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
3 Ecole Centrale Paris
4 LJLL - Laboratoire Jacques-Louis Lions
5 BANG - Nonlinear Analysis for Biology and Geophysical flows

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.

Mots clés: absolute stability; distributed delays; global stability; acute leukemia

Domaines: Automatique / Robotique; Cancer

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