Variable maturation velocity and parameter sensitivity in a model of haematopoiesis

We analyse an age-structured model for haematopoiesis, describing the development of specialized cells in the blood from undifferentiated stem cells and including the controlling effects of hormones. Variation in the length of time for maturing of precursor cells in this model has a stabilizing influence. When the maturing process does not vary, then the age-structured model reduces to a delay differential equation. Depending on the death process considered, either a differential equation with two time delays or a differential 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.