I'm never the specialist either in Asia and in Africa, but the following previous questions and answers might satisfy OP's interest. In short, the plague outbreak around the middle of the 14th century certainly hit at least the latter, but the source problem prevented us from estimating the plausible figure.

• (East Asia): The answers by /u/mikedash in Why can't I find very much information about the 14th Century black death in Asia? should be OP's starting point. I also summarized the problems in Chinese/ Mongolian contemporary sources in Is there any Mongolian accounts of dealing with Black Plague? AFAIK only Japan, separated by the Chinese sea and not conducted much trade with Yuan China, could certainly evade the outbreak in East Asia.
• (Middle East) I also wrote a very brief summary in What was the response to the Black Death like in the Islamic world? before. Put it simply, the outbreak ravaged Syria and Egypt just as it did in Europe, but it was just one of the many catastrophe that hit these regions in the 14th century so that we cannot distinguish the exact damage caused by the plague alone from those of other catastrophe with ease.
• (Africa) I was impressed greatly by /u/bobbleheader's recent answer in Africa during the Black Death. You can also check /u/Commustar's comment in What do we know about the effects of the Black Death on African societies?

(Edited): Fixed the broken link to the last question thread (thank you for /u/Commustar's notice)!