Those red bands actually represent the two principal routes between Syria and into Baghdad. They converge at Baghdad. If you look closely at a map of Iraq, you'll notice that most of the cities and the infrastructure are really centralized on those two bands. Iraq has wide swaths of desert—for instance, to the south of that bottom band—where there simply isn't anyone there, really.
As to their area of influence, it's in fact the direct route they've taken between Syria and Baghdad.