Fluctuations in circulating cell numbers following chemotherapy or bone marrow transplant

We study the effect of noise on the behaviour of a dynamic cell population model in which cell replication and maturation take place simultaneously. We assume that the maximum proliferative potential v fluctuates uniformly about a mean value of v, and show that a decrease in v and/or the input flux uin into the population can lead to an increase in the variance in the cellular efflux uf. We draw a qualitative correspondence between this behaviour and the commonly observed increase in the variance of circulating blood cell numbers following chemotherapy and radiotherapy, both of which lead to a decrease in v and uin, and bone marrow transplant which probably corresponds to a decrease in uin.