Fractional order modeling and analysis of dynamics of stem cell differentiation in complex network

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 ${\mathcal{R}}_0$ 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 non-fractional 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.