The solution is to stop all aid to Africa. Stop government welfare.
You can have your purge. But I suggest the first purge should include all the corrupt and treasonous government officials that allow mass immigration to the first world.
Oh and I think nuking Africa, Haiti and a few other third world hell holes would drop the population numbers much faster. A single Tzar Bomba will take out Haiti. Sure there will be radiation but not the end of the world.