Zero.

Corpses would present no threat whatsoever, due to necrosis; they would simply rot away within a few weeks if not sooner. Carrion-eating animals such as birds and rodents, not to mention flies would simply eat these creatures away along with the rot doing the job for them.

Also, lacking higher brain functions they could be outsmarted with ease, and mown down by automatic weapons or herded into mincing machines and the like.

Unless magic was involved, there is nothing that could reanimate a corpse, certainly not in the way TV portrays it. Even if the brain came back to life, as portrayed in The Walking Dead, this would do nothing about the other parts of the body; dead muscles cannot contract, so the body would have no movement. It’s just totally unrealistic.

Even if we ignore most of the scientific impediments to shambling corpses infecting everybody, the eyes of the corpse rot within two to three days, meaning all of the zombies would be blind and therefore about as harmful as a snail.

The closest to ”realism” I’ve encountered is probably The Last of Us’ mutated cordyceps fungus

In reality, a zombie virus, even if it were real and could reanimate the dead (which it couldn’t) simply could not spread fast enough to destroy society as is commonly portrayed in films and on television. Braindead humans smambling around biting people is not efficient enough a vector of the disease. Even the Romero/Walking Dead scenario, where everybody is already infected but only turns post-mortem, wouldn’t do it for the reasons stated above; corpses are just too vulnerable and would be blasted to pieces by any sort of resistance

Tl;dr: No chance at all.

Footnotes