I know u don't like poison, but ants are hard to kill. An effective method for us has been to use boric acid infused sugar. They carry the borax back to the nest and share it with their brood.
Man, I saw a program on Animal Planet where they rated the top 10 deadliest predators in Africa. Number 1 was some breed of red ant. These suckers would kill PEOPLE in their sleep.
Ants are like weeds. You can't just kill what you see. Best to apply something at the surface that is taken back to the roots and kills it deep down.