[sliverstorm]

Humanity is still an animal race. Our birth rates still self-regulate. If children stop dying in Africa, people will in time stop having as many children.

There will very likely be issues like you describe, but they should run their course and go away so long as outsiders don't try to meddle too much.

Unlike accelerated disease propegation between nomadic tribes, the problem of having extra people is one of the better problems to have.