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Mathematical Modelling of Natural Phenomena (1)

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Periodic Solutions in a Mathematical Model for the Treatment ofChronic Myelogenous Leukemia
A. Halanay
Journal:

Mathematical Modelling of Natural Phenomena / Volume 7 / Issue 1 / 2012

Published online by Cambridge University Press:

25 January 2012, pp. 235-244

Print publication:

2012
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Existence and stability of periodic solutions are studied for a system of delaydifferential equations with two delays, with periodic coefficients. It models theevolution of hematopoietic stem cells and mature neutrophil cells in chronic myelogenousleukemia under a periodic treatment that acts only on mature cells. Existence of a guidingfunction leads to the proof of the existence of a strictly positive periodic solution by atheorem of Krasnoselskii. The stability of this solution is analysed.