Geodesic
Stability Analysis of Cell Dynamics in Leukemia
H. Özbay1 ; C. Bonnet2 ; H. Benjelloun3 ; J. Clairambault4, 5
1 Dept. of Electrical and Electronics Eng., Bilkent University, Ankara, 06800, Turkey
2 INRIA Saclay - Île-de-France, Equipe DISCO, LSS - SUPELEC 3 rue Joliot Curie, 91192 Gif-sur-Yvette, France
3 Ecole Centrale Paris, Grande Voie des Vignes, Châtenay-Malabry, France
4 INRIA Paris-Rocquencourt, Domaine de Voluceau, B.P. 105, 78153 Le Chesney
5 INSERM team U 776 “Biological Rhythms and Cancers”, Hôpital Paul-Brousse 14 Av. Paul-Vaillant-Couturier, 94807 Villejuif, France
Mathematical modelling of natural phenomena, Tome 7 (2012) no. 1, pp. 203-234.

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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 investigate 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.
DOI : 10.1051/mmnp/20127109

H. Özbay 1 ; C. Bonnet 2 ; H. Benjelloun 3 ; J. Clairambault 4, 5

1 Dept. of Electrical and Electronics Eng., Bilkent University, Ankara, 06800, Turkey
2 INRIA Saclay - Île-de-France, Equipe DISCO, LSS - SUPELEC 3 rue Joliot Curie, 91192 Gif-sur-Yvette, France
3 Ecole Centrale Paris, Grande Voie des Vignes, Châtenay-Malabry, France
4 INRIA Paris-Rocquencourt, Domaine de Voluceau, B.P. 105, 78153 Le Chesney
5 INSERM team U 776 “Biological Rhythms and Cancers”, Hôpital Paul-Brousse 14 Av. Paul-Vaillant-Couturier, 94807 Villejuif, France 
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H. Özbay; C. Bonnet; H. Benjelloun; J. Clairambault. Stability Analysis of Cell Dynamics in Leukemia. Mathematical modelling of natural phenomena, Tome 7 (2012) no. 1, pp. 203-234. doi : 10.1051/mmnp/20127109. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20127109/

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