Stability Analysis of Cell Dynamics in Leukemia

H. Özbay; C. Bonnet; H. Benjelloun; J. Clairambault

Mathematical Modelling of Natural Phenomena (2012)

  • Volume: 7, Issue: 1, page 203-234
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Özbay, H., et al. "Stability Analysis of Cell Dynamics in Leukemia." Mathematical Modelling of Natural Phenomena 7.1 (2012): 203-234. <http://eudml.org/doc/222196>.

@article{Özbay2012,
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.},
author = {Özbay, H., Bonnet, C., Benjelloun, H., Clairambault, J.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {acute leukemia; distributed delays; global stability; absolute stability},
language = {eng},
month = {1},
number = {1},
pages = {203-234},
publisher = {EDP Sciences},
title = {Stability Analysis of Cell Dynamics in Leukemia},
url = {http://eudml.org/doc/222196},
volume = {7},
year = {2012},
}

TY - JOUR
AU - Özbay, H.
AU - Bonnet, C.
AU - Benjelloun, H.
AU - Clairambault, J.
TI - Stability Analysis of Cell Dynamics in Leukemia
JO - Mathematical Modelling of Natural Phenomena
DA - 2012/1//
PB - EDP Sciences
VL - 7
IS - 1
SP - 203
EP - 234
AB - 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.
LA - eng
KW - acute leukemia; distributed delays; global stability; absolute stability
UR - http://eudml.org/doc/222196
ER -

References

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