Browsing by Author "Clairambault, J."

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Open Access
Analysis of blood cell production under growth factors switching
(Elsevier B.V., 2017) Djema, W.; Özbay, Hitay; Bonnet, C.; Fridman, E.; Mazenc, F.; Clairambault, J.
Hematopoiesis is a highly complicated biological phenomenon. Improving its mathematical modeling and analysis are essential steps towards consolidating the common knowledge about mechanisms behind blood cells production. On the other hand, trying to deepen the mathematical modeling of this process has a cost and may be highly demanding in terms of mathematical analysis. In this paper, we propose to describe hematopoiesis under growth factor-dependent parameters as a switching system. Thus, we consider that different biological functions involved in hematopoiesis, including aging velocities, are controlled through multiple growth factors. Then we attempt a new approach in the framework of time-delay switching systems, in order to interpret the behavior of the system around its possible positive steady states. We start here with the study of a specific case in which switching is assumed to result from drug infusions. In a broader context, we expect that interpreting cell dynamics using switching systems leads to a good compromise between complexity of realistic models and their mathematical analysis. © 2017
Open Access
A coupled model for healthy and cancerous cells dynamics in Acute Myeloid Leukemia
(IFAC, 2014) Avila, J. L.; Bonnet, C.; Özbay, Hitay; Clairambault, J.; Niculescu, S. I.; Hirsch, P.; Delhommeau, F.
In this paper we propose a coupled model for healthy and cancerous cell dynamics in Acute Myeloid Leukemia. The PDE-based model is transformed to a nonlinear distributed delay system. For an equilibrium point of interest, necessary and sufficient conditions of local asymptotic stability are given. Simulation examples are given to illustrate the results.
Open Access
A new model of cell dynamics in Acute Myeloid Leukemia involving distributed delays
(2012) Avila, J. L.; Bonnet, C.; Clairambault, J.; Özbay, Hitay; Niculescu, S. I.; Merhi, F.; Tang, R.; Marie, J. P.
In this paper we propose a refined model for the dynamical cell behavior in Acute Myeloid Leukemia (AML) compared to (Özbay et al, 2012) and (Adimy et al, 2008).We separate the cell growth phase into a sequence of several sub-compartments. Then, with the help of the method of characteristics, we show that the overall dynamical system of equations can be reduced to two coupled nonlinear equations with four internal sub-systems involving distributed delays. © 2012 IFAC.
Open Access
Stability analysis of cell dynamics in leukemia
(E D P Sciences, 2012) Özbay, Hitay; Bonnet, C.; Benjelloun, H.; Clairambault, J.
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.
Open Access
Stability analysis of systems with distributed delays and application to hematopoietic cell maturation dynamics
(IEEE, 2008-12) Özbay, Hitay; Bonnet, C.; Clairambault, J.
We consider linear systems with distributed delays where delay kernels are assumed to be finite duration impulse responses of finite dimensional systems. We show that stability analysis for this class of systems can be reduced to stability analysis of linear systems with discrete delays, for which many algorithms are available in the literature. The results are illustrated on a mathematical model of hematopoietic cell maturation dynamics. © 2008 IEEE.