"There is an excellent short story about a plantation that is about to be overun by waves of army ants. The battle to survive against something that has minimal ability to plan attacks, yet has overwhelming numbers and the will to destroy anything in its path becomes quite difficult. It's a set of circumstances that requires a great deal of thought in order to solve the problem and survive.
Once I started reading the ant story, I could not stop reading until I finished it. The zombie thing is the same type of scenario, with bigger army ants."
Remember seeing a movie with that theme many, many years ago. May have even been in black & white. Made a big impression on me as a kid. Forced me think about not just ants but dealing with more the abstract issue of merciless, unrelenting & overwhelming opposition.