Masters Theses
Date of Award
8-2000
Degree Type
Thesis
Degree Name
Master of Science
Major
Mathematics
Major Professor
Don Hinton
Committee Members
Charles Collins, William Wade
Abstract
The motivation for this discussion comes from a set of exercises in Borelli and Coleman's Ordinary Differential Equations: A Modeling Approach. In this particular set of exercises the focus is to model the amount of cold medication (antihistamines and decongestants) in the body. We will consider a two-compartment model with the two components being the GItract and the bloodstream, producing a two-dimensional system of ordinary differential equations. Initially we assume a simple linear model,then we increase the complexity by including a saturation effect in the amount of the drug clearing the bloodstream. We also examine three ways of doing the medication, administering just one dose, continuous dosing, and periodic dosing. Closed-form solutions are determined for the one dose, continuous dosing and non-saturation periodic cases, but only numerical solutions are given for the nonlinear, periodic cases. While we do not find closed-form solutions for the nonlinear, periodic cases we do explore their existence and stability. A software package called ODEArchitectis used to generate the numerical solutions to all the models in this thesis.
Recommended Citation
Bleavins, Brenda, "Some mathematical models of cold pill concentration in the body. " Master's Thesis, University of Tennessee, 2000.
https://trace.tennessee.edu/utk_gradthes/9281