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A Discrete-Maturity Interconnected Model of Healthy and Cancer Cell Dynamics in Acute Myeloid Leukemia

Catherine Bonnet 1, 2 Jose Luis Avila Alonso 1, 2 Hitay Ozbay 3 Jean Clairambault 4, 5 Silviu-Iulian Niculescu 2 Pierre Hirsch 6
1 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France
2 L2S - Laboratoire des signaux et systèmes
3 Department of Electrical and Electronics Engineering
4 LJLL - Laboratoire Jacques-Louis Lions
5 MAMBA - Modelling and Analysis for Medical and Biological Applications
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt
6 Service d'hématologie clinique et de thérapie cellulaire [CHU Saint-Antoine]
Abstract : In this paper we propose a coupled model forhealthy and cancer cell dynamics in Acute Myeloid Leukemiaconsisting of two stages of maturation for cancer cells andthree stages of maturation for healthy cells. The cell dynamicsare modeled by nonlinear partial differential equations (PDE).Applying the method of characteristics enable us to reducethe PDE model to a nonlinear distributed delay system. For anequilibrium point of interest, necessary and sufficient conditionsof local asymptotic stability are given. The results are illustratedwith numerical examples and simulations.
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Conference papers
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https://hal.inria.fr/hal-01110309
Contributor : Catherine Bonnet <>
Submitted on : Tuesday, January 27, 2015 - 7:22:40 PM
Last modification on : Thursday, July 9, 2020 - 4:08:02 PM

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  • HAL Id : hal-01110309, version 1

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CNRS | INRIA | SUP_LSS | L2S | SUP_SYSTEMES | UPMC | LJLL | SORBONNE-UNIVERSITE | SU-SCIENCES | UNIV-PARIS7 | USPC | SUPELEC

Citation

Catherine Bonnet, Jose Luis Avila Alonso, Hitay Ozbay, Jean Clairambault, Silviu-Iulian Niculescu, et al.. A Discrete-Maturity Interconnected Model of Healthy and Cancer Cell Dynamics in Acute Myeloid Leukemia. The 10th AIMS Conference on Dynamical Systems,Differential Equations and Applications, Jul 2014, Madrid, Spain. ⟨hal-01110309⟩

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