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

Mostafa Adimy 1, 2, 3 Abdennasser Chekroun 3, 1 Bogdan Kazmierczak 4
1 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
CGPhiMC - Centre de génétique et de physiologie moléculaire et cellulaire, Inria Grenoble - Rhône-Alpes, ICJ - Institut Camille Jordan [Villeurbanne]
3 MMCS - Modélisation mathématique, calcul scientifique
ICJ - Institut Camille Jordan [Villeurbanne]
Abstract : 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 an age-structured reaction-diffusion system. The method of characteristics reduces this model to a coupled reaction-diffusion equation and difference equation with delay. We study the existence of traveling wave fronts connecting the zero steady state with the unique positive uniform one. We use a monotone iteration technique coupled with the upper and lower solutions method.
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Mostafa Adimy, Abdennasser Chekroun, Bogdan Kazmierczak. Traveling waves in a coupled reaction-diffusion and difference model of hematopoiesis. Journal of Differential Equations, Elsevier, 2017, 262, pp.4085 - 4128. ⟨10.1016/j.jde.2016.12.009⟩. ⟨hal-01573613⟩



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