SIMIODE (Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations) held its third annual SCUDEM Differential Equations Modeling Challenge from October 19-27 with the culminating presentation given on Saturday, October 27. Undergraduate mathematics students Holly Caldes, Thomson Kneeland, and Katherine Ruddy formed the Department of Mathematical Sciences’ inaugural team with Dr. Baojun Song acting as coach and mentor. Prior to the Challenge, Caldes, Kneeland, and Ruddy met with Dr. Song to review different differential equations modeling techniques. Once the Challenge began, the students were given one week to select one of three possible problems and to build a mathematical model to be presented at the October 27 symposium.
The Montclair State team chose to model The Effects of Temperature Variation on the Northern Pine Snake Population with its relevance to modern day climate change in our own New Jersey backyard. The three members worked together throughout the week, assigned themselves different roles based on their strengths, used differential equations to build a mathematical model, and validated the model with numerical simulations. Presenting their findings at Manhattan College to a roomful of other teams and faculty from the region, the Montclair State team performed terrifically, and received top marks from the judges for their mathematics work and presentation.
The team took a data-oriented approach to the problem, noting that recent field data shows the sex ratio and survival rates of hatchling pine snakes to vary directly with temperature. They used this research data to build a logistic model of the female snake population. After determining the equilibrium states and performing stability analysis, they validated the model with Monte Carlo simulations of hypothetical temperature distributions over a 100 year period. The theoretical and numerical studies both showed that greater variance of temperature would negatively affect the Northern Pine Snake population over time, potentially even resulting in extinction of the species.
The Challenge offers a wonderful opportunity for students interested in applied mathematics, differential equations, and mathematical modeling to investigate a real world problem. The Montclair State students thoroughly enjoyed the experience and encourage interested undergraduate students to join the team for next year’s Challenge. Students who would like to participate should contact Dr. Eric Forgoston, firstname.lastname@example.org.