Periodic Solutions in a Mathematical Model for the Treatment of Chronic Myelogenous Leukemia

A. Halanay

Mathematical Modelling of Natural Phenomena (2012)

  • Volume: 7, Issue: 1, page 235-244
  • ISSN: 0973-5348

Abstract

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Existence and stability of periodic solutions are studied for a system of delay differential equations with two delays, with periodic coefficients. It models the evolution of hematopoietic stem cells and mature neutrophil cells in chronic myelogenous leukemia under a periodic treatment that acts only on mature cells. Existence of a guiding function leads to the proof of the existence of a strictly positive periodic solution by a theorem of Krasnoselskii. The stability of this solution is analysed.

How to cite

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Halanay, A.. "Periodic Solutions in a Mathematical Model for the Treatment of Chronic Myelogenous Leukemia." Mathematical Modelling of Natural Phenomena 7.1 (2012): 235-244. <http://eudml.org/doc/222325>.

@article{Halanay2012,
abstract = {Existence and stability of periodic solutions are studied for a system of delay differential equations with two delays, with periodic coefficients. It models the evolution of hematopoietic stem cells and mature neutrophil cells in chronic myelogenous leukemia under a periodic treatment that acts only on mature cells. Existence of a guiding function leads to the proof of the existence of a strictly positive periodic solution by a theorem of Krasnoselskii. The stability of this solution is analysed.},
author = {Halanay, A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {periodic solution; guiding function; index of an isolated solution; stability; chronic myelogenous leukemia},
language = {eng},
month = {1},
number = {1},
pages = {235-244},
publisher = {EDP Sciences},
title = {Periodic Solutions in a Mathematical Model for the Treatment of Chronic Myelogenous Leukemia},
url = {http://eudml.org/doc/222325},
volume = {7},
year = {2012},
}

TY - JOUR
AU - Halanay, A.
TI - Periodic Solutions in a Mathematical Model for the Treatment of Chronic Myelogenous Leukemia
JO - Mathematical Modelling of Natural Phenomena
DA - 2012/1//
PB - EDP Sciences
VL - 7
IS - 1
SP - 235
EP - 244
AB - Existence and stability of periodic solutions are studied for a system of delay differential equations with two delays, with periodic coefficients. It models the evolution of hematopoietic stem cells and mature neutrophil cells in chronic myelogenous leukemia under a periodic treatment that acts only on mature cells. Existence of a guiding function leads to the proof of the existence of a strictly positive periodic solution by a theorem of Krasnoselskii. The stability of this solution is analysed.
LA - eng
KW - periodic solution; guiding function; index of an isolated solution; stability; chronic myelogenous leukemia
UR - http://eudml.org/doc/222325
ER -

References

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