What's the issue. If the region is used to families having numerous children because they are likely to die in early childhood due to disease, and resources are already critically stretched; then you fix the problem of dying children you are now left with too much population to support which in turn may mean over grazing/over hunting.
But it should balance out eventually, as people die of starvation they will (hopefully) resort to having less children, as long as sally struthers isn't there, and then the plants and animals should return.