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Periodic Oscillations of Blood Cell Populations in Chronic Myelogenous Leukemia

Michael C. Mackey·Chunhua Ou·Laurent Pujo-Menjouet·Jianhong Wu
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Abstract

We 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.

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Michael C. Mackey, Chunhua Ou, Laurent Pujo-Menjouet, Jianhong Wu. 2004-09-01. Periodic Oscillations of Blood Cell Populations in Chronic Myelogenous Leukemia. https://arxiv.org/abs/q-bio/0409002

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