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Adimy Mostafa .♦, Chekroun A.♦, Kaźmierczak Bogdan ., Traveling Waves For Reaction-Diffusion Pde Coupled To Difference Equation With Nonlocal Dispersal Term And Time Delay,
MATHEMATICAL MODELLING OF NATURAL PHENOMENA, ISSN: 0973-5348, DOI: 10.1051/mmnp/2022021, Vol.17, pp.1-31, 2022 Abstract:
We consider a class of biological models represented by a system composed of reactiondiffusion PDE coupled with difference equations (renewal equations) in n-dimensional space, with nonlocal dispersal terms and implicit time delays. The difference equation generally arises, by means of the method of characteristics, from an age-structured partial differential system. Using upper and lower solutions, we study the existence of monotonic planar traveling wave fronts connecting the extinction state to the uniform positive state. The corresponding minimum wave speed is also obtained. In addition, we investigate the effect of the parameters on this minimum wave speed and we give a detailed analysis of its asymptotic behavior Keywords:
Planar monotone traveling wave front ,Reaction-diffusion PDE with delay,Difference equation,Monostable equation Affiliations:
| Adimy Mostafa . | - | National Institute for Research in Digital Science and Technology (FR) | | Chekroun A. | - | National Institute for Research in Digital Science and Technology (FR) | | Kaźmierczak Bogdan . | - | IPPT PAN |
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Adimy M.♦, Chekroun A.♦, Kaźmierczak B., Traveling waves in a coupled reaction–diffusion and difference model of hematopoiesis,
Journal of Differential Equations, ISSN: 0022-0396, DOI: 10.1016/j.jde.2016.12.009, Vol.262, No.7, pp.4085-4128, 2017Abstract:
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. Keywords:
hematopoiesis, age-structured population, reaction–diffusion system with delay, difference equation, traveling wave front, asymptotic speed of spread Affiliations:
| Adimy M. | - | National Institute for Research in Digital Science and Technology (FR) | | Chekroun A. | - | National Institute for Research in Digital Science and Technology (FR) | | Kaźmierczak B. | - | IPPT PAN |
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