resumen

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 cells, and this formulation removes an apparent inconsistency in these earlier models. Three different controls are included in the model: proliferative control of stem cells, proliferative control of differentiating cells, and peripheral control of stem cell committal rate. It is shown that an increase in sensitivity of these controls can cause oscillations to occur through their interaction with time delays associated with proliferation and differentiation, respectively. We show that the characters of these oscillations are quite distinct and suggest that the model may explain an apparent superposition of fast and slow oscillations which can occur in cyclical neutropeni

RESUMEN

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 solutions of a linear differential delay equation under stochastic perturbation is identical to that of the unperturbed system. However, the stability of the second moment is altered by the perturbation. We obtain, using Laplace transform techniques, necessary and sufficient conditions for the second moment to be bounded. In applying the results to the HSC system, we find that the system stability is sensitive to perturbations in the stem cell differentiation and death rates, but insensitive to perturbations in the proliferation rate.