Available at: https://digitalcommons.calpoly.edu/theses/3022
Date of Award
6-2025
Degree Name
MS in Mathematics
Department/Program
Mathematics
College
College of Science and Mathematics
Advisor
Dana Paquin
Advisor Department
Mathematics
Advisor College
College of Science and Mathematics
Abstract
This thesis centers around a model for chronic myelogenous leukemia (CML) as it behaves under imatinib treatment, a common medication for CML patients, and the anti-leukemia immune response. The dynamics are represented with a system of nonlinear delay-differential equations first constructed by Kim et al. in 2008, capturing population changes of T-cells and various CML growth stages. We investigate stability in both the clinical and mathematical sense. Through numerical simulations, we computationally incorporate a supplementary treatment plan to determine its effectiveness in aiding immune response and medication in achieving remission and full elimination. The primary goal is to conduct a stability analysis of the system. We derive two steady states, one for a cancer-free environment and one for CML persistence in the presence of T-cells. Through linearizing the system with Jacobian matrices with respect to non-delayed and delayed state variables, we seek parameter restrictions toward negative eigenvalues (or those with negative real part), and hence asymptotic stability.
Included in
Dynamical Systems Commons, Immunotherapy Commons, Non-linear Dynamics Commons, Numerical Analysis and Computation Commons, Ordinary Differential Equations and Applied Dynamics Commons