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 1, 2 Pierre Hirsch 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 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 for healthy and cancer cell dynamics in Acute Myeloid Leukemia consisting of two stages of maturation for cancer cells and three stages of maturation for healthy cells. The cell dynamics are modeled by nonlinear partial differential equations (PDE). Applying the method of characteristics enable us to reduce the PDE model to a nonlinear distributed delay system. For an equilibrium point of interest, necessary and sufficient conditions of local asymptotic stability are given. The results are illustrated with 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 : Tuesday, June 25, 2019 - 1:26:55 AM

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  • HAL Id : hal-01110309, version 1

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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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