Cornell University researchers have designed a model for a potential outbreak of zombie infection.
Using data from the 2010 U.S. census and the SIR model, an epidemiological tool that can project the progress of actual infectious diseases, the scientists created "large-scale exact stochastic dynamical simulation" of a such an outbreak. Their findings were to be presented Thursday to the august American Physical Society.
The interactive map shows how the zombie infection can spread. You can adjust several parameters for your apocalypse scenario. In the map shown, I began the outbreak in the most obvious place, Atlanta. In this scenario, zombies only kill one out of every four persons they bite, and it takes a zombie 18 minutes to walk a mile. Yet in only 48 hours, they’ve spread the infection over a huge part of the South. If you begin a scenario, you should leave it running for as long as it takes to determine the safest geographical area to hide. -via Metafilter
Any of those things by themselves would help slow the spread. All of them together would likely stop it in its tracks before it got much out of one city, no matter where it starts in the US. In a third world country I could see it spreading slightly faster than in a first world country, but even then you have citizen militias and such that will stamp that *$@$ out as fast as it starts in even the most rural villages.
Almost any starting point I can imagine that starts with a zombie or two ends with a group of frightened people beating the unlife out of that thing with anything at hand (shovels, sticks, w/e) until there's no more threat. Even if we suppose 90% of people run in fear or freeze, the 10% will fight back and stop it with brooms and mops if necessary.
The one scenario I can come up with where most of those things I mentioned are made less effective is a terrorist-style mass-seeding of the virus at hundreds or thousands of geologically separate locations across the globe simultaneously. Make every country deal with a ton of separate outbreaks simultaneously and maybe the virus would have a chance to get a foothold somewhere before it got stamped out. Even then, each area would be dealt with eventually, so that the worst case scenario might get 50% of the population before it was stopped.
Honestly, the mobile game Plague Inc. does a better job of simulating a zombie apocalypse with their zombie virus DLC, and that's with the virus being controlled by a vindictive god who's specifically trying to infect everyone and can tactically react to whatever the world tries to do to stop it. And with all of that in it's favor, the infection is typically stopped rather quickly if the god in control doesn't do things just right.