Math. Model. Nat. Phenom.
Volume 7, Number 1, 2012Cancer modeling
|Page(s)||203 - 234|
|Published online||25 January 2012|
Stability Analysis of Cell Dynamics in Leukemia
Dept. of Electrical and Electronics Eng., Bilkent
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
Corresponding author. E-mail: firstname.lastname@example.org
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.
Mathematics Subject Classification: 93D10 / 93D15 / 93B52 / 93B60 / 93C80
Key words: acute leukemia / distributed delays / global stability / absolute stability
© EDP Sciences, 2012
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