# how to (optimally) prepare for a zombie outbreak

Are you prepared for a zombie apocalypse?  The CDC is apparently very concerned about this: they recently issued some advice for a zombie outbreak.  Some of their advice includes identifying optimal evacuation routes and quarantine plans. It sounds like operations research could play a critical role in surviving a zombie apocalypse and propagating the human species. I’m game. Are you?

Unlike the vampire threat, I take zombie threats very, very seriously. Zombie outbreaks in movies and films consistently exhibit exponential growth, which one would expect if they modeled a zombie outbreak using mathematical tools such as birth-death models or differential equations.  This consistency with mathematical modeling obviously means that zombie apocalypse is a real threat, doesn’t it?

A similarly concerned student gave me a book chapter (see the reference below) that appeared in an academic book about infectious diseases that is helpful for preparing for a zombie attack.  They set up a series of differential equations to model a zombie outbreak and then determine optimal strategies for responding.  Their model consists of three sub-populations:

• Susceptible (S): humans,
• Zombies (Z): this is self-explanatory, and

Humans can die (i.e., they are removed) through natural causes (with rate d).  The removed humans can become zombies with rate z, and suscpetibles can become zombies through a zombie encounter with rate b.  Zombies die with rate a. Since zombies only crave human flesh, other species do not need to be considered.  The birth rate is a constant P.  Therefore, the differential equations modeling these interactions are

S’ = P – bSZ – dS

Z’ = bSZ + zR – aSZ

R’ = dS + aSZ – zR

The key difference between this model and other infectious disease models is that the dead can be resurrected.  The authors identify the conditions under which the human species is wiped out(!)  However, they show that quick, aggressive attacks can stave off a zombie apocalypse.

* P. Munz, I. Hudea, J. Imad, and R.J. Smith, 2009. “When Zombies Attack!: Mathematical Modelling of an Outbreak of Zombie Infection.” In Infectious disease modelling research progress, Nova Science Publishers, Inc., p. 133 – 150.

Strangely enough, this book chapter was supported by several grants, including a NSERV Discovery grant, an Ontario Early Researcher Award, and funding from MITACS.  With its low population density, you’d think Canada would be less susceptible to a zombie attack.

How have you prepared for a zombie attack?

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#### 6 responses to “how to (optimally) prepare for a zombie outbreak”

• Paul A. Rubin

Re preparation: Zombies eat human brains, right? I live half-way between the state legislature and a major university. That should discourage zombies from hunting anywhere around here, so I’m good.

I’m not sure the zombification term (bSZ) should be quadratic, but I’m almost positive that in the equation for S’ the first term should be pS and not a constant P. No females, no births. (I’ve been told – by females – that the males are optional, if not vestigial.)

Do zombies die (starve) if they run out of humans? If so, a predator-prey model might make more sense. (I worked on programming one of those in a previous millenium.)

• Laura McLay

@Paul, I agree with you about the “pS” term (although although not with your claim about men being vestigal. I couldn’t manage my three little bundles of joy without my husband).

The authors justify their bSZ term:

“Mass-action incidence specifies that an average member of the population makes contact sufficient to transmit infection with bN others per unit time, where N is the total population without infection. In this case, the infection is zombification. The probability that a random contact by a zombie is made with a susceptible is S/N; thus, the number of new zombies through this transmission process is:
bN(S/N)Z = bSZ.”

The model is also extended in a straightforward manner to consider latent infection, quarantine, and treatment.

And I’m glad you’ll be safe — if there’s a zombie apocalypse, there will still be good OR blogs! (-:

• Norman

Late to the party, I realize, but still. What bothers me about the model is not the quadratic terms, but rather the fact that zombies killed by humans (aSZ), meaning the brain has been destroyed, are returned to the Removed group. This implies zombies can return as zombies again even after the brain is destroyed, which is pretty well disallowed by every version of the zombie apocalypse I am aware of. I haven’t worked out the model, but my instinct is that this addition would greatly reduce the direness of the predictions.

• prubin73

Careful analysis of the budget/debt ceiling debate suggests that zombies reviving sans brain may actually be the most realistic part of this model.

• Edward

I really dont even know who made those models..lol equations….i just know that zombies females if pregnate will give birth to a zombie baby and will still eat human flesh well not without teeh but still they may not grow as bigger as they are when they turned so even if the population of zombies is bigger than the human i mean a well 10 years trained french leggionaire can kill 10 zombies at once with only one knife(he still will know about them-zombie).My option is get supplies and upgrade your home to a fotress or go to a mail and make it as a fotress..both options are good but you must move from one to another when you are out of supplies…still the weaponary must be heavy like spas shotguns m16 sniper rifles and more..even if you can’t arrange one of them,..a medium pistol and sub-machine gun is enough but not when a horde of 100 zombies attack at once therefor you must prepare some traps flamethrowes granades moltoves anything that can burn and of course…a heavy barricade!!!!!