Stability analysis of cell dynamics in leukemia

Date
2012
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Instructor
Source Title
Mathematical Modelling of Natural Phenomena
Print ISSN
0973-5348
Electronic ISSN
Publisher
E D P Sciences
Volume
7
Issue
1
Pages
203 - 234
Language
English
Type
Article
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Abstract

In order to better understand the dynamics of acute leukemia, and in particular to find theoretical conditions for the efficient delivery of drugs in acute myeloblastic leukemia, we investigate stability of a system modeling its cell dynamics. The overall system is a cascade connection of sub-systems consisting of distributed delays and static nonlinear feedbacks. Earlier results on local asymptotic stability are improved by the analysis of the linearized system around the positive equilibrium. For the nonlinear system, we derive stability conditions by using Popov, circle and nonlinear small gain criteria. The results are illustrated with numerical examples and simulations.

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Keywords
Absolute stability, Acute leukemia, Distributed delays, Global stability, Absolute stability, Acute leukemia, Cell dynamics, Distributed delays, Global stability, Linearized systems, Local asymptotic stability, Nonlinear small gain, Numerical example, Positive equilibrium, Stability analysis, Stability condition, Sub-systems, System modeling, Asymptotic stability, Diseases, Dynamics, Nonlinear feedback, Stability criteria, System stability
Citation
Published Version (Please cite this version)