Modeling, analysis and numerical simulation of chronic myeloid leukemia

Leukemia is a blood cancer characterized by the abnormal proliferation of blood cells and chronic myeloid leukemia (CML) is a type of leukemia disease that is noted by inappropriate increase of leukemic stem cell in hematopoietic niche. Mathematical modeling gives a strict conceptualization of disease development and the assessment of possible therapeutic reactions. This paper introduces the comparative study and analysis of the three known models of CML including Niche competition, Niche independent, and partial Niche dependence (PND). In case of every model, we determine the equilibrium points, calculate the basic reproduction number $R_0$ , and examine the local stability. We can compare the mathematical frameworks of the models, even though they have mathematical differences, and identify the essence of the role that niche interactions play in the persistence of leukemia. Numerical simulations, which were conducted by the fourth-order Runge-Kutta (RK-4) method, demonstrate the threshold dynamics of and shows clear qualitative behavior in different models. PND model proves to be the most biologically consistent behavior which is consistent with the known CML niche ecology. Our results give us a coherent understanding of CML modeling and a solid basis of the PND framework on the development of more clinically sound models that consider immune interactions, effects of treatment, and patient heterogeneity.