A new model of cell dynamics in Acute Myeloid Leukemia involving distributed delays

Jose Luis Avila Alonso 1, 2 Catherine Bonnet 1, 2 Jean Clairambault 3, 4 Hitay Ozbay 5 Silviu-Iulian Niculescu 1, 2 Faten Merhi 6 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 Division Systèmes - L2S
L2S - Laboratoire des signaux et systèmes : 1289
4 BANG - Nonlinear Analysis for Biology and Geophysical flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt
Abstract : In this paper we propose a refined model for the dynamical cell behavior in Acute Myeloid Leukemia (AML) compared to (Ozbay et al, 2012) and (Adimy et al, 2008). We separate the cell growth phase into a sequence of several sub-compartments. Then, with the help of the method of characteristics, we show that the overall dynamical system of equations can be reduced to two coupled nonlinear equations with four internal sub-systems involving distributed delays.
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Submitted on : Tuesday, December 18, 2012 - 4:54:35 PM
Last modification on : Tuesday, June 4, 2019 - 11:08:04 AM

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Jose Luis Avila Alonso, Catherine Bonnet, Jean Clairambault, Hitay Ozbay, Silviu-Iulian Niculescu, et al.. A new model of cell dynamics in Acute Myeloid Leukemia involving distributed delays. 10th IFAC Workshop on Time Delay Systems, Jun 2012, Boston, United States. pp.55-60, ⟨10.3182/20120622-3-US-4021.00047⟩. ⟨hal-00766709⟩



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