Mathematical Modelling of Leukemia Treatment

Abstract

Leukemia is a cancer that can be treated in a variety of ways: chemotherapy, radiation therapy and stem cell transplant. Recovery rates for this disease are relatively high, the treatment itself has a painful effect on the body and is accompanied by numerous side effects that can persist years after the patient is cured. For this reason, efforts are underway worldwide to develop more selective therapies that will only affect leukemia cells and not healthy cells. Knowledge of developmental GRN is yet scarce, and it is early for a systematic comparative effort. We consider mathematical model of genetic regulatory networks. This model consists of a nonlinear system of ordinary differential equations. We describe the changes that system undergoes if the entries of the regulatory matrix are perturbed in some way. We discuss, how attractors for high-dimensional systems can be constructed, using known attractors of low-dimensional systems. Examples and visualizations are provided.