Publication Date

Spring 2019

Advisor(s) - Committee Chair

Dr. Richard Schugart (Director), Dr. Dominic Lanphier, and Dr. Claus Ernst

Degree Program

Department of Mathematics

Degree Type

Master of Science


For this project, we use a modified version of a previously developed mathematical model, which describes the relationships among matrix metalloproteinases (MMPs), their tissue inhibitors (TIMPs), and extracellular matrix (ECM). Our ultimate goal is to quantify and understand differences in parameter estimates between patients in order to predict future responses and individualize treatment for each patient. By analyzing parameter confidence intervals and confidence and prediction intervals for the state variables, we develop a parameter space reduction algorithm that results in better future response predictions for each individual patient. Moreover, use of another subset selection method, namely Structured Covariance Analysis, that considers identifiability of parameters, has been included in this work. Furthermore, to estimate parameters more efficiently and accurately, the standard error (SE- )optimal design method is employed, which calculates optimal observation times for clinical data to be collected. Finally, by combining different parameter subset selection methods and an optimal design problem, different cases for both finding optimal time points and intervals have been investigated.


Applied Mathematics | Medical Biomathematics and Biometrics | Non-linear Dynamics | Numerical Analysis and Computation | Ordinary Differential Equations and Applied Dynamics