Author ORCID Identifier
https://orcid.org/0000-0001-5943-2703
Defense Date
2026
Document Type
Dissertation
Degree Name
Doctor of Philosophy
Department
Mathematical Sciences
First Advisor
David Chan
Second Advisor
Laura Ellwein Fix
Abstract
In clinical settings, patients are exposed to many risks and stressors that could result in adverse health outcomes. Here we present mathematical models that seek to address these risks. First, we present a Markov Chain model to investigate the effect of medication reconciliation (MR) completion on patient health outcomes in the intensive care unit. Using this model, we simulate the annual incidence of adverse drug events (ADEs) for three different ADE rates. Based on the simulated results, we conduct a cost-benefit analysis for various levels of compliance to determine the financial implications of increasing MR completion depending on the baseline ADE rate and cost per ADE. Second, we present an ordinary differential equation model of cortisol and catecholamine dynamics through the hypothalamic-pituitary-adrenal (HPA) and sympathoadrenal (SA) axes to describe the acute physiological stress response. We expand an existing model of the HPA axis to incorporate the SA axis and use sensitivity analysis and parameter estimation to fit the model to data for cortisol, epinephrine, and norepinephrine from individuals under acute physical stress. Then we extend our HPA and SA axis model to investigate the effects of chronic health conditions on the physiological stress response. We perform sensitivity analysis and estimate model parameters to fit data for cortisol, epinephrine, and norepinephrine from both lean and obese individuals under acute mental stress. The parameterizations of the model for each group are compared to investigate potential physiological differences. These models and their results serve as steps toward improving patient care by gaining better understanding of the underlying biology.
Rights
© The Author
Is Part Of
VCU University Archives
Is Part Of
VCU Theses and Dissertations
Date of Submission
5-7-2026