The scenario is familiar to us all – Some sort of disease begins in a small town or large city, it spreads rapidly, infecting everyone in its wake, the infected become mindless, murderous creatures, hellbent on consuming or converting everyone they encounter, the walking dead. Finally, through some heroic effort, the survivors either turn back the tide or find a stronghold from which the human race can be rebuilt. It is the Zombie Apocalypse.

Hollywood is full of hype and heroic exploits. Of simple people overcoming tremendous odds, of triumph in the face of certain destruction. But how well would we really fare in a zombie apocalypse? Fortunately, Munz et al. (2009) have done the math for us, and the outcome does not look good. These are, of course, the shambling, slow-witted classical zombies, hungry for your flesh, not the sleek, mean zombies of whimsy.They propose 5 scenarios – basic outbreak (no quarantine, no cure, no coordinated response), an outbreak with a latency period, an outbreak with quarantine, an outbreak with a cure, and an outbreak with coordinated attacks. For all but the last two, the zombies make short work of the human race, with the only variation being in time and number of zombies produced. In the cure scenario, a small population of humans survives (10% the zombie population), and in the attack model, frequent, increasingly aggressive attacks eventually eradicate the zombies.

Listen to an interview with the lead author here.

The future does not look good for the human race during a zombie apocalypse. But what about our other undead brethren? Vampires are dependent on us for survival, both as a food source and a template for reproduction. As the human population declines, what happens to the vampire population? Can vampires survive a zombie apocalypse?

Several studies of vampire population dynamics and predator/prey relationships have been conducted over the years. In “The Transylvanian Problem of Renewable Resources” and its follow-up “Cycles of Fear: Periodic Bloodsucking Rates for Vampires”, Hartl et al. attempted to solve the optimal conditions for vampire feeding strategies and equate it with periodic empirically observed vampire appearances. Physicists Efthimiou and Gandhi attempted to prove the impossibility of vampires through an exponential growth curve. Basically, if insatiable vampires produced a new vampire every month, beginning in 1600, the whole human race would be vampire before the end of 1602.

Mathematician Dino Sejdinovic has something to say about that. Exponential growth is a sub-optimal condition. Building on the pioneering work of Hartl et al, Sejdinovic did something no previous vampire ecologist had done before, he added variables to account for a vampire death rate – unfortunate encounters with stakes, garlic, holy water, Southern Fried Scientists, and the occasional slayer. Brian Thomas, a graduate student in ecology at Stanford University, put together a nifty little treatise, using a fictional California town as a model. In short, a town of 36,000 can support about 18 vampires. Extrapolating out to the whole world (and this is a suspect figure at best) that gives us a standing vampire population of about 3.25 million.

But all these models rely on one important assumption – that vampires are the top predators. What happens when we pit the undead against the undead?

First, a few assumptions:

Vampires need to feed on humans. Although technically immortal, starving vampires are weak and easily killed. Vampires cannot feed on zombies. Most recent cases of zombie outbreaks are the result of a blood-born vector, so zombie blood is tainted. Vampires cannot become zombies. That just gives me the willies. Vampires are strong, but not invincible. The Zombie Survival Guide estimates that an average human can fend of 8 to 9 zombies. Assuming vampires are at least 10 and at most 50 times stronger than humans, then a single vampire could fight off between 80 to 450 zombies. Vampire victims, if not turned or destroyed, will eventually be infected an become zombies. Vampires are capable of feeding without killing, but it requires discipline. Although not susceptible, vampires can transmit the infection to humans. A vampire that’s bitten an infected – but not yet zombified – human can spread the disease to new hosts. Zombies eat anything with a brain, undead or not.

If we start with the basic model – Humans are quickly eradicated and zombies take over, infecting everyone – then vampires obviously lose too. With their food source completely tainted, the vampires grow weaker as the zombie population reaches an asymptote around 2.5 billion. this is more than enough to handle the 3.25 million vampires, who at full strength could handle only about 1.7 billion zombies. Starving and outnumbered, the vampires would be overrun.

The same is true for the latent infection scenario. With an even greater zombie population, the vampires would fall. However, there is a twist. Because vampires would be able to sense latent infection (the blood would be undrinkable) they could screen out infected individuals and remove them. In the quarantine scenario, this means that a buffer could be built to keep out the infected. The trade-off is that human-vampire cooperation in this scenario is unfeasible. Vampires can still spread the infection, so “farming” uninfected humans would be ineffective. The time to Armageddon may be delayed, but eventually zombies would rule the earth.

The cure model holds the most promise for vampires, but not necessarily humans. With a surviving human population reduced to 50 million, only 25,000 vampires could be supported. Since the initial vampire population is much higher than this, a feeding frenzy would commence, decimating the human population. Human “farming” could be an effective solution, but the vampires would be faced with a desolate future with few humans and billions of roving zombies to fend off. The human race would be reduced to livestock.

The most interesting scenario for both dead and undead alike is a coordinated attack of increasing intensity. This is the only scenario that showed promise for the human race, hit them hard and hit them often with overwhelming force. Provided vampires could be convinced that their existence depends on this tactic (perhaps that is my goal here) they could provide an extra level of overwhelming force that would allow us to drive the zombies back before the apocalypse. How the human-vampire conflict will change post-zombie-eradication is best left to the scholars.

In conclusion, Vampires can only survive if humans also survive, and the vampire population is so small as to have no effect on human survival. Vampires are helpless to alter their fate unless they join forces with their living brethren for an all out zombie-human-vampire rumble.

Both zombie and vampire population growth is directly proportional to food consumed. In both cases the food is us. Zombies represent one end of the spectrum – uncontrolled consumption with exponential growth eventually leading to a complete population collapse, while vampires represent the other extreme, controlled consumption and a stable state directly proportional to the size of the prey population.

The only question left then is “who’s managing our fisheries?”

Happy Halloween.

~Southern Fried Scientist

Munz P, Hudea I, Imad J, and Smith? RJ (2009). WHEN ZOMBIES ATTACK!: MATHEMATICAL MODELLING OF AN OUTBREAK OF ZOMBIE INFECTION Infectious Disease Modelling Research Progress, 133-150

C. J. Efthimiou, & S. Gandhi (2006). Cinema Fiction vs Physics Reality: Ghosts, Vampires and Zombies Skeptical Inquirer v. 31, issue 4 (2007), p. 27 arXiv: physics/0608059v2

D Sejdinovic (2008). Mathematics of the Human-Vampire Conflict Math Horizons

Hartl, R., Mehlmann, A., & Novak, A. (1992). Cycles of fear: Periodic bloodsucking rates for vampires Journal of Optimization Theory and Applications, 75 (3), 559-568 DOI: 10.1007/BF00940492