Zombies are the most overrated, exaggerated modern monster that there is. At least the classic Romero/Brooks zombies anyhow are. Ever notice that NONE of these zombie movies or shows logically explain HOW the epidemic got so large and threatening in the first place? It always starts after the zombie 'virus' has already become a widespread problem. But I honestly think that if this really happened, the zombie threat would never escalate to such a huge problem and would easily be over within a couple weeks.
Lets examine why. The MAIN reason why zombies would never be a large threat is for two basic principles--first, the fact that the only way the 'virus' is spread is through a bite, and second, the fact that zombies are incapable of running or even walking at a normal pace. Biting is an extremely inefficient way to spread a disease, combined with the fact that we could easily avoid them seeing how slow they are. If you don't believe me, then go outside and try to tackle and bite a squirrel. Chances are it easily escaped your grasp before you even had a chance at biting it. This is what it would be like for zombies, except, in the case with zombies, it would be even more difficult because zombies lack any intellectual prowess and the speed to be able to pursue and/or pin down a human being and then successfully bite that human in question.
Secondly, zombies are inferior to normal humans in literally almost every physical and mental aspect. Their bodies are slowly deteriorating day by day making them weaker, along with their inability to heal, they lack intellectual capacity, they lack speed as we mentioned earlier, and they lack reproduction ability. The ONLY way for a zombie to produce another zombie is to infect a human--and guess what, humans are zombies' biggest predator. That is a horrible way to reproduce. Zombie movies always start AFTER a large horde of zombies has already been formed--which, admittedly would be a bigger problem if that were the case. But the reality is that such a large horde would never be formed in the first place because humans have nearly every advantage over zombies. A couple of lone zombies throughout the world would not really be any problem at all. All we have to do is be carefully alert, fortify our houses a little bit, never travel at night and take a weapon with us everywhere and I assure you that literally like 96% of us would be fine. Maybe in areas with a high risk of potential zombie stragglers we could set up volunteer groups of armed civilians to patrol the neighborhood at night. Even urbanized areas wouldn't be in that much danger. If anything, they would actually be safer because there are more people that would be alert that could eliminate the threat on sight and communicate the news to the rest of the country so that close areas potentially at risk could be extra-alert.
Zombies have ONLY 1 advantage over humans; that the only way to kill them is to destroy their brain (ie headshot). But other than that, they are inferior to us in everything else. I admit, shooting a target the size of a human head is very difficult, but it is not impossible, and even if some panicked civilians are incapable of hitting the head, they could still easily evade the zombie or even trap it inside of a bedroom easily and then call for the police or volunteer defense group to come dispatch of it. Problem solved. World militaries are trained to aim for center mass, which, could admittedly be a problem, however, our first world militaries are very quick to adapt to new situations and learning, they could easily re-train themselves to aim for the head. Plus, we already have snipers in the military that ARE in fact trained to aim for the head. I don't even think that military action would be required at all because zombies would be such a tiny threat. Maybe a couple of national guard trucks and checkpoints to moniter larger areas and/or more 'at risk' areas, but other than that, I think we are pretty sufficient to defend ourselves from the random straggling zombie or two. Society would not fall.