Analysis of a Model of Dormancy in Cancer as a State of Coexistence Between Tumor and Healthy Stem Cells

W Djema 1 C. Bonnet 1 J Clairambault 2 F Mazenc 1 P Hirsch 3 F Delhommeau 3
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 MAMBA - Modelling and Analysis for Medical and Biological Applications
LJLL - Laboratoire Jacques-Louis Lions, Inria de Paris
Abstract : We study a mathematical model of co-habitation of healthy and unhealthy stem cells, in order to address some new biological concerns. In short, we will investigate the existence and the stability properties of a positive steady state of a model that is well adapted to the study of dormancy of cancer stem cells. Mathematically, we are concerned with the analysis of a nonlinear retarded system coupled to a nonlinear differential-difference system, in the time-domain framework, via a Lyapunov-like method.
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W Djema, C. Bonnet, J Clairambault, F Mazenc, P Hirsch, et al.. Analysis of a Model of Dormancy in Cancer as a State of Coexistence Between Tumor and Healthy Stem Cells. IEEE American Control Conference (ACC) 2017, May 2017, Seattle, United States. pp.5135-5140, ⟨10.23919/ACC.2017.7963751⟩. ⟨hal-01677927⟩

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