In the bloodstream of its mammalian host, the ‘slender’ form of Trypanosoma brucei replicates extracellularly, producing a parasitaemia. At high density, the level of parasitaemia is limited at a sublethal level by differentiation to the non–replicative ‘stumpy’ form and by the host immune response. Here, we derive continuous time equations to model the time–course, cell types and level of trypanosome parasitaemia, and compare the best fits with experimental data. The best fits that were obtained favour a model in which both density–dependent trypanosome differentiation and host immune response have a role in limiting the increase of parasites, much poorer fits being obtained when differentiation and immune response are considered independently of one another. Best fits also favour a model in which the slender–to–stumpy differentiation progresses in a manner that is essentially independent of the cell cycle. Finally, these models also make the prediction that the density–dependent trypanosome differentiation mechanism can give rise to oscillations in parasitaemia level. These oscillations are independent of the immune system and are not due to antigenic variation.