Date of Award

May 2026

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mathematics

First Advisor

Ryan Zerr

Abstract

Type 2 diabetes (T2D) remains one of the most significant chronic health conditionsworldwide and continues to place pressure on healthcare systems through its long-term complications, treatment costs, and growing prevalence. The progression of T2D is influenced by multiple interacting factors, including hereditary predisposition, lifestyle behavior, treatment access, remission, relapse, and the development of complications. Because of this complexity, mathematical models can provide useful insight into disease dynamics and the possible effects of intervention strategies over time. This study develops a compartmental model for T2D progression using a system of ordinary differential equations. The population is divided into epidemiologically meaningful classes representing susceptible individuals, at-risk individuals, prediabetic individuals, diabetic individuals, individuals in remission, individuals with complications, and cumulative mortality. The model incorporates hereditary risk, lifestyle-related progression, treatment effects, remission, relapse, and disease-related complications. Qualitative analysis of the model is carried out by establishing positivity and boundedness of solutions, identifying equilibrium points, and examining stability behavior under relevant threshold conditions. These results help confirm that the model is mathematically well posed and biologically meaningful. Numerical simulations are performed to illustrate the effect of selected parameters on disease progression and long-term outcomes. The simulations show that improvements in prevention, timely treatment, and sustained remission can reduce progression into severe disease states, while high hereditary risk and relapse may increase long-term burden. The study contributes a broader modeling framework that captures several important clinical and public health features of T2D within one mathematically tractable system. The results may support future research in disease prevention, treatment planning, and health policy decision-making.

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