In every society, birth rates drop precipitously as soon as 1) modern medicine reduces infant mortality and 2) women get a better education. Both of these things are already happening in many parts of Africa, and the trend will hopefully accelerate greatly over the next couple of decades. Those 20 Syrian kids will be lucky to want 2 kids each by the time they've grown up, having been exposed to European culture and technology.
I don't trust any prediction about what Africa will look like by the end of this century. Every prediction I've seen is little more than a projection of past trends into the far future, but far too much change is going on across the continent right now to make such projections even remotely realistic.