Date of Award

5-2005

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

Arup Mukherjee

Committee Member

John Stevens

Abstract

Many childhood diseases can be modeled mathematically using a system of differential equations that group the overall population into compartments. Much research has been done to understand and control the spread of these diseases within a single population and between coupled populations with constant parameters. In this thesis, we are concerned with how a disease is spread through and between coupled populations using models with time-varying parameters and asymmetric coupling.

Measles outbreaks in the West African country of Cameroon present a good example of disease spread with seasonality. By dividing Cameroon into two subpopulations and using parameters that reflect recent measles data, we develop a coupled system of SEIR models to qualitatively capture the current disease dynamics of these subpopulations. This asymmetric, non- autonomous system is analyzed mathematically utilizing tools from dynamical systems.

We have identified when very small changes in the coupling parameter can create significant changes in the behavior of the system. We conjecture that in this system, we are able to induce a periodicity of the lowest common multiple of the two subpopulations when there is sufficient coupling.

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