Date of Graduation

Spring 2016

Document Type

Honors Research Project

Degree Name

Bachelor of Science

Major

Applied Mathematics - BS/MS

Research Sponsor

Dr. J. Patrick Wilber

First Reader

Dr. Curtis Clemons

Second Reader

Dr. Kevin Kreider

Abstract

In combining two classes of models, we are able to analyze the dynamics of two species that compete for the same resources while fighting a disease. The native species is the disease host and the invasive species enters their habitat and encounters the disease for the first time. Their natural response is to evolve resistance to the disease, and this can assist in their invasion of the natives' habitat. We find conditions for coexistence of the two species, conditions under which an invasion would succeed and wipe out all native individuals, and conditions under which the invasion fails. We explore the timing of the invasion by causing the invasion to occur before the natives equilibrate with the disease.

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