Browsing by Author "Avila, J. L."
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Item 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.Item 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.