Masters Theses

Date of Award

8-2014

Degree Type

Thesis

Degree Name

Master of Science

Major

Mathematics

Major Professor

Suzanne M. Lenhart

Committee Members

Judy D. Day, Steven M. Wise

Abstract

Those who suffer from Celiac Disease have an autoimmune response to the protein complex gluten. The goal of this work is to better understand the biological mechanisms in Celiac Disease through modeling with a system of ordinary differential equations. We first develop a model for the way in which gluten induces a response in zonulin in those with Celiac Disease and estimate parameters for such a model using limited data. We then extend this model to include the interactions between zonulin and the permeability of the intestine, and the effect of this interaction on the immune response. Finally, we perform stability analysis on our model. In doing so, we see that, in our model, a gluten-free diet is always effective in treating the disease. This result may point to the need for additional mechanisms in our model in the future.

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