I dont think Earth is actually in danger of being over populated.
China and inda have plenty of problems, crowding is merely a symptom of disease.

Seriously, most of russia, japan, and the US are sparsely populated.
There is a lot of space which is not inhabited. Its just major cities and third world area which suffer from crowding population.

Besides, Im positive some freak virus would pop up if the population were exessively dense. Living in extremely close quarters with lots of people does make a noticeable impact on your resistance to illness.