If they are typical zombies who have to spread the contagion via bites and scratches, and are slow and stupid, then my guess is the remaining humans would find

If they are typical zombies who have to spread the contagion via bites and scratches, and are slow and stupid, then my guess is the remaining humans would find it relatively easy to reduce the infection rate below 1. Zombie movies and shows are for drama, not realism. You'd need 28 Days Later or Resident Evil style zombies to overwhelm well armed humans who employ strategy. But this is a fictional scenario we're arguing about.