Antelope, which have existed with the tsetse fly and trypanosomiasis for millions of years longer than human, have immunity against animal sleeping sickness. Humans, cattle and other animals do not. Historically, humans avoiding tsetse-infested areas which reduced the likelihood of acquiring immunity against sleeping sickness. But what if humans had acquired that immunity?
Tsetse and the sleeping sickness were one of the major limitations on the human population of Africa and the expansion of agriculture into fertile lands. Removal of this constraint would see a greater expansion of human numbers in sub-Saharan Africa and the wider and more successful use of agriculture. The increased population would then be much more likely to reach the demographic pressure point for economic, social and political change and development.
Animal trypanasomiasis would still be an issue, however. So regions where tsetse are found would likely be devoted to agricultural with human power, while other areas used for raising cattle. Could see an interesting cultural divide between these two groups. The expansion of farmers at the expense of hunter-gatherers ITTL may occur earlier.
Africa, with a higher and more dynamic population, would likely have earlier and more sustained contact with Eurasia. It would become a source of disease, particularly if Eurasians lack immunity to the sleeping sickness. As Eurasian, and later American, crops reach Africa they will bolster the gains made by the defeat of sleeping sickness.
We are likely to see states and empires over a larger area of Africa than OTL, and more warfare. Other restrictions on human population expansion still exist, however. Malaria and bilhazaria will plague this Africa as OTL, and human farmers competition with elephants over land will be an issue. But in general the range and numbers of the human population of Africa would be much higher, which would make the region much more important and influential to world history.