Zombies reproduce by chomping on humans. So long as there are enough new humans to feed the zombie population, there will be new zombies. Animals can be substituted for people, but they prefer to gnaw on human flesh. Once zombies run out of food, they will die out. This was demonstrated in (spoiler alert!) “28 Weeks Later,” when the survivors outlived the lifespan of the zombies. It should be noted that those were British zombies, which are weaker and more prone to tooth decay than American zombies.