I had a problem earlier this summer with tiny ants. Can't quite remember what color they were, but they were the tiny ones that smell very strongly of formic acid when you squish them. I don't think they were red, I think they were darker. Can't remember, they are so tiny. But that odor is very strong.
I found a trail of them coming from the back porch (my house is one story, set on concrete slab, so they can't come from underneath), in the kitchen a few weeks ago. Squished them, and all was well. Then a few days later, there were a lot more, from the back door, leading to Heidi's food dish. I finally gave up and sprayed, did a MAJOR cleanup, and haven't had any trouble since.
Nolena gave me a tip, which I didn't know about, but which worked well. Sprinkle some Ajax (or similar product) across the line where the ants are entering. Worked like a charm, and I haven't had a problem since.
Of course, I was vacuuming doggie ajax footprints off the carpet, but that's a lot better than ants, to my way of thinking.....