Sleeping sickness is a neglected tropical disease that affects rural populations in Africa. Deadly when untreated, it is being targeted for elimination through case finding and treatment. Yet, fundamental questions about its transmission cycle remain unanswered. One of them is whether transmission is limited to humans, or whether other species play a role in maintaining circulation of the disease. In this snapshot, we introduce a mathematical model for the spread of Trypanosoma brucei, the parasite responsible for causing sleeping sickness, and present some results based on data collected in Cameroon. Understanding how important animals are in harbouring Trypanosoma brucei that can infect humans is important for assessing whether the disease could be reintroduced in human populations even after all infected people have been successfully treated.