Date of Graduation

Spring 2015

Document Type

Honors Research Project

Degree Name

Bachelor of Science

Major

Applied Mathematics

Research Sponsor

Dr. J. P. Wilber

First Reader

Dr. G. Young

Second Reader

Dr. C. Clemons

Abstract

Starting with the original 1926 formulation of the SIR (Susceptible-Infected-Removed) model for infectious diseases, mathematical epidemiology continued to grow. Many extensions such as the SEIR, MSIR, and MSEIR models were developed using SIR as a basis to model diseases in a variety of circumstances. By taking the original SIR model, and reducing the system of three first-order equations to a single first-order equation, analysis shows that the model predicts two possible situations. This analysis is followed by discussion of an alternative use of the SIR model which allows for one to track the amount of sustainable genetic variation in a population of pathogens as a quantity π. Finally, using the 2014 West African Ebola epidemic as an example, an alternative model to SIR is presented and discussed.

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