Stability of the cell dynamics in acute myeloid leukemia

Emilia Fridman*, Catherine Bonnet, Frederic Mazenc, Walid Djema

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 nonlinearity 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.

Original languageEnglish
Pages (from-to)91-100
Number of pages10
JournalSystems and Control Letters
StatePublished - Feb 2016


  • Leukemia model
  • Lyapunov method
  • Positive systems
  • Time-delay systems
  • Transport equations


Dive into the research topics of 'Stability of the cell dynamics in acute myeloid leukemia'. Together they form a unique fingerprint.

Cite this