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29 March 2024
 
  » arxiv » q-bio.TO/0409002

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Periodic Oscillations of Blood Cell Populations in Chronic Myelogenous Leukemia
Michael C. Mackey ; Chunhua Ou ; Laurent Pujo-Menjouet ; Jianhong Wu ;
Date 1 Sep 2004
Subject Tissues and Organs | q-bio.TO
AbstractWe develop some techniques to prove analytically the existence and stability of long period oscillations of stem cell populations in the case of periodic chronic myelogenous leukemia. Such a periodic oscillation $p_infty $ can be analytically constructed when the hill coefficient involved in the nonlinear feedback is infinite, and we show it is possible to obtain a contractive returning map (for the semiflow defined by the modeling functional differential equation) in a closed and convex cone containing $p_infty $ when the hill coefficient is large, and the fixed point of such a contractive map gives the long period oscillation previously observed both numerically and experimentally.
Source arXiv, q-bio.TO/0409002
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