NDLI: Analysis of leukaemic cells dynamics with multi-stage maturation process using a new non-linear positive model with distributed time-delay

Content Provider	IET Digital Library
Author	Zenati, Abdelhafid Chakir, Massaoud Tadjine, Mohamed Denai, Mouloud
Abstract	This study proposes a new non-linear positive model with distributed time-delay describing the dynamics of leukaemic cells lineages and their levels of maturity. The dynamic model is first reformulated into coupled non-linear equations with distributed time-delay using an appropriate transformation of the age-structured transport partial differential equations that govern the dynamics of leukaemic cell populations. After assessing the positiveness of the proposed model, the conditions for the existence of positive steady-states are established. Furthermore, the necessary and sufficient conditions for boundedness of the solutions are derived. Finally, the convergence of the proposed model to the origin is studied as this has an important biological interpretation which is the extinction of all generations of leukaemic cells following anti-leukaemia treatments. To investigate the global asymptotic stability of this important equilibrium point, both model properties (i.e. positiveness and boundedness) are used to construct a suitable Lyapunov function for the characterisation of leukaemic cells dynamics. The results demonstrate a significant improvement for the treatment of leukaemia. Some simulations are presented to illustrate the effectiveness of the proposed model.
Starting Page	3052
Ending Page	3064
Page Count	13
ISSN	17518644
Volume Number	13
e-ISSN	17518652
Issue Number	Issue 18, Dec (2019)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-cta/13/18
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-cta.2019.0331
Journal	IET Control Theory & Applications
Publisher Date	2019-09-03
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Age-structured Transport Partial Differential Equation Asymptotic Stability Cancer Coupled Nonlinear Equation Delay Distributed Time-delay Dynamic Modelling Function Theory And Analysis Leukaemic Cell Dynamics Leukaemic Cell Lineages Leukaemic Cell Populations Lyapunov Method Model Property Multistage Maturation Process Nonlinear Positive Model Partial Differential Equation Positiveness Stability in Control Theory
Content Type	Text
Resource Type	Article
Subject	Control and Optimization Control and Systems Engineering Human-Computer Interaction Electrical and Electronic Engineering Computer Science Applications

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