In this paper, we consider a system of nonlinear delay-differential equations
(DDEs) which models the dynamics of the interaction between chronic myelogenous
leukemia (CML), imatinib, and the anti-leukemia immune response. Because of the
chaotic nature of the dynamics and the sparse nature of experimental data, we
look for ways to use computation to analyze the model without employing direct
numerical simulation. In particular, we develop several tools using
Lyapunov-Krasovskii analysis that allow us to test the robustness of the model
with respect to uncertainty in patient parameters. The methods developed in this
paper are applied to understanding which model parameters primarily affect the
dynamics of the anti-leukemia immune response during imatinib treatment. The
goal of this research is to aid the development of more efficient modeling
approaches and more effective treatment strategies in cancer therapy.