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Abstract

We propose a model to describe the interaction between a diseased fish population and their predators. Analysis of the system is performed to determine the stability of equilibrium points for a large range of parameter values. The existence and uniqueness of solutions is established and solutions are shown to be uniformly bounded for all nonnegative initial conditions. The model predicts that a deadly disease and a predator population cannot co-exist. Numerical simulations illustrate a variety of dynamical behaviors that can be obtained by varying the problem data.

Author Bio

This work was performed in the summerfollowing my Junior year as a mathematics major. Iattended the Budapest Semesters in Mathematics andimmediately entered the REU at the University ofNebraska at Lincoln. I am in the class of 2003 andwill attend the University of Maryland at College Parkto commence work on a Ph.D. in mathematics. Thefrequent periods when I am not working, you can findme in the gym or out on the golf course.

Currently I'm a senior, majoring in Applied Mathematics at California State University at Fullerton. My interest in doing research in mathematics began after I took a Mathematical Modeling course with Dr. Charles Lee, who later became my mentor. He encouraged me to apply to the REU Program at the University of Nebraska (UNL) and that was where this project was conducted. Under the guidance of Dr. Glenn Ledder at UNL, my teammates and I were able to complete this project within the 8-week period. This experience has lead me to decide to pursue a higher degree. I plan to obtain my Master's degree at Southern Illinois University.

The research for this paper was completed in a summer REU program at the University of Nebraska at Lincoln. As a chemistry major with math and biology minors, I have always been intrigued by the interplay between mathematics and the life sciences. This problem appealed to me for its interdisciplinary nature. For me, this project truly demonstrated the relevance of mathematics in the biological sciences. As a senior at Midland Lutheran College I have plans to attend graduate school in the area of Environmental Health and Toxicology. I am especially interested in the health effects of exposure to environmental contaminants on various biological systems. I intend to incorporate mathematics into my graduate studies and research.

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