First, I imagine there would be a supercrew of vampire fighters (see "Vampire Hunter D" or "John Carpenter's Vampires") that would already be at work before the general populous was made aware of the situation. Humanity would be able to sneak up on the bloodsuckers, drive a garlic-soaked stake through their dead hearts and drag their sorry carcases into the brightest of the bright, sunny days. Woot!
Second, small pockets of strong resistance would build up and strike major blows in guerrilla warfare engagements (see Stephen King's "Salem's Lot"). People young and old would know their own home terrains well enough to remove large swatches of the living dead attackers.
And if that weren't enough, some science guys have come up with the mathematical proof that a vampire takeover is destined to fail. Here is what they have to say:
It would take 2.5 years for vampires to wipe out the entire human race (supposing their victims become vampires)Therefore, if there really were vampires and they really got their act together to attack the rest of the world, their efforts would ultimately fail.
After n months there would be 2 x 2 x 2 ... x 2 = 2n, or a geometric progression with ratio 2. (In other words, "The vampire population increases geometrically and the human population decreases geometrically.")
To sum up -- "Using the principle of reductio ad absurdum, they conclude that vampires can't exist as their existence contradicts the existence of humans."
You can now sleep better tonight . . . until the zombie hoard arrives.