Stability of the cell dynamics in acute myeloid leukemia

Emilia Fridman; Catherine Bonnet; Frederic Mazenc; Walid Djema

doi:10.1016/j.sysconle.2015.09.006

Stability of the cell dynamics in acute myeloid leukemia

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

^*Corresponding author for this work

School of Electrical Engineering

Research output: Contribution to journal › Article › peer-review

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 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 language	English
Pages (from-to)	91-100
Number of pages	10
Journal	Systems and Control Letters
Volume	88
DOIs	https://doi.org/10.1016/j.sysconle.2015.09.006
State	Published - Feb 2016

Keywords

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

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10.1016/j.sysconle.2015.09.006

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title = "Stability of the cell dynamics in acute myeloid leukemia",

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 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.",

keywords = "Leukemia model, Lyapunov method, Positive systems, Time-delay systems, Transport equations",

author = "Emilia Fridman and Catherine Bonnet and Frederic Mazenc and Walid Djema",

year = "2016",

month = feb,

doi = "10.1016/j.sysconle.2015.09.006",

language = "אנגלית",

volume = "88",

pages = "91--100",

journal = "Systems and Control Letters",

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TY - JOUR

T1 - Stability of the cell dynamics in acute myeloid leukemia

AU - Fridman, Emilia

AU - Bonnet, Catherine

AU - Mazenc, Frederic

AU - Djema, Walid

PY - 2016/2

Y1 - 2016/2

N2 - 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.

AB - 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.

KW - Leukemia model

KW - Lyapunov method

KW - Positive systems

KW - Time-delay systems

KW - Transport equations

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VL - 88

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JO - Systems and Control Letters

JF - Systems and Control Letters

ER -

Stability of the cell dynamics in acute myeloid leukemia

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Keywords

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