It is possible to successfully fend off a zombie attack, according to Canadian mathematicians. The key is to "hit hard and hit often." Oh yes, somebody actually did a study on mathematics of a hypothetical zombie attack, and published it in a book on infectious disease. So, while we still don’t know what to do if a deadly asteroid takes aim at Earth, an unlikely but technically possible situation, we now know what to do in case of a zombie attack.
Having spent a fair amount of time mixing science with beer in the wee hours while trying to finish a thesis, I’m guessing that at some point, a graduate student who had spent far too many hours tweaking a mathematical model of infectious disease in the basement of a Canadian university said something like this: "What would happen if we made it so they could come back to life?"
You can read the full paper, When Zombies Attack!: Mathematical Modelling of an Outbreak of Zombie Infection. (PDF file) for yourself, the mathematics paints a grim picture for human survival. From the paper’s conclusion:
In summary, a zombie outbreak is likely to lead to the collapse of civilisation, unless it is dealt with quickly. While aggressive quarantine may contain the epidemic, or a cure may lead to coexistence of humans and zombies, the most effective way to contain the rise of the undead is to hit hard and hit often. As seen in the movies, it is imperative that zombies are dealt with quickly, or else we are all in a great deal of trouble.
One of the sources for the paper is Max Brooks, author of World War Z, which is one of my favourite books (though not the best one to read in the waiting room just before surgery). My maths can’t quite keep up with all of the equations, but I get the general idea. Unless you wipe out the zombies fast, and the zombie event doesn’t last long enough to affect normal birth/death ratios, humans will be wiped out. Even if you do manage to get rid of them, the population will be greatly reduced.