I think it was to be assumed that the cure, being the very food for vamps, would be viral in its spreading. If you think about it, let's say 2 vamps feed on 1 cure. Cure dies (or even survives by luck, either way), then 2 vamps become cures. Then 4 vamps feed on those 2 cures, thus becoming cures themselves. Regardless of whether the vamps actually bleed the cures to death isn't exactly irrelevant, but even if it were, you still end up with a growing cure-to-vamp ratio. Eventually the vamps will die off simply due to the fact that an expanding percentage of their food supply are now their own cures, given the fact that the vamp-to-human ratio was expressed vividly throughout the movie anyway.

Basically, what you have, is a virus. Except the virus is the cure. The only probably downside is that by the end of it all, you'll very likely have quite a smaller population, but it's inevitable that the vamps will die off.