Age-structured model of hematopoiesis dynamics with growth factor-dependent coefficients

• Main Authors: Mostafa Adimy, Youssef Bourfia, My Lhassan Hbid, Catherine Marquet
• Format: Article
• Language: English
• Published: Texas State University 2016-06-01
• Series: Electronic Journal of Differential Equations
• Subjects: Age-structured partial differential equation; delay differential system; Lyapunov function; characteristic equation; cell dynamic
• Online Access: http://ejde.math.txstate.edu/Volumes/2016/140/abstr.html

We propose and analyze an age-structured partial differential model for hematopoietic stem cell dynamics, in which proliferation, differentiation and apoptosis are regulated by growth factor concentrations. By integrating the age-structured system over the age and using the characteristics method, we reduce it to a delay differential system. We investigate the existence and stability of the steady states of the reduced delay differential system. By constructing a Lyapunov function, the trivial steady state, describing cell's dying out, is proven to be globally asymptotically stable when it is the only equilibrium of the system. The asymptotic stability of the positive steady state, the most biologically meaningful one, is analyzed using the characteristic equation. This study may be helpful in understanding the uncontrolled proliferation of blood cells in some hematological disorders.