[Équations différentielles et aux différences à retard pour des modèles de dynamique des cellules souches hématopoïétiques]
Toutes les cellules sanguines sont produites dans la moelle osseuse lors de l'hématopoïèse à partir d'une petite population de cellules appelées cellules souches hématopoïétiques (CSHs). Les CSHs ont la capacité de s'auto-renouveler et également de se différencier en tous types de cellules sanguines. Le sytème mathématique que nous considérons pour modéliser ces populations de CSHs est un système de deux équations aux dérivées partielles structurées en âge. Par intégration suivant les caractéristiques, le modèle est réduit à un système composé d'une équation différentielle et d'une équation aux différences à retard. Nous étudions le comportement asymptotique des états d'équilibre et l'existence d'une bifurcation de Hopf. Nous concluons notre travail par des simulations numériques.
All functional blood cells are generated in the bone marrow through hematopoiesis from a small population of cells called hematopoietic stem cells (HSCs). HSCs have the capacity to self-renew and also the capacity to differentiate into any types of blood cells. We consider a system of two age-structured partial differential equations, describing the evolution of the HSC population. By integrating this system over the age and using the characteristics method, we reduce it to a system composed of a differential equation and a delay difference equation. We investigate the asymptotic stability of steady states and the existence of a Hopf bifurcation. We conclude our work by numerical simulations.
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@article{CRMATH_2015__353_4_303_0,
author = {Adimy, Mostafa and Chekroun, Abdennasser and Touaoula, Tarik-Mohamed},
title = {A delay differential-difference system of hematopoietic stem cell dynamics},
journal = {Comptes Rendus. Math\'ematique},
pages = {303--307},
publisher = {Elsevier},
volume = {353},
number = {4},
year = {2015},
doi = {10.1016/j.crma.2015.01.018},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2015.01.018/}
}
TY - JOUR AU - Adimy, Mostafa AU - Chekroun, Abdennasser AU - Touaoula, Tarik-Mohamed TI - A delay differential-difference system of hematopoietic stem cell dynamics JO - Comptes Rendus. Mathématique PY - 2015 SP - 303 EP - 307 VL - 353 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2015.01.018/ DO - 10.1016/j.crma.2015.01.018 LA - en ID - CRMATH_2015__353_4_303_0 ER -
%0 Journal Article %A Adimy, Mostafa %A Chekroun, Abdennasser %A Touaoula, Tarik-Mohamed %T A delay differential-difference system of hematopoietic stem cell dynamics %J Comptes Rendus. Mathématique %D 2015 %P 303-307 %V 353 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2015.01.018/ %R 10.1016/j.crma.2015.01.018 %G en %F CRMATH_2015__353_4_303_0
Adimy, Mostafa; Chekroun, Abdennasser; Touaoula, Tarik-Mohamed. A delay differential-difference system of hematopoietic stem cell dynamics. Comptes Rendus. Mathématique, Tome 353 (2015) no. 4, pp. 303-307. doi : 10.1016/j.crma.2015.01.018. http://www.numdam.org/articles/10.1016/j.crma.2015.01.018/
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