Stability of a Delay System Coupled to a Differential-Difference System Describing the Coexistence of Ordinary and Mutated Hematopoietic Stem Cells

Abstract : A new mathematical model that represents the coexistence between normal and leukemic populations of cells is proposed and analyzed. It is composed by a nonlinear time-delay system describing the dynamics of ordinary stem cells, coupled to a differential-difference system governing the dynamics of mutated cells. A Lyapunov-like technique is devel- oped in order to investigate the stability properties of a steady state where healthy cells survive while leukemic ones are eradicated. Exponential stability of solutions is established, estimate of their decay rate is given and a subset of the basin of attraction of the desired steady state is provided.
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https://hal.inria.fr/hal-01389870
Contributor : Frederic Mazenc <>
Submitted on : Monday, January 9, 2017 - 5:22:24 PM
Last modification on : Friday, December 20, 2019 - 11:48:05 AM

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  • HAL Id : hal-01389870, version 2

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Walid Djema, Frédéric Mazenc, Catherine Bonnet, Jean Clairambault, P Hirsch, et al.. Stability of a Delay System Coupled to a Differential-Difference System Describing the Coexistence of Ordinary and Mutated Hematopoietic Stem Cells. Conference on Decision and Control , Dec 2016, Las Vegas, United States. ⟨hal-01389870v2⟩

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