Using Math to Prevent the Spread of Disease
Cholera is something that most Americans never have to think about. But, tragically, between three and five million cases of cholera occur worldwide each year, with approximately 120,000 people dying from the disease.
At Marymount, math and biology students have taken note and are working together to develop mathematical models that reflect real-world factors and can help to clarify best practices for prevention and treatment. Read More
Through an ongoing, interdisciplinary epidemiology research initiative, the MU undergraduates and their faculty are tackling questions like, What factors affect the spread of cholera in an outbreak? How effective is vaccination? What control methods can best be implemented in a cost-effective manner?"
Matthew Villemarette '13, a mathematics major, explains, "Using real-world data, we adjust assumptions and model parameters to fit actual scenarios and, by implementing our model, identify optimal treatment methods to address an epidemic."
Previous Marymount students have used a deterministic model with set parameters to predict outcomes. In his research, Villemarette decided to introduce chance and probability into the equation with a stochastic model. "In real life," he points out, "random changes occur. So introducing chance provides additional insight."
Working under the guidance of Dr. Will Heuett, assistant professor of Mathematics, Villemarette used MATLAB, a matrix-based computer software language and development environment, to simulate different scenarios. He explains, "The stochastic approach uses the same system of equations as the deterministic model, but each term is interpreted probabilistically. Events and times are selected randomly, and probabilities of event occurrences are continually updated as time progresses. In this way, different simulations yield different results, with examples of delayed peaks of outbreak, early peaks, and even no outbreaks."
A Marymount DISCOVER research grant enabled Matt Villemarete to continue his work during summer 2011. Henry Turcios '13, a Biology major, has also participated in the cholera research project, working under the supervision of Dr. Elsa Schaefer, professor of Mathematics, with funding from the National Science Foundation.
Dr. Schaefer notes that collaboration between biology and math students strengthens the research. She explains, "The biology students take leading roles in researching the current understanding of cholera dynamics, such as the length of immunity, efficacy of vaccinations, and proportion of asymptomatic cases; while the math students take the lead on mathematical model development and computational analysis."
Matt Villemarette adds, "There's a shift inherent in combining math and biology. Students are taking courses in each other's disciplines, so we end up with a better understanding of how the two fields can work together to provide real-world solutions."
As Villemarette continues with his research, he will implement tau-leap and multi-scale techniques, investigate variables and changing parameters, and analyze the effectiveness of multiple intervention methods. He explains, "Ultimately, our aim is to investigate intervention strategies to help limit the spread of this disease."
With Dr. Heutte's encouragement, Villemarette presented his work at the regional conference of the Mathematical Association of America (MAA) in April 2012. At the conference, he was also a member of the winning team in the Radical Dash, a timed competition in which mathematical modeling is used to tackle a wide variety of medical scourges, from malaria to HIV infection.
This past summer, Villemarette participated in a prestigious DOD/NSF Research Experience at George Mason University, focused on Computational Mathematics and Nonlinear Dynamics of Biological, Bio-inspired, and Engineering Systems. He again used MATLAB software, but this time worked with a deterministic model to simulate HIV infection in the body by adding new factors.
Looking forward, Matt Villemarette says, "I know that I want to continue with math. I plan to go straight to grad school after graduation and hope to be accepted into one of the top applied math programs in the country."