Date of Award
Master of Science (MS)
College of Science and Mathematics
Thesis Sponsor/Dissertation Chair/Project Chair
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.
Viz, Kirsten Maggie, "Disease Outbreaks in Coupled Populations : An Application to Measles Spread in Cameroon" (2005). Theses, Dissertations and Culminating Projects. 1341.