African sleeping sickness is a parasitic disease transmitted through the bites of tsetse flies of the genus Glossina. We constructed mechanistic models for the basic reproduction number, R0, of Trypanosoma brucei gambiense and Trypanosoma brucei rhodesiense, respectively the causative agents of West and East African human sleeping sickness. We present global sensitivity analyses of these models that rank the importance of the biological parameters that may explain variation in R0, using parameter ranges based on literature, field data and expertize out of Uganda. For West African sleeping sickness, our results indicate that the proportion of bloodmeals taken from humans by Glossina fuscipes fuscipes is the most important factor, suggesting that differences in the exposure of humans to tsetse are fundamental to the distribution of T. b. gambiense. The second ranked parameter for T. b. gambiense and the highest ranked for T. b. rhodesiense was the proportion of Glossina refractory to infection. This finding underlines the possible implications of recent work showing that nutritionally stressed tsetse are more susceptible to trypanosome infection, and provides broad support for control strategies in development that are aimed at increasing refractoriness in tsetse flies. We note though that for T. b. rhodesiense the population parameters for tsetse - species composition, survival and abundance - were ranked almost as highly as the proportion refractory, and that the model assumed regular treatment of livestock with trypanocides as an established practice in the areas of Uganda experiencing East African sleeping sickness.