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

Walid Djema 1 Frederic Mazenc 1 Catherine Bonnet 1 Jean Clairambault 2, 3 P Hirsch 4, 5 François Delhommeau 5, 6, 7
1 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
2 Sorbonne Universités
3 MAMBA - Modelling and Analysis for Medical and Biological Applications
LJLL - Laboratoire Jacques-Louis Lions, Inria de Paris
4 Service d'hématologie clinique et de thérapie cellulaire [CHU Saint-Antoine]
5 CR Saint-Antoine - Centre de Recherche Saint-Antoine
6 CHU Saint-Antoine [APHP]
7 CHU Trousseau [APHP]
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.
Keywords : Exponential stability Delay Nonlinear
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Conference papers
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https://hal.inria.fr/hal-01389870
Contributor : Frederic Mazenc <>
Submitted on : Wednesday, February 8, 2017 - 2:14:27 PM
Last modification on : Sunday, March 31, 2019 - 1:26:08 AM

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UPMC | LJLL | L2S | INRIA | U938 | UNIV-PARIS-SACLAY | SUP_LSS | CENTRALESUPELEC | SUP_SYSTEMES | INRIA-ROCQ | SORBONNE-UNIVERSITE | SU-MEDECINE | SU-SCIENCES | UNIV-PARIS7 | USPC

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Walid Djema, Frederic 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. 55th IEEE Conference on Decision and Control (CDC 2016), Dec 2016, Las Vegas, United States. ⟨10.1109/cdc.2016.7798328 ⟩. ⟨hal-01389870v3⟩

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