It turns out Robert Smith? (question mark intentional!) has done the math, quite literally. A chapter in a forthcoming book on modeling infectious diseases called, “When Zombies Attack!: Mathematical Modeling of an Outbreak of Zombie Infection”, tells the story.
If you try to quarantine the zombies you won’t catch them all, so “it’s basically humans fighting it out with slightly fewer zombies than there were before.” That’s not what you want, given that you’re dealing with flesh-eating, undead monsters that will either kill you or bite you and turn you into one of them.
If you go for a cure, “unless the cure was 100%, which it would never be in reality, you can’t turn all the zombies back.” You wind up with “this equilibrium where people are always switching back and forth” between human and zombie. Entirely unsatisfactory.
The only solution — and if we haven’t learned this from zombie movies, we haven’t learned a damn thing — is to mount wave after wave of military attacks.
Read more here.