A discrete-maturity Interconnected Model of Healthy and Cancer Cell Dynamics in Acute Myeloid Leukemia

José Luis Avila Alonso 1, 2, 3 Catherine Bonnet 1, 2, 3 Hitay Ozbay 4 Jean Clairambault 5, 6 Silviu-Iulian Niculescu 1, 2, 3
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
3 Division Systèmes - L2S
L2S - Laboratoire des signaux et systèmes : 1289
5 MAMBA - Modelling and Analysis for Medical and Biological Applications
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt
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 modelled 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.
Document type :
Conference papers
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https://hal.inria.fr/hal-00940305
Contributor : José Luis Emanuelle Avila Alonso <>
Submitted on : Friday, January 31, 2014 - 4:58:57 PM
Last modification on : Tuesday, June 25, 2019 - 1:26:54 AM

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  • HAL Id : hal-00940305, version 1

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José Luis Avila Alonso, Catherine Bonnet, Hitay Ozbay, Jean Clairambault, Silviu-Iulian Niculescu. A discrete-maturity Interconnected Model of Healthy and Cancer Cell Dynamics in Acute Myeloid Leukemia. Mathematical Theory of Networks and Systems, Jul 2014, Groningen, Netherlands. ⟨hal-00940305⟩

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