BenU faculty since 2010
Ph.D., University of Nebraska-Lincoln (2010)
B.S., Benedictine University (2005)
Calculus with Analytics, Calculus with Analytics Laboratory, Calculus for Life Sciences, Mathematical Research
Math biology, including ecological problems with financial analogs and epidemiology
Current Research Projects
- "An Epidemic Model with a Multi-Stage Vaccine" This project will be a continuation of work done with Reema Khatri, Kiran Munir, and Katie Hunzinger over the past two summers. So far, we have constructed mathematical models to help us study the spread of a disease through a population such that immunity can be given through a series of multiple vaccines. A perfect example of such a disease would be Hepatitis B, which requires three vaccines for immunity. Up to this point, however, we have proven that, assuming the population has births and deaths, it is not possible to completely eradicate a disease unless the disease was going to die out anyway. So, this summer, I hope to extend this to looking at repeating the vaccination cycle numerous times and/or changing how the vaccine is given so that we can kill the disease off, or even better, suppress it for a longer period of time. If time permits, we may also try to build in more realistic contact patterns.
- "A Model for Disease Spread With Different Susceptibility Levels" For some diseases, such as the common cold, it really seems like certain individuals just have a much better chance of getting sick than others (or even not getting sick at all!) when coming into contact with an infected individual. This project will concern constructing and studying a model for disease spread such that people are placed into different susceptibility groups, where some groups are more likely to get sick by coming into contact with infectives than others, and some people may even have full immunity to the disease. Specifically, we want to study how sensitive the spread of disease throughout a population is based on how the make-up of the susceptible groups is. That is, if one group is pretty much the driver toward having a disease become endemic, can we quarantine the group (or some similar strategy) to stop the spread of the disease?
- "Monopoly: The Speed Die" Monopoly is arguably one of the world's most popular board games. It is so popular that, every so often, a world championship tournament is held. In the past tournament, however, a new rule was introduced, which has also made its way into the home game: the "Speed Die." Rolling the speed die not only, as its name suggests, speeds up the game play, but it can also affect strategy greatly. A player could simply move extra spaces with it, could have the choice to move using only one die as opposed to two, or end up getting to purchase two properties in a single turn (or, even worse, paying rent on two properties in a single turn). The strategy for the classic game of Monopoly has been extensively studied, but this project will investigate if those strategies are still the best ones to do when playing with the "Speed Die." If time permits, we will also investigate playing under tournament rules (games are timed) to see if those strategies should be adapted in the tournament setting at all.