We propose a new model for the Stumpy Induction Factor-induced slender to stumpy transformation of Trypanosoma brucei gambiense cells in immunosuppressed mice. The model is a set of delay differential equations that describe the time-course of the infection. We fit the model, using a maximum-likelihood method, to previously published data on parasitaemia in four mice. The model is shown to be a good fit and parameter estimates and confidence intervals are derived. Our estimated parameter values are consistent with estimates from previous experimental studies. The model predicts the following. Slender cells can be classified as uncommitted, committed and dividing, and committed and non-dividing. A committed slender cell undergoes about 5 divisions before exiting the cell-cycle. Committed slender cells must produce SIF, and stumpy cells must not produce SIF. There are two mechanisms for differentiation, a background differentiation rate, and a SIF-concentration-dependent differentiation rate, which is proportional to SIF concentration. SIF has a half-life of about 1.4 h in mice. We also show, with suitable changes in the parameter values, that the model reflects behaviours seen in other host species and trypanosome strains.