World wars as a category may be expanded to include wars among European nations that were carried around the world through naval actions and colonial infighting. Certainly the competition between the European nations in the age of colonization (in response in part to the wars against Europe earlier by Muslim, Mongol and Turkic forces) influenced the peace and choice of activity in Africa and other non-European regions of the world suitable for colonization.
Nevertheless World War One had German East Africa as a battle site. The wiki article of the East African campaign notes that the German strategy was to divert forces from the Western front, and the tactic was not terribly successful.
The article entails some technical political descriptions of how GEA was divided after the German surrender- “GEA became two League of Nations Class B Mandates, Tanganyika Territory of the United Kingdom and Ruanda-Urundi of Belgium, while the Kionga Triangle was ceded to Portugal.”
World War Two involved most of the Axis and Allied Powers. The historical scale is substantial and more than a quick summary would serve well. East African Campaign (World War II) – Wikipedia
The Cold War could also be considered a world war and once again East Africa was drawn into the conflict through a perfusion of arms in proxy ideological battles between Communism and Western Democracy nominally although there were a number of ulterior motives for the parties in the conflicts.
Numerous sources exist for reports on how the Cold war affected East Africa. A few are…