Variable maturation velocity and parameter sensitivity in a model of haematopoiesis

We analyse an age-structured model for haematopoiesis, describing the devel opment of specialized cells in the blood from undifferentiated stem cells a nd including the controlling effects of hormones. Variation in the length o f time for maturing of precursor cells in this model has a stabilizing infl uence. When the maturing process does not vary, then the age-structured mod el reduces to a delay differential equation. Depending on the death process considered, either a differential equation with two time delays or a diffe rential equation with a state-dependent delay is obtained. Each of these is analysed in turn, for its linear stability. A sensitivity analysis of the parameters in this model shows which biochemical processes in the negative feedback most strongly affect the solutions.