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    Dynamical Behavior of Biological Healthy Steady State in Leukemia Using a New Leukemic & Healthy Stem Cells Cohabitation Model with Distributed Delay

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    Type
    Conference Paper
    Authors
    Zenati, Abdelhafid
    Chakir, Messaoud
    Tadjine, Mohamed
    Laleg-Kirati, Taous-Meriem cc
    KAUST Department
    Electrical Engineering Program
    Computational Bioscience Research Center (CBRC)
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2019-11-25
    Permanent link to this record
    http://hdl.handle.net/10754/660342
    
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    Abstract
    Acute Myeloid Leukemia (AML) treatment protocol from clinical point of view, aims to maintain a normal amount of healthy cells and to eradicate all malignant cells. This particular objective is biologically qualified as a positive healthy situation. In this paper, we give sufficient and necessary conditions for the global stability of such a healthy situation. To this end, we first propose a new distributed delay model of AML. The latter is an improvement of an existing delayed coupled model describing the dynamics of hematopoesis stem cells in AML. We modify the PDEs equations and transform them into a set of distributed delay equations. The proposed model is more suitable for biological phenomena than constant delay models as the proliferation time differs from a cell type to another. Furthermore in the proposed model, we consider the sub-population of cells that have lost their capacity of self-renewal and became progenitors. In second, we derive sufficient and necessary conditions for the global stability of healthy steady state. For this, the positivity of the obtained model and sequences of functions theory are used to construct new Lyapunov function candidates. Finally, we conduct numerical simulations to show that the obtained results complete and generalize those published in the literature.
    Citation
    Zenati, A., Chakir, M., Tadjine, M., & Laleg-Kirati, T.-M. (2019). Dynamical Behavior of Biological Healthy Steady State in Leukemia Using a New Leukemic & Healthy Stem Cells Cohabitation Model with Distributed Delay. 2019 American Control Conference (ACC). doi:10.23919/acc.2019.8814334
    Publisher
    IEEE
    Conference/Event name
    2019 American Control Conference (ACC)
    DOI
    10.23919/acc.2019.8814334
    Additional Links
    https://ieeexplore.ieee.org/document/8814334/
    ae974a485f413a2113503eed53cd6c53
    10.23919/acc.2019.8814334
    Scopus Count
    Collections
    Conference Papers; Electrical Engineering Program; Computational Bioscience Research Center (CBRC); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

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