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Journal Articles Systems and Control Letters Year : 2016

Stability of the cell dynamics in acute myeloid leukemia


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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Dates and versions

hal-01257577 , version 1 (17-01-2016)



Emilia Fridman, Catherine Bonnet, Frederic Mazenc, Walid Djema. Stability of the cell dynamics in acute myeloid leukemia. Systems and Control Letters, 2016, 88, pp.91-100. ⟨10.1016/j.sysconle.2015.09.006⟩. ⟨hal-01257577⟩
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