%0 Journal Article
%T Periodic Oscillations of Blood Cell Populations in Chronic Myelogenous Leukemia
%A Michael C. Mackey
%A Chunhua Ou
%A Laurent Pujo-Menjouet
%A Jianhong Wu
%J Quantitative Biology
%D 2004
%I arXiv
%X 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.
%U http://arxiv.org/abs/q-bio/0409002v1