Stability Analysis of Cell Dynamics in Leukemia

Hitay Ozbay 1 Catherine Bonnet 2 Houda Benjelloun 3 Jean Clairambault 4, 5
1 Department of Electrical and Electronics Engineering
2 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 Ecole Centrale Paris
4 LJLL - Laboratoire Jacques-Louis Lions
5 BANG - Nonlinear Analysis for Biology and Geophysical flows
LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt
Abstract : In order to better understand the dynamics of acute leukemia, and in particular to find theoretical conditions for the efficient delivery of drugs in acute myeloblastic leukemia, we inves- tigate stability of a system modeling its cell dynamics. The overall system is a cascade connection of sub-systems consisting of distributed delays and static nonlinear feedbacks. Earlier results on local asymptotic stability are improved by the analysis of the linearized system around the positive equilibrium. For the nonlinear system, we derive stability conditions by using Popov, circle and nonlinear small gain criteria. The results are illustrated with numerical examples and simulations.
Keywords : absolute stability acute leukemia distributed delays global stability
Type de document :
Article dans une revue
Mathematical Modelling of Natural Phenomena, EDP Sciences, 2012, Cancer Modeling, 7 (1), pp.203-234. 〈10.1051/mmnp/20127109〉
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https://hal.inria.fr/hal-00766052
Contributeur : Catherine Bonnet <>
Soumis le : lundi 17 décembre 2012 - 14:51:39
Dernière modification le : vendredi 31 août 2018 - 09:06:03

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Hitay Ozbay, Catherine Bonnet, Houda Benjelloun, Jean Clairambault. Stability Analysis of Cell Dynamics in Leukemia. Mathematical Modelling of Natural Phenomena, EDP Sciences, 2012, Cancer Modeling, 7 (1), pp.203-234. 〈10.1051/mmnp/20127109〉. 〈hal-00766052〉

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