Dynamical Systems Properties of a Mathematical Model for the Treatment of CML

Abstract

A mathematical model for the treatment of chronic myeloid leukemia (CML) through a combination of tyrosine kinase inhibitors and immunomodulatory therapies is analyzed as a dynamical system for the case of constant drug concentrations. Equilibria and their stability are determined and it is shown that, depending on the parameter values, the model exhibits a variety of behaviors which resemble the chronic, accelerated and blast phases typical of the disease. This work provides qualitative insights into the system which should be useful for understanding the interaction between CML and the therapies considered here.

Mathematical models of tumor cell proliferation: A review of the literature

“…ODE models that consider cancer proliferation and the immune response generally focus on T cell binding and chemical signaling between the immune and tumor cells [86, 87, 88]. A current limitation of such models is that they require detailed and temporally refined data for calibration and validation, which are extraordinarily difficult to measure in an intact system with routinely available methods.…”

Optimal dynamic control approach in a multi-objective therapeutic scenario: Application to drug delivery in the treatment of prostate cancer

“…Combination of different active compounds, are the rule rather than the exception in oncology and other therapeutic areas, but the potentially high number of different possible combinations (including different dosing schemes), makes drug selection an unaffordable task from an experimental trial and error perspective. Therefore any guide on how to administer these therapies to achieve the best possible responses is of great potential as shown by [ 27 , 28 ].…”

On the role of pharmacometrics in mathematical models for cancer treatments

“…Comments on robustness properties of solutions. We close with brief comments about the robustness of optimal controls for a model for long-term drug administration (on the scale of several years) for CML (chronic myeloid leukemia) which are based on the papers [12,13,23] by U. Ledzewicz and H. Moore. This model does not fall into the class of problems defined in [CC0] and [CC1], but is a multi-drug optimization problem over an a priori prescribed therapy horizon (on the order of 5 years).…”

“…After suitable mathematical scalings of variables and parameters which is indicated by tildes on the respective quantities [12], and only to give an impression of the complexity of the nonlinear structure of the model, the dynamics can be represented in the following form:…”