Graduation Term

Spring 2026

Degree Name

Master of Science (MS)

Department

Department of Mathematics

Committee Chair

Olcay Akman

Committee Member

Perry Kleinhenz

Committee Member

Tom Hammond

Abstract

Type II diabetes mellitus affects one in ten adults worldwide, yet the effects of treatment type and adherence level on developing complications and quality of life have not been well characterized at the population level, and mathematical modeling offers a structured way to examine these dynamics. This thesis adapts the Boutayeb et al. (2004) model to incorporate dynamic treatment types and levels of adherence, producing nine scenarios in which complication development rate and complication recovery rate differed, to compare peak complications and quality of life across treatment and adherence conditions. Using a system of ordinary differential equations and compartment modeling, three treatment types (lifestyle, medication, and a combination) and three adherence levels (low, moderate, high) were examined in R. The examination found that the best case scenario was combination treatment with high adherence and the worst case was lifestyle treatment with low adherence. Treatment type impacted complications, but adherence provided more of a drastic change in complication levels. Quality of life was equally impacted by treatment type and level of adherence. These findings indicate that a more intense treatment can prolong a patient's years without complications and adherence is important in determining that outcome, as a low intensity treatment with high adherence outperformed a high intensity treatment with low adherence.

Access Type

Thesis-Open Access

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