A Canadian infectious-diseases boffin has published an authoritative mathematical model of zombie plagues. He concludes that the only scenario in which our civilisation could survive a zombie outbreak is one in which normal humans react immediately using extreme violence against the undead, without any attempt to cure or quarantine them.
Professor Robert Smith?* of Ottawa Uni is a mathematician specialising in the modelling of infectious diseases such as HIV/AIDS ("I started off in the rectal microbicide team, but then switched to the vaginal team. The jokes were never-ending, I can assure you"). Now he has turned his skills to analysing the fashion in which a zombie plague might affect the human population.
According to Smith?, a major factor restraining normal plagues from utterly devastating humanity is that they tend to kill their victims, after which the sufferers can no longer move about and infect others. This is one reason the frightful Ebola virus has never spread, for instance: it knocks people down and then kills them so fast that they have only a limited chance to pass it on.
Not so with zombification. Once someone has died of Z-plague, they remain a mobile carrier. The factors which have prevented humanity being rendered extinct by the Black Death, smallpox, cholera etc don't apply. Smith?'s models assume traditional dull-witted shuffler zombies rather than the nimbler types popular in some recent film offerings, but nonetheless the dynamics of undead contagion remain implacable.
In essence, as soon as there are any zombies in existence, humanity's only chance for survival is to instantly and effectively extirpate them. According to Smith?:
Human-zombie coexistence is impossible... Since all eigenvalues of the doomsday equilibrium are negative, it is asymptotically stable. It follows that, in a short outbreak, zombies will likely infect everyone.
He considers the use of schemes in which efforts are made to place zombies in quarantine of some sort, so rendering them unable to infect more people. Apparently this won't work: such a scheme can never completely contain the plague. It will therefore break out of confinement with disastrous results.
Likewise, even if a cure for zombification could be developed, it wouldn't work unless it also made the re-humanised undead immune to further infection. If it merely turned a zombie back into a human who could then be re-zombified once again, end results would be unpleasant. Some humans could survive, but only as a minority among the brain-scoffing swarms.
Suppose we are able to quickly produce a cure for ‘zombie-ism’. Our treatment would be able to allow the zombie individual to return to their human form again. Once human, however, the new human would again be susceptible to becoming a zombie; thus, our cure does not provide immunity... In this case, humans are not eradicated, but only exist in low numbers.