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.
https://hal.inria.fr/hal-01257577
Contributor : Frederic Mazenc
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Submitted on : Sunday, January 17, 2016 - 7:06:30 PM
Last modification on : Friday, December 20, 2019 - 11:48:05 AM
Long-term archiving on: Friday, November 11, 2016 - 9:10:11 AM
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⟩
