A revised arithmetic model of long slender to short stumpy transformation in the African trypanosomes.

An arithmetic model that closely approximates an African trypanosome infection in immunosuppressed mice is presented. The final model was based on an examination of the following parameters: the rate of long slender to short stumpy transition, the maximum percentage of long slender to short stumpy stages that can be induced, the survival time or half life of the short stumpy stage in vivo, and the rate (%) of long slender to short stumpy stage transition following the peak in transformation. The model is based on the assumption that the long slender to short stumpy transition is parasite population dependent and that in mice the long slender to short stumpy transition only begins when the trypanosome population reaches a density of 1 x 10(7) trypanosomes/ml. The model predicts that the parasitemia during the first several days of an infection is controlled solely by the kinetics of the transition of the dividing long slender stage to the nondividing short stumpy stage. It was not necessary to include in the model the host's immune response in order to simulate the early growth kinetics of pleomorphic trypanosomes in infected mice.