Odds of surviving a zombie attack

Originally posted on Facebook - October 26, 2009

I went and saw Zombieland yesterday, and on the way home I started thinking about zombie movies in general, and how long it would take for an infection to work its way completely out of a population.

First, we need some assumptions. There are no authoritative numbers for the efficiency of a zombie curse/virus, so all we have to go on is the anecdotal evidence of what we see on the silver screen. There are some basic facts that everyone can agree on, but how they fit into the simulation will depend on some assumptions on my part: first, the spread of zombification divides the populace into three distinct groups - zombies, zombie vittles, and survivors. We need to determine a ratio for these groups, and I'm going to suggest a 400:600:1 ratio. In other words, out of every 1001 people, 400 of them will become zombies, 600 will be eaten by zombies, and 1 will survive.

If it hasn't sunk in yet, let me make it abundantly clear: the odds of surviving the initial infection are 1/1000, or 0.1%. Chances are you're dead or zombified within the first 48 hours, which is the time period I'm going to assume it takes for the infection to spread from patient zero to pandemic status.

Second, odds of survival dramatically increase after the initial spread of infection. This happens for several reasons. Whatever it was that kept you alive to begin with (fitness, training, reflexes, instincts, weapons, luck, etc.) will continue to keep you alive. Also, your sense of self will have begun to adapt to the new situation and you will start to develop rules and strategies for survival. I estimate that from the 1/1000 odds of surviving the first 48 hours, the likelihood of death will make a staggering drop to only 1/10 in the rest of the first week. In other words, after one week, 0.09% of the initial population will still be alive and uncursed. In the following week and thereafter, I assume that only 5% of the survivors will die over each 7-day period.

Third, the survivors will be forced to destroy zombies in order to survive. Even if there is plenty of food, water, and ammunition, foraging, hunting, and scouting parties will have to leave shelter routinely, and groups of survivors will often have to remain on the move for days at a time until defensible shelter can be found. I assume an average kill rate of 10 zombies per survivor per day.

Fourth, geography plays a major role. A person alone in an open field with zombies converging has almost no chance of survival. On the other hand, a person in an urban setting with multiple escape routes and elevated vantage points can often gain an upper hand over a mob of mindless monsters. I will assume a closed urban district - such as an island city with all of the bridges and tunnels destroyed.

Fifth, zombie efficiency is a delicate balance. If zombies are too effective, then everyone they get hold of becomes food and no new zombies are made. If they are not effective enough, then they are easily warded off. For the sake of the simulation, I will assume that after the initial infection there is no appreciable increase in numbers of zombies - survivors who get bitten either get eaten, or mercifully executed by their companions.

So, given these assumptions, how long would someone have to survive in order to reclaim their city from the zombies, and how many survivors would be left to begin to rebuild? Or would the zombies eventually dominate, destroying their primary food source and thus eating themselves into oblivion?

Well, the results may be surprising. In an island city of 1M people, it takes 1000 survivors only 53 days to kill all of the zombies and reclaim their city - less than two months. And how many uncursed are left? According to these numbers, over 650. Yes, almost two-thirds of the initial survivors make it to the end of the zombieocalypse. More than enough to begin to rebuild. I like those odds.

Now they just have to figure out what to do with the hundreds of thousands of corpses. Yuck.