Date of Award

5-2012

Document Type

Thesis

Degree Name

Master of Science (MS)

College/School

College of Science and Mathematics

Department/Program

Mathematical Sciences

Thesis Sponsor/Dissertation Chair/Project Chair

Lora Billings

Committee Member

David Trubatch

Committee Member

Eric Forgoston

Abstract

Mathematical models provide a great deal of information about the dynamics of disease spread. In this paper, we use stochastic simulation to investigate spontaneous disease extinction and réintroduction in a SIR model. We begin by investigating path to extinction and time to extinction in single population models, and then expand to a multipopulation model linked with linear migration. We have found that in a single population model, it is more effective to use random pulse vaccinations less per year at a higher removal rate. We have expanded this result by developing a vaccination strategy giving one large, well timed pulse to bring dieout within one oscillation. We then extended these methods to multipopulations to analyze the sustainability of extinction in one population. Through this, we found a means of optimally distributing a limited childhood vaccination supply in two populations. We then generalized the model for n populations and described how to simulate for different topologies. A more complete understanding of disease dynamics will enable us to develop better vaccination strategies and protect communities from infection.

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