Surviving a Zombie Apocalypse: Just Do the Math

This equation could spell your doom: (bN)(S/N)Z = bSZ. That is, if you ever found yourself in the midst of a zombie pandemic.

That's because the calculation describes the rate of zombie transmission, from one walking dead individual to many, according to its creators, Robert J. Smith?, a mathematics professor at the University of Ottawa who spells his name with a "?" at the end, and his students. Smith's work has inspired other researchers to create zombie mathematical models, which will be published with Smith's work in the upcoming book, "Mathematical Modeling of Zombies" (University of Ottawa Press, 2014).

Though of course done tongue-in-cheek, Smith's study demonstrates why zombies are the viruses of the monster world. Their likeness to viruses makes the creatures ideal subjects for theoretical epidemiological analyses, which can be used to capture the public's imagination as well as explore scientific principles, Smith said.

As for a zombie apocalypse, Smith's model shows that a zombie infection would spread quickly (with N representing total population, S the number of susceptible people, Z the zombies, and bthe likelihood of transmission). It also shows that zombies would overtake the world— there's no chance for a "stable equilibrium" in which humans could coexist with the undead or eradicate the disease.

Only coordinated attacks against the zombies would save humanity, the model shows.

Models of disease outbreaks, like the one Smith developed, play a prominent role in real-life epidemiology, Smith said.

"Unlike most popular monsters, zombies are inherently biological in nature," said Mat Mogk, founder of the Zombie Research Society. "They don't fly or live forever, so you can apply real-world biological models to them."

It also shows that zombies would overtake the world— there's no chance for a "stable equilibrium" in which humans could coexist with the undead or eradicate the disease.

Zombies are dead, they will not reproduce and have child zombies, and don't heal up all that well. They would have to continue decomposing at some rate, even if they are reanimated. In any real zombie infestation, out lasting them would be pretty easy if you have a good supply of food and water to last a couple of months and locked your doors.

In the original Night of the Living Dead, the main characters had to spend one night boarded up in a farmhouse. By the next morning, the remaining townspeople had rallied together, brought out weapons, and were on the attack, swiftly slicing through the undead like a hot knife through butter. A real infestation would be more like that.

Too many unknowns.

Are we talking about SLOW zombies or QUICK ones? In the original movie the zombies were slow-witted and none too agile. In some movies you could outrun them easily in the daytime and sleep safely in trees at night. Other movies had much more capable zombies, able to run, speak, and reason in a limited fashion. Which variables in the equation define these factors?

Are these standard flesh-eaters or the finicky brain-eating variety of animated corpse? Food availability is limited if zombies only eat brains. There could be severe shortages, especially in liberal enclaves.

In WWZ we see the debut of the 12-second zombie - from first infection to rabid monster in literally 12 seconds. Much more dangerous than in other films, where it takes anywhere from 3 minutes to several days to succumb. Once again, are these calculations for quick or slow zombies?

Contrary to popular belief, zombies can't live forever. They should have to obey natural laws like the rest of us. They expend energy shambling around, and must replace it somehow (eat) or run down and stop like unwound watches. I think it was 28 Days Later where the zombies all eventually ran down, fell on the ground and although they didn't die, they could move no more. The people were safe as long as they didn't actually step on one...

I think it was 28 Days Later where the zombies all eventually ran down, fell on the ground and although they didn't die, they could move no more.

In 28 Days Later, the "zombies" weren't technically zombies, which is to say that they weren't dead - they were just infected with a virus that made them act like zombies. So, they eventually starved themselves to the point of weakness, then died. And the virus took 8-20 seconds from point of infection to full zombie-like status.

The one thing that bugged me about that movie (which happens if you analyze these types of movies too much) is that, with such a short incubation period, the original infection probably never would have made it out of the London area. Virtually everyone in London and the suburbs (within walking or running distance) would have been infected right away, and then would never have had a state of mind intelligent enough to travel to any of the more distant areas. I don't know the goegraphy of England that well, but even if there were only, say, 20 miles from the London metro area to the nearest town, it is hard to believe that someone infected would know to run 20 miles to hunt new humans, and no newly infected people could have remained sane long enough to carry the virus to the next town.

The traditional zombie movies didn't have this problem, because either an infected person took hours or days to turn, or ANYONE who died became a zombie (because Hell was full).

By the way, I love a good zombie movie.

Totally agree. A good zombie movie is always welcome. As for the slow versus fast zombies. For it to be truly realistic they have to be fast, otherwise once the threat is identified slow zombies are simply too easy to kill. In the films, the only way slow zombies take over the earth is when they are ignored, and ignored, and .....ignored ....until they number in the millions, at which point the equilibrium has significantly shifted to their favor. For slow movie domination, the level of ignorance has to be very high and very protracted, which is the only way a threat that could be easily annihilated becomes terminal.

Somewhat similar to how the West let liberalism take over. At one point it would have been easy to remedy things, then at a later point difficult but still possible with rolled up sleeves and lots of work, but now it is at a point where even 'conservatism' is, for the most part, a more conservative form of liberalism. Compare the average 1971 Democrat with the average 2013 Republican. The 70s Dem is far more conservative. Maybe that is what the true meaning of slow zombies is. That ignoring an easily handled threat for long enough, be it consumerism (I believe that was the target for the Romero movies????), liberalism, or simply a growing belly and pant size, eventually leads to a situation where losing that weight is almost impossible.

As for fast zombies, they are the viable ones. Immediate infection that fuels frenetic attack. Even with a gun it would be difficult taking one down unless you see it coming from some distance. Kind of like the 21 foot rule, but with teeth instead of a knife. You need to shoot it in the head since a center mass shot is useless. It only needs to break your skin with its teeth. Add two, or more, and the situation can truly be bad. The only option would be massive quarantines, followed by massive culling, since once the equilibrium shifts there is nothing else to do apart from either wait to be infected, or start dropping nuclear warheads.

However, your point about instant infection is valid. For true global spread the rate of infection has to be slow, to enable people who know they have been bitten, but do not want to be quarantined (read: liquidated) to travel and escape. A slow infection rate, coupled with the fast variant of zombies and the ease and speed of modern air travel, would lead to outbreaks in major population centers around the world.

An easy way of seeing this is how the flu spreads annually. Always from Asia, and then spreading outwards from there. That is how they are able to come up wiht a vaccine ...simply see what is brewing and cook up something for it.

Anyways, the slow zombie types from the Romero movies and the Walking Dead series could never take over the world. The moment people started becoming aware of reanimated things shuffling and shambling about biting people, they would eliminate them. They are slow, dumb, and provide ample warning with their moans. Once the initial shock passed even 9th graders would be killing them with hockey sticks!

However, if it is fast zombies then unless there is immediate quarantine and mass culling, which would even include people who are not infected, the entire world would be overrun. An apartment of fast infected could easily take over the entire block, a block of fast infected could easily take over an entire city, a city of fast infected ...the math becomes quite clear. By the time people became aware what was happening several cities around the world would already have a small but rapidly growing population of fast infected that would be more than doubling every day. Actually far more than 2X, considering that every moment the fast infected would be biting non-infected. Could be close to 100X.

Gehenna.

Now let me leave fantasy land and go do some real work. However, the same applies for virulent diseases like small pox (google a story called 'The Demon in the Freezer' to see how beating that thing was difficult, and while it is 'eradicated' from the population the virus still exists in various labs) and, ofcourse, the potential threat of a super-flu. Not the H1N1 that many FReepers stupidly mock as a fake threat, but a redux of the Spanish Flu. Their spread would be similar to that of fast zombies.

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