the zombies are infected by a virus, they are clinically dead, yet still able to move around, are compelled to seek out non-infected living people, and are gradually rotting away.
Notes: If the head is completely separated from the body then they are no longer active, this would allow other zombies to eat them, but zombies won't kill each other. They require, at least, some remnant of muscle tissue to move around. Once all the flesh has rotted off they are simply inanimate skeletons.
Zombies can be considered to retain a degree of intelligence (perhaps half their original IQ), but are driven by a lust for fresh human flesh even though there is no longer any available.
How long would the zombies last until they run out of humans to eat?