The Walking Dead: A Statistically Terrifying Introduction
Many people have a love/hate relationship with zombies. Mostly people hate them, but they generally love to hear about them and watch movies/play games/read stories with them in. But while it’s fun to watch zombies slowly shuffle their way towards their next feast of brains, arguably it’s more interesting to think about the practicalities about an actual zombie attack. And what better way to explore these scenarios than through the medium of mathematics?!
Zoiks!!! Zombies!!! Epidemiology 102.5
If people have a love/hate relationship with zombies, then they definitely have one towards mathematics! And it teeters more on hate than not. But, dear readers, I must confess that the usefulness of mathematics far outweighs having to do pointless exam after pointless exam on algebraic calculations and so on and so forth. And it’s especially useful when we’re trying to model the spread of infectious diseases: in this case, the fabled zombie virus! Well, ok, admittedly I know that there are many other ‘explanations’ for the whole zombie scenario, but I’m going to keep it to a virus or other form of parasitic disease. Incredibly tasteful!
OK, before I continue, I will need to give myself (and, by that train of thought, you guys) a crash course in epidemiological modelling. And I’ll adapt it to the zombie situation specifically, since that’s what we’re talking about right here.
There are four basic classes, or groups, of individuals we’re going to consider in our model:
- S = Susceptible. This class is essentially all of those people that aren’t infected (=regular humans) that have the potential to become zombies, hence the ‘susceptible’ label. Pretty easy going so far!
- I = Infected. This class are the people that have been infected by the zombie virus – a ‘latent infectious’ period. They’re not fully fledged zombies yet but they’re in a ‘waiting’ phase where they’re not really infectious. The time between becoming infected and becoming one of the (un)living dead is debatable, but can commonly be around 24 hours.
- Z = Zombies. Pretty self-explanatory! They want to eat flesh, infected the susceptible and essentially drag their limp and rotting bodies around the place.
- R = Removed. Any susceptibles/infected/zombies that have been removed from these populations come into this class. This might be through being ‘defeated’ (e.g. a well timed bullet to the head or destroying the brain) or, for humans, through death from natural causes. If any people in this class are humans, then they can resurrect to become zombies as well. Egad!
- C = Cured/Immune. Any individual that was a zombie but has somehow received a timely antidote/cure or an individual that is genetically immune/vaccinated from the outset. Either way, we’ll say that even dead cured/immune individuals can’t ever become zombified. Fair assumption to make I’d think.
These five classes form our basic CSIZR model. So we have:
C <- S -> I -> Z -> R
with S -> C if they are vaccinated and genetically immune individuals being put in the C class straight away.
It should be noted that there are more arrows in the above model than I can notate on here. But I will explain these in the list below
Now there are a lot of other terms and specialist symbols I could throw around, but I’ll try to keep it (vaguely) simple. Essentially:
- S -> I / R -> I = can happen either via Susceptible individuals being infected by being bitten by another zombie or viral/parasitic/bacterial infection (take your pick!). Removed individuals can move to the infected class if they resurrect by zombies upon death (mostly down to infection by the zombifying biological organism)
- I -> Z = pretty self explanatory. After the latent period of infection, Infected individuals become zombies.
- I/Z -> R = BOOM! HEADSHOT! With a pretty accurate bullet or a shovel or whatever else you can use, BANG! And the zombie is gone! Well, the body won’t be but it won’t trouble you anymore! Unless it’s one of them pesky regenerating types. For I -> R, see below!
- S/I/Z -> C = we’ll assume, in our model, that Susceptible, Infected and Zombified individuals can be cured. Pretty far-reaching assumption to make, granted…but we’ll assume that our zombie apocalypse scenario is in a world that has some pretty darn bright people in the biological sciences. /shameless biology plug
Without overcomplicating it, there is a lot of thought that has to go into a model such as this one. Here are just a few of many that you have to consider:
- What is the rate of Susceptibles either being cured or turned into Infected individuals? That will be how many Susceptible Individuals are Infected as opposed to how many resist infection?
- How long will it take for Infected individuals to become Zombies? And, what kind of state are they in whilst they’re infected? Will they be like regular humans, albeit a bit ill, or paralysed cocoons or some such? This will affect so many things – namely, how we go about ensuring people go from Infected to Removed. If they are pretty benign whilst Infected, then that could possibly make it a lot easier to counter a zombie plague. However, if they are rabid carriers of infectious zombifying disease……………………………………..it was nice knowing you.
- Assuming that we do end up developing a cure (yay biologists!), then how long will it take to deploy/work? What is the rate of individuals from other classes become Cured individuals? If this rate plus the rate of those becoming Removed individuals is greater than the rate of those becoming Infected/Zombies, then we’re fine. If it’s less, then we’re probably really not fine. Eep!
- Is the zombie plague spread via a bacteria/virus/parasite? This will have implications for formulating a cure but also can dictate if the disease is airborne or not. If it is, I’d personally think we have no chance to survive a zombie apocalypse. If it isn’t, and it can only be spread from zombie to zombie.
- Cure or not, just what will the dynamics be of attacking zombies? The paper that I cite below mentions that the best way to combat a zombie attack would be with repeated and aggressive attacks, rather than one prolonged one. A nice idea but, depending on points 1-4, how feasible would that be? If the rate of transmission of the zombie virus/parasite/bacteria is too high, then our attacks my be potentially ineffective.
- How clever will the zombies be? Will they shuffle around aimlessly, trying to look for the nearest brains to consume or will they be clever and calculating? One quite amusing idea I’ve read is to put treadmills all around the house, so the frightful horrors will be stuck indefinitely! Another is to take a boat or raft out and get well away from the shore, as they would be unable to swim. Hopefully they won’t develop the ability to turn off the treadmills or, potentially even worse, learn how to swim…that would seriously not be good for us!
OK, so we have our scenario and a basic understanding of how zombie epidemiology works. I purposely left out many different aspects because it would really confuse the flow of the post.
Join me next time, as I delve into the closest that nature gets to ‘real life zombies’. Ants, snails…no one is safe! Thank you for reading, friends, and may your explorations at the edge of reality be both weird and wonderful!
And a specially terrifying thanks goes to…
Munz et al (2009), a group of Canadian scientists, have written a PHENOMENAL paper describing exactly what I have been delving into this post. And, admittedly, I have used their model and dipped into some of their assumptions, taking liberties and using my own conjecture where relevant. I encourage anybody vaguely interested in this topic to read this incredibly well written, well thought and accessible out paper, linked below: