University of Ottawa and Carleton University statisticians Philip Munz, Ioan Hudea, Joe Imad, and Robert J. Smith have mathematically modeled a zombie apocalypse, as published in the peer-reviewed book Infectious Disease Modeling Research Progress.
The analysis and conclusion of WHEN ZOMBIES ATTACK!: MATHEMATICAL MODELLING OF AN OUTBREAK OF ZOMBIE INFECTION, which can be used to model other real-world infectious diseases, is grim:
"An outbreak of zombies infecting humans is likely to be disastrous, unless extremely aggressive tactics are employed against the undead. While aggressive quarantine may eradicate the infection, this is unlikely to happen in practice. A cure would only result in some humans surviving the outbreak, although they will still coexist with zombies. Only sufficiently frequent attacks, with increasing force, will result in eradication, assuming the available resources can be mustered in time."
So, how long do humans have if the zombie outbreak happens? Eight days.