To those saying it's logical even armies would be overwhelmed.

Armies DO NOT OPEN THE FRONT DOOR, let alone the front door to a bunch of mindless zombies.

The story could only be explained with a sudden lethal event that killed the majority of people, even in barricaded places. e.g. an "alien beam from space" or a insta-turning virus that only ignores 20% of the population, even inside barricades.

And EVEN THEN it has problems since if a little kid with a stick can kill hundreds of them from a treehouse or behind a fence, then a properly armed force can kill millions in days. This story does not stand without those initial devastating lethal events or with more intelligent zombies. Get over it and stop trying to justify it logically. It makes you look like a fanboy. You can only accept it's fiction and that's fine.