Physical Sciences and Mathematics Commons^™

Analyzing Cholera Dynamics In Homogeneous And Heterogeneous Environments, Drew Posny

Mathematics & Statistics Theses & Dissertations

Cholera continues to be a serious public health concern in developing countries and the global increase in the number of reported outbreaks suggests that activities to control the diseases and surveillance programs to identify or predict the occurrence of the next outbreaks are not adequate. Mathematical models play a critical role in predicting and understanding disease mechanisms, and have long provided basic insights in the possible ways to control infectious diseases. This dissertation is concerned with mathematical modeling and analysis of cholera dynamics. First, we study an autonomous model in a homogeneous environment with added controls that involves both direct …

A Mathematical Model Of The Dynamics Of An Optically Pumped Four-Level Solid State Laser System, Lila Freeman Roberts

Mathematics & Statistics Theses & Dissertations

This is a study of a mathematical model of the dynamics of an optically pumped four-level solid state laser system. A general mathematical model that describes the spatial and temporal evolution of the electron populations in the laser rod as well as the development of the left and right traveling photon fluxes in the cavity is developed. The model consists of a coupled set of first order semilinear partial differential equations. While the model was developed for Titanium-doped sapphire lasers, it is applicable to three and four level lasers in general.

The analysis of the model is conducted in two …