the Americas, where it has since then been infecting more than one million people in 44 (out of 55) countries.
Forecasting the course of an outbreak is an important problem regularly faced by public health responders. Decisions (in my colleague’s words, “whether to fly in surgeons, paliative care providers, or mortuary services”) have to be made quickly and misjudgments have significant consequences. Mathematicians can help by developing a range of models that address both the short and long term dynamics of infectious diseases.
Predicting the spread of chikungunya fever
Heidi and I eventually decided to participate in the DARPA challenge. Last May, we were awarded first place and received a $150,000 prize, which we will use to support our research activities. Our solution is extremely simple: it consists in representing the growth rate of the epidemic as a quadratic function of the number of cases, finding the parameters that best fit the reported data for each country, and making predictions on the basis of this simple model. In some instances, using a combination of two quadratic functions gave better results, revealing the presence of two phases (most likely due to geographic constraints) in the spread of the epidemic. At first, we were amazed that a model that did not include mosquito dynamics could still have predictive value, but we later realized that specific circumstances in the PAHO countries could justify our approach: the disease was new to the area, spread very quickly, and was carried by mosquitoes that were already in abundance in the region – dengue, an endemic disease in the Americas, is indeed transmitted by the same mosquitoes!
This realization was tremendously exciting because simplicity in modeling is both beautiful and practical. We are now working on a tool, currently in MATLAB (see figure), that implements the above approach for chikungunya and other diseases. EpiGro takes a file containing epidemiological data and gives a best guess for the future of a particular outbreak, assuming of course specific conditions are satisfied. We believe this has the potential to assist public health decision makers and thus guide mitigation efforts in certain circumstances.
The take-away message from this short article is that collaboration fosters innovation. Learning how to communicate with colleagues in other fields is a worthwhile investment, leading to synergistic activities that in turn provide unique training opportunities for graduate and undergraduate students.
 F. Murray, S. Sternb, G. Campbell, A. MacCormack, Grand Innovation Prizes: A theoretical, normative, and empirical evaluation, Research Policy 41, 1779–1792 (2012)
 Browse for instance the talk lineup for the conference Innovation Law Beyond IP held at Yale University in March 2014
 S. Shavell and T. van Ypersele, Rewards versus Intellectual Property Rights, Journal of Law and Economics XLIV, 525-547 (2001)