There are a number of interesting periodic hematological diseases [Haurie et al. Blood (1998), {\it 92}, 2629-2640] and some are understood through mathematical modeling [M.C. Mackey. ``Mathematical models of hematopoietic cell replication and control", pp. 149-178 in {\bf The Art of Mathematical Modeling: Case Studies in Ecology, Physiology and Biofluids} (H.G. Othmer, F.R. Adler, M.A. Lewis, and J.C. Dallon eds.) Prentice Hall (1997)]. A number of these diseases are most certainly due to a Hopf bifurcation in the dynamics of peripheral control, triggered by alteration of cellular death rates, e.g. periodic auto-immune anemia and cyclical thrombocytopenia. Others, like cyclical neutropenia, are due to a bifurcation in stem cell dynamics arising from elevated levels of apoptosis. This talk will give an overview of the status of mathematical modeling of these diseases, and the role that this modeling is playing in shaping treatment strategies. For papers related to these topics, go to

http://www.cnd.mcgill.ca/bios/mackey/mackey_newpubl.html