A Control Delay Differential Equations Model of Evolution of Normal and Leukemic Cell Populations Under Treatment

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

“…Note that, in this way, both β l and k l became decreasing functions of u 1 . For more details, see [21]. The treatment acts on the apoptosis through the function f 1a on the stem cells and through the function f 2a on the mature ones.…”

A comparison between the stability properties in a DDE model for leukemia and the modified fractional counterpart

“…There is a vast literature on mathematical modeling the normal and pathologic hematopoiesis ( [1], [6], [10], [11], [17], [18], [32], [33]). In some papers, CML models with competition between cell lines are studied using stochastic differential equations ( [7], [31]) while in others ordinary differential equations (ODEs) are used [24], [16], [25], [14].…”

“…The DDEs model we present in Section 2 follows the lines of the models for leukemia developed by Mackey and collaborators ( [6], [11], [30]) and is part of a larger study of Halanay and colleagues about CML ( [4], [8], [17], [18], [32], [33]). One of the novelties in this study is the consideration of three types of division that a stem-like cell can undergo: asymmetric division, symmetric self-renewal and differentiation ( [35]).…”

“…In the following section, the delay competition model of CML, which was first introduced in [32] (see also [8]), is presented and explained. Based on this model, in Section 3 we introduce the fractional-order DDEs system for CML.…”