# Student Feature - Adrienna Bingham

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I earned my Bachelor of Science degree in Mathematics with Highest Honors from Angelo State University in San Angelo, Texas in 2014 with minors in Computer Science and Spanish. The summer after my sophomore year, I received the chance to participate in an REU at Valparaiso University in Indiana. Our project, led by Dr. Daniel Maxin, was to model the control of pest populations using ordinary differential equations and analyzing the stability of steady states [1]. This project opened my eyes to the world of mathematical modeling. Though never 100% accurate, the information mathematical models can provide on a myriad of fields, from microbiology to economics, was fascinating to me. The ability to code simulations also grabbed my interests.

I am now a fourth year PhD student at the College of William and Mary in the Applied Science Department working under the direction of Dr. Leah Shaw. I was eager to continue learning different methods of modeling, and I began a project on modeling an epidemic using Ebola parameters from Hu et al. [2]. We focused on how modeling the distributions of exposed and infectious time periods affected the prediction of the infectious steady state when a control measure (such as, in our case, quarantine) was applied to the infectious population. While ordinary differential equations are simple and quick to analyze, they can provide some error due to their use of the exponential distribution in modeling exposed and infectious time periods and the exponential distribution’s wide variance. We hypothesize that the use of delay differential equations, though more difficult to solve, is a more appropriate method of modeling predictions since they use a delta distribution for time periods with a variance of zero. To compare the two models, we implement a multi-infected compartment model to interpolate between the models and investigate which time delay (either in the infectious class or the exposed class) has a greater impact on the infectious steady state. We also investigate whether the magnitude of the delay has an impact. Finally, we examine other methods of control, such as applying a vaccine to the susceptible class or a quarantine on the exposed class. At the moment, we are in the process of preparing our results for publication.

I have also recently begun to collaborate with William and Mary biologist, Dr. Helen Murphy, on analyzing RNA-sequencing data to find differentially expressed genes in the formation of biofilms in multiple environmental isolates of Saccharomyces cerevisiae, the common baker’s yeast. Biofilms are a community of one or more species that are protected by an extracellular matrix and attached to a surface, making them difficult to remove. This can cause damage in industrial settings and infection on medical implants. These communities are cooperative, meaning each individual contributes to a pool of public goods. However, this makes them susceptible to cheaters, individuals who do not contribute to the pool of public goods but still use them. I am also involved in mentoring an undergraduate student who uses Monte Carlo simulations to investigate the impact cheater strains have on the cooperative strains. I enjoy working on these projects as it allows me to gain a different skill set while still using mathematics as a tool to help fight disease or infection.

This past summer, I had the opportunity to intern at the National Institute of Environmental Health Sciences working in the Biostatistics and Computational Biology Branch, and I really enjoyed using mathematics to contribute to cancer research. I hope to continue to follow this path, taking the skills I gain from working towards my PhD, and enter the field of public health.

[1] D. Maxin, L. Berec, A. Bingham, D. Molitor, J. Pattyson. Is more better? Higher sterilization of infected hosts need not result in reduced pest population. Epub June 2014, Journal of Mathematical Biology.

[2] K. Hu, S. Bianco, S. Edlund, J. Kaufman. The impact of human behavioral changes in 2014 West Africa Ebola outbreak. In: Social Computing, Behavioral-Cultural Modeling, and Prediction, pp. 75–84. Springer (2015).

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