City Research Online

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.

Publication Type:	Conference or Workshop Item (Paper)
Additional Information:	© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Publisher Keywords:	Leukemia; New Model; Distributed Delay; Healthy steady state; Global stability
Subjects:	Q Science > QH Natural history > QH301 Biology R Medicine > RC Internal medicine > RC0254 Neoplasms. Tumors. Oncology (including Cancer)
Departments:	School of Science & Technology > Engineering

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