If people were smart, when someone in their group dies, they would shoot them in the brain, seeing as that how zombies will always exist in this universe. So what needs to happen is all of the walkers need to be dealt with, a long and gruesome task that would more than likely be never completed. But if it was completed in say, ten years or so, a new society would rise based on the threat of walkers. So, rules would be instated, for example, as soon as someone takes their last breath, head shot. If someone is in an accident, head shot. If the brain is damaged, then the person won't rise again as a zombie. It would be this precaution that would lead to the world being safe again.
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