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This paper analyzes the dynamics of a G 0 cell cycle model of pluripotential stem cells to understand the origin of the long period oscillations of blood cell levels observed in periodic chronic myelogenous leukemia (PCML). The model dynamics are described by a system of two delayed differential equations. We give conditions for the local stability of the… (More)

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… (More)

We study a class of delay differential equations which have been used to model hematological stem cell regulation and dynamics. Under certain circumstances the model exhibits self-sustained oscillations, with periods which can be significantly longer than the basic cell cycle time. We show that the long periods in the oscillations occur when the cell… (More)

We study the moment stability of the trivial solution of a linear differential delay equation in the presence of additive and multiplicative white noise. The results established here are applied to examining the local stability of the hematopoietic stem cell (HSC) regulation system in the presence of noise. The stability of the first moment for the… (More)

Stem cells and their relationship with mature tissues are of increasing interest in the biomedical sciences, but the dynamics of stem cell/tissue interactions are not well understood. We give a generic stem cell/tissue model and examine the dynamics of a specific case of this, namely, a four-compartment model of blood cell production and regulation. We… (More)

We present a mathematical model of blood cell production which describes both the development of cells through the cell cycle, and the maturation of these cells as they differentiate to form the various mature blood cell types. The model differs from earlier similar ones by considering primitive stem cells as a separate population from the differentiating… (More)

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