It's a temporary problem that'll correct itself. It's played out in most other places around the world.
Since we're linking wikipedia pages,
here's the article on "demographic transition".
When places are poorer and not as industrialized, people have a lot of babies. Because:
1) The infant mortality rate is high, so most of them won't survive til adulthood
2) The general death rate is high, so you need to have lots of babies to replace the people who are dying
3) In pre-industrial societies, you need lots of people, because you get more work done that way
4) There's generally not a lot for people (particularly women) to do besides have kids, which is compounded by the fact that
5) Contraception is not widely available
Advances in healthcare and food production cause the infant mortality rate to fall and life expectancy to increase. But that's generally the first thing that happens, and there hasn't been a cultural shift yet. People are still used to having lots of kids, resulting in an exploding population. As society gets more industrialized, more education is available (especially to women), the birth rate will fall.
In fact, sometimes it even falls
below the death rate, as has happened in a lot of european countries.
