Hey, remember that time when that dog got rabies, and then a day later, every single other dog on the continent had it, except for a small band of survivors huddled in a basement? No? That never happened?
Nearly all of the zombie movies agree on one thing: They reproduce like a disease, one that spreads via a bite from the infected (like they have a virus carried by zombie saliva or whatever). But this also means their spread should be subject to the same rules of a normal epidemic, and biting is a shitty way to get an epidemic going.
The successful diseases have some really clever way to invisibly spread from victim to victim. The flu has killed tens of millions because it floats right through the air, the black plague was spread by fleas, etc. Not a single one of them requires the infected to get within biting distance to spread their infection. Sure, sexually transmitted diseases like AIDS work that way, but that's only because the infected can pass for the uninfected. Nobody is going to be having sex with a zombie.
Though Google Image Search does turn up a large volume of zombie porn
But let's say there is an outbreak, like if one zombie was able to bite 30 people in the crowd at an Insane Clown Posse concert before they figured out it wasn't part of the show. It's not like mankind is just utterly confused about what to do when an infection breaks out. In America you have the Center for Disease Control (CDC,) who don't tend to fuck around. Seriously, it's on their business cards.
Remember the SARS outbreak? That originated in China. The CDC and the World Health Organization put the clamps down on international travel the second it was found to have spread to North America. Flights were grounded, travel between borders was locked tight and only 43 people on the entire continent died.
No one was overlooked.
With zombieism, they don't even have to solve the mystery about how it's transmitted. It's that guy biting people. Shoot him in the head.