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2016 IEEE 55th Conference on Decision and Control (CDC)

DOI: 10.1109/cdc.2016.7798328

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

Proceedings article published in 2016 by Walid Djema, Frederic Mazenc, Catherine Bonnet, Jean Clairambault, P. Hirsch, François Delhommeau ORCID
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This paper is available in a repository.

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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.