That makes the assumption that the "disruption to the neighboring continent" is going to be worse as a result of overpopulation than it already is dealing with neighbors who are poor and impoverished and disease ridden.

In both cases I don't think the "civilized" neighbor continent is enjoying the benefits of its poorer neighbor. There is an equal argument to be said that by eradicating these diseases that the poorer neighbor is able to pull itself out of that poverty.

Regardless, history is filled with population surges and mass societal disruption -- I am sure we can resolve it over time.