A discrete mathematical model of unlabelled granulocyte kinetics. A preliminary study of feedback control.

The equations used in formulating the continuous model of granulocyte kinetics developed by O'Fallon et al. (1971) were analyzed to see if they could be altered to simulate a feedback mechanism operating on the production and development of granulocytes. After extensive study and modification of the continuous model, it was found that a discrete model based on a Leslie matrix procedure was more effective for simulating the feedback system. This discrete model was used to show experimentally, from a mathematical view point, that a feedback mechanism of some kind must be operating on the production and development of granulocytes. Further, the discrete model was subjected to preliminary tests (simultaneous and cascading feedback) to demonstrate that it has the capability of responding to feedback control.