Abstract
In this study, a mathematical model for the differentiation of stem cells is proposed to understand the dynamics of cell differentiation in a complex network. For this, myeloid cells, which are differentiated from stem cells, are introduced in this study. We introduce the threshold quantity R0 to understand the population dynamics of stem cells. The local stability analysis of three equilibria, namely (i) free equilibrium points, (ii) absence of stem and progenitor cells, and (iii) endemic equilibrium points are investigated in this study. The model is first formulated in nonfractional order and after that converted into a fractional sense by utilizing the Atangana-Baleanu derivative in Caputo (ABC) sense in the form of a non-singular kernel. The model is solved by using numerical techniques. It is seen that the myeloid cell population significantly affects the stem cell population.