A simple arithmetic model is developed that is based upon the assumption: (1) that transformation of replicating long slender Trypanosoma brucei to nonreplicating short stumpy forms is parasite population density dependent; (2) that as the slender population increases there is a change in the external environment that triggers the slender to stumpy transformation; and (3) that stumpy forms of T. brucei do not induce the change in external environment that triggers slender to stumpy transformation or do so to a lesser extent than slender forms, thus preventing the proportion of stumpy forms in a population from reaching 100%. A simulation based on these assumptions shared many features with curves on numbers of long slender, intermediate, and short-stumpy forms of T. brucei during the first parasitemic wave of the 3 T. brucei subspecies in intact and immunosuppressed inbred mice.