More specifically, I would like to find out how did the world's population look while these two continents were up and running?
(When I say ancient Africa, I mean the Egyptians.)
When you say Asia, did you have any particular place or time in mind, or are you thinking the whole continent generally?
Various Chinese dynasties kept pretty good census records, so it's possible to get a rough idea of the populations of their states. If you can narrow it down a little bit, I can track down the appropriate records for you.