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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Submitted on : Wednesday, February 8, 2017 - 2:14:27 PM
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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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