Zombie Mathematics

While a zombie attack is one of the least likely ways the world could end, four Canadian mathematicians/graduate students did a mathematical analysis of a hypothetical zombie outbreak to determine the likelihood of human eradication, should such an attack ever occur. According to their model, “a zombie outbreak is likely to lead to the collapse of civilization, unless it is dealt with quickly. While aggressive quarantine may contain the epidemic, or a cure may lead to coexistence of humans and zombies, the most effective way to contain the rise of the undead is to hit hard and hit often.” (HT: Marginal Revolution) [%comments]


Sadly the study uses a flawed model. It doesn't distinguish between dead humans and dead zombies, so previously decapitated zombies count as being able to (re-)reanimate.

Michael F. Martin

So do the authors have plans for future work on zombie banks?


In addition to the shortcoming pointed out by Leafcat, the model presents only two outcomes for a human-zombie interaction: zombie destruction and human infection. They should have included 4:zombie destruction, mutual survival, infection, and consumption. This would significantly limit the growth in zombie numbers, as they are sure to eat a fair number of humans instead of producing more zombies.


as much as i recall those b-movies, zombies cannot drive cars, they can't and they just have ability to do the most basic tasks, neither can they plan or cooperate in any way. in such a situation, it'd be much easier to deal with them than commonly portrayed on movies. Once you were aware, they wouldn't stand a chance, they'd fall to the most banal traps, their only advantage being the "surprise factor". Supposing they began from one focal point, the news would spread much faster than the disease itself (at least in movies, it usually took some time (like some few days) for someone infected actually becoming a zombie).

in the worst scenario, just for the sake of argument, still humankind would survive in islands and places not reachable by feet alone....

well, afterall i've written more than i'd like about this fruitless discussion... no offense intended.


Also curious to me is the assumption that an uninfected corpse can reanimate.

On the upside, this may be good news against the werewolf invasion, where one needs to be alive when bitten.

Suggested alternative models:
- Zombie starvation, where renewed feeding is needed to live
- Zombies may also attack/defeat other zombies


There also does not seem to be a parameter for "rate at which naturally dying humans are removed": once it becomes clear that the dead are rising, a precautionary bullet in grandpa's head once he's no longer clearly breathing will soon become standard procedure. (Sure, Mistakes Will Be Made...)

(We really also have to make the assumption that zombies lack the traditional love of brains: if a zombie is killed when its brain is badly damaged, and zombies eat the brains of those they catch, only _survivors_ of zombie attacks can become zombi.)

Steve Jones

Maybe the researchers can use this study to help eradicate AIDS. Its an infectious disease that really cannot be cured, The infected are basically living dead, infect others, etc. etc.


Joe raises an interesting point, but it does not affect the model. It simply changes the value of some parameters.

If a zombie eats an arm or a leg, the corpse can be zombified with limited effectiveness. It is hard to hold your prey without arms.

If zombies eat brains, then fewer humans can be re-animated. This only reduces the parameter value for Removed to Zombification, but it cannot go to zero. This may slow the rate of infection but not eliminate the infection. Eventually the Zombies will win.

As for Removed humans becoming zombified, read ‘Night on Mispec Moor' by Larry Niven. It offers a way for normally dead humans to be zombified as well as examine a possible 'cure'.

I must disagree with the authors about the result of the 'cure' returning a human to normal life. If this were so, a dead human could be resurrected as a zombie, then returned to life - practical immortality. Also, the body must deal with the effects of accident or decay while dead. It's hard to live if an MI stopped your heart permanently once before.

I would be interested in extending the model to examine the possibility that a cure results in permanent removal of the zombie. Logically this should speed the eradication of zombies and preserve civilization.

The authors should also consider a change in cultural habits. Humans would simply behad the dead before burial, or use cremation. Again, this slows the rate of infection and speeds eradication.

After due consideration, the authors have reached a sound conclusion. It's either us or them!



good argument for cremation


I believe this will be addressed in the new legislation i.e. the Obama Zombie Panels.


You can actually see this in action if you visit this game;


They graph the population levels of the humans and zombies as the game progresses, it's pretty fascinating to see what happens when 'care packages' of cure serum are dropped.


I've looked at the paper and think they may be on to something. By adjusting a few variables and definitions we may be able to prove that the zombie's dominating infection has already swallowed up a sizeable portion of the population. If the infectious saliva is modeled as the traditional thinking of big name management consulting shops and the susceptible non-zombies are the gullible managers that hire the consultants, then we have a rigorous explanation for all of the undead, zombie companies that hang on in perpetuity slowly destroying shareholder wealth.

I think I've found some evidence in my own portfolio. AAAAARGH! Run!


The equation on page 136 where S = live humans, Z = zombies, R = dead non-zombie humans, for non-zero birth rate:
S+Z+R -> Inf as t->Inf
they then conclude that as S does not go to infinity, this represents a doomsday scenario. This is incorrect: doomsday is S->0. The equation solutions include the 'real life' scenario: S (life population) remains approximately constant, R (dead people) increases with time, Z is zero for all time. Because of this error, they make no further examination of non-zero birth rate models, so miss any possibility of stable human-zombie coexistence solutions.

With zero birth rate, it is obvious that the 'everyone survives' equilibrium must be unstable, because once you cease to be a live human, there is no way to every return to being a live human. With no births, the live population has no way to go but down.

Also, they do not explicitly model the (very likely and well supported by the zombie movie sources) possibility that infected humans will be killed by uninfected humans or will suicide - knowing that zombiehood is inevitable*. To some extent this can be included within the 'quarantine' model where we instead interpret the quarantine state as 'killed by mercy killing' instead. We need to set the 'escape from quarantine' parameters to zero for this.

* A question for the Pope: is suicide still a mortal sin if you've been infected by zombieism?


Linda T S

Um, does anyone think it might NOT be a good idea to list everything right here for all the zombies (or zombi) to see? What if they can evolve like AI, read all this, and then create new ways to destroy us all???!!!



I look forward to the ZETH (Zombies for the Ethical Treatment of Humans) to lead the movement toward vegetarian zombies. These enlightened living dead will shuffle about, groaning "grains... grains... grains".


The book "World War Z" (by the same author of the 'Zombie Survival Guide', one of the references in the paper) shows that the war really is not winnable, and the only outcome is cohabitation.

Humans are able to setup survival camps in areas of natural boundries and are able to stay vigilant to protect those areas (as Alex says, above), but islands ARE reachable by walking..... eventually (zombies don't need to breathe, and will walk on the ocean floor).

I think the 'strike hard and fast' won't work because not all humans will react to a pandemic the same way at the same speed. Look at H1N1 - some quarantine, some just give health advice - and imagine if H1N1 made everyone into zombies.


@leafcat, actually I think the model does account for this, I made the same mistake. quote:

"Humans in the removed class can resurrect and become
a zombie (parameter ?)."

"Zombies move to the removed class upon being ‘defeated'. This can be done by removing the head or destroying the brain of
the zombie (parameter a)."

Note that Z' has -aSZ, so in fact these zombies are not reanimated.


@Larry, that's only in the first iteration. The aSZ component is added to R', which is then used in Z''. To properly handle it they would have to split R into RS (can revive) and RZ (permanently dead) and have Z' use only RS.


Do zombie qualify for Social Security?

science minded

As I see it, the problem is with the problem of asking a what if question-- there are an unlimited number of what ifs........................... When it comes to real Mathematics, there is only one problem and it already has been resolved. See Goldstein, Freakonomics, what's been said about Math, our daily bleg. 2008