Date of Award


Document Type


Degree Name

Master of Science (MS)


College of Science and Mathematics


Mathematical Sciences

Thesis Sponsor/Dissertation Chair/Project Chair

Lora Billings

Committee Member

Arup Mukherjee

Committee Member

Philip A. Yecko


The goal of this thesis is to model the spread of disease between populations and find ways to prevent its continued epidemic. This thesis studies disease spread as a function of migration in epidemiological models. The models are constructed using the compartmental approach, and we compare discrete and continuous time approximations. In the discrete model, we will look at ways that induced migration can cause an epidemic case to turn into a dieout case. It will be shown that migration can only effect the size of an outbreak, but cannot create or destroy one. For the continuous cases, we will be looking at periodic solutions and what bifurcations they exhibit. We find that high amplitude outbreaks do not occur for ’’strong” migration rates. It will be shown from real world data gathered from Cameroon that quarantine does not always reduce the size of the oncoming outbreak.

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