New Computational Tools for Modeling Chronic Myelogenous Leukemia

Abstract

Abstract. 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.

A Complex Mathematical Model with Competition in Leukemia with Immune Response - An Optimal Control Approach

“…Even if a variety of mathematical papers have applied a range of modeling approaches to study tumor-immune interactions in general (see, for example the recent review [7]), only a few described the specific leukemia-immune interaction. Leukemia-immune models have been formulated using mostly ordinary differential equations (ODE) ( [16], [17]) or delay differential equations (DDE) ( [2], [5], [12], [19]). Some models that specifically study the immune response to CML are [12], [2], [18] and [16].…”