Analysis of a New Model of Cell Population Dynamics in Acute Myeloid Leukemia

José Luis Avila Alonso 1, 2 Catherine Bonnet 1, 3 Jean Clairambault 4 Hitay Ozbay 5 Silviu-Iulian Niculescu 1, 3 Faten Merhi 6 Annabelle Ballesta 7 Ruoping Tang 6 Jean-Pierre Marie 6
1 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
2 L2S - Laboratoire des signaux et systèmes
3 Division Systèmes - L2S
L2S - Laboratoire des signaux et systèmes : 1289
4 MAMBA - Modelling and Analysis for Medical and Biological Applications
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt
5 Department of Electrical and Electronics Engineering
6 UPMC - Université Pierre et Marie Curie - Paris 6
7 Department of pharmacology and systems therapeutics [Mount Sinai]
Abstract : A new mathematical model of the cell dynamics in Acute Myeloid Leukemia (AML) is considered which takes into account the four different phases of the proliferating compartment. The dynamics of the cell populations are governed by transport partial differential equations structured in age and by using the method of characteristics, we obtain that the dynamical system of equation can be reduced to two coupled nonlinear equations with four internal sub-systems involving distributed delays. Equilibrium and local stability analysis of this model are performed and several simulations illustrate the results.
Type de document :
Chapitre d'ouvrage
Tomáš Vyhlídal and Jean-François Lafay and Rifat Sipahi. Delay Systems : From Theory to Numerics and Applications, 1, Springer, pp.315-328, 2014, Advances in Delays and Dynamics, 978-3-319-01695-5. 〈10.1007/978-3-319-01695-5_23〉
Liste complète des métadonnées
https://hal.inria.fr/hal-00932779
Contributeur : José Luis Emanuelle Avila Alonso <>
Soumis le : vendredi 17 janvier 2014 - 16:15:54
Dernière modification le : jeudi 21 mars 2019 - 14:41:40

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Citation

José Luis Avila Alonso, Catherine Bonnet, Jean Clairambault, Hitay Ozbay, Silviu-Iulian Niculescu, et al.. Analysis of a New Model of Cell Population Dynamics in Acute Myeloid Leukemia. Tomáš Vyhlídal and Jean-François Lafay and Rifat Sipahi. Delay Systems : From Theory to Numerics and Applications, 1, Springer, pp.315-328, 2014, Advances in Delays and Dynamics, 978-3-319-01695-5. 〈10.1007/978-3-319-01695-5_23〉. 〈hal-00932779〉

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