Realistically, how many zombies would you have to kill to get rid of them all?

In zombie movies, and now TV shows (I’m thinking of The Walking Dead), the implication seems to be that there is an unlimited number of zombies, and no matter how many you kill, more are just going to keep coming.

But this seems implausible to me. The maximum number of zombies has to be a function of the total number of living people plus, depending on the zombie movie (?), some quantity of formerly dead people, minus the living people who do not become zombies.

So, realistically, what kind of number would we be looking at, here? And presumably there would be separate numbers for distinct landmasses, right? I’m imagining zombies are not going to have much success navigating through large bodies of water.