Now heavily mine the area and throw in a few hundred gators for good measure.
You have stated the unfortunate solution to this problem. Unless and until crossing the border illegally has a very high probability of being the last thing one does in their lifetime, the invasion will not abate.
Try crossing a border illegally in the middle east. If caught, you will most likely be executed on the spot and your body thrown into a ravine where the night creatures will dine upon it until nothing is left. Your execution will not be reported. Your family will never know what happened and will have only memories of you.