Stability of the cell dynamics in acute myeloid leukemia

Emilia Fridman 1 Catherine Bonnet 2, 3 Frederic Mazenc 4, 3 Walid Djema 4, 3
4 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
Abstract : In this paper we analyze the global asymptotic stability of the trivial solution for a multi-stage maturity acute myeloid leukemia model. By employing the positivity of the corresponding nonlinear time-delay model, where the nonlin-earity is locally Lipschitz, we establish the global exponential stability under the same conditions that are necessary for the local exponential stability. The result is derived for the multi-stage case via a novel construction of linear Lyapunov functionals. In a simpler model of hematopoiesis (without fast self-renewal) our conditions guarantee also global exponential stability with a given decay rate. Moreover, in this simpler case the analysis of the PDE model is presented via novel Lyapunov functionals for the transport equations.
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Emilia Fridman, Catherine Bonnet, Frederic Mazenc, Walid Djema. Stability of the cell dynamics in acute myeloid leukemia. Systems and Control Letters, Elsevier, 2016, 88, pp.91-100. ⟨10.1016/j.sysconle.2015.09.006⟩. ⟨hal-01257577⟩

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