Traveling waves in a coupled reaction–diffusion and difference model of hematopoiesis

• Published in: Journal of Differential Equations Vol. 262; no. 7; pp. 4085 - 4128
• Main Authors: Adimy, M., Chekroun, A., Kazmierczak, B.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 05.04.2017; Elsevier
• Subjects: Age-structured population; Asymptotic speed of spread; Difference equation; Hematopoiesis; Mathematics; Reaction–diffusion system with delay; Traveling wave front; Reaction–diffusion system with delay; Asymptotic speed of spread; Traveling wave front; Hematopoiesis; 35K08; 35B50; 35K57; Age-structured population; Difference equation; 35C07; Difference equation 2010 MSC: 35B50; 35K57 Corresponding author; Reaction-diffusion system with delay
• ISSN: 0022-0396; 1090-2732
• DOI: 10.1016/j.jde.2016.12.009

The formation and development of blood cells is a very complex process, called hematopoiesis. This process involves a small population of cells called hematopoietic stem cells (HSCs). The HSCs are undifferentiated cells, located in the bone marrow before they become mature blood cells and enter the blood stream. They have a unique ability to produce either similar cells (self-renewal), or cells engaged in one of different lineages of blood cells: red blood cells, white cells and platelets (differentiation). The HSCs can be either in a proliferating or in a quiescent phase. In this paper, we distinguish between dividing cells that enter directly to the quiescent phase and dividing cells that return to the proliferating phase to divide again. We propose a mathematical model describing the dynamics of HSC population, taking into account their spatial distribution. The resulting model is a coupled reaction–diffusion equation and difference equation with delay. We study the existence of monotone traveling wave fronts and the asymptotic speed of spread.