The Calculus Diaries - Jennifer Ouellette [63]
Smith?’s model doesn’t end there; that’s just the process for calculating the rate of change in the zombie population. We also have to run equations for how the number of dead and the number of uninfected humans change, which means factoring in the birth and death rates of humans as well. This is called a coupled system of ordinary differential equations, which is really just a fancy way of saying that the system must be described by not one, but three connected equations: one for how the number of humans changes, one for how the number of zombies changes, and one for how the number of dead changes. Furthermore, Elizabeth Bennett’s good friend Charlotte has been bitten but is not yet a zombie, although doomed to become one in a matter of weeks—as good an explanation as any for her marriage to the odious Mr. Collins. Smith? and company call these people Latents, giving us a total of four coupled equations. The coupling occurs because the same variables appear in all four equations—or, practically speaking, because the different populations interact with one another.
Assuming the zombie infection occurs quickly, the birth and death rates of humans will be insignificant during the time over which the infection occurs, so we still have the same scenario: Everyone will be turned into zombies very quickly, at which point the population will become unsustainable. In the worst-case scenario, Smith? estimates it would take a mere four days to wipe out the humans. The outcome remains the same: The zombies get us all in the end.
Quarantining the few healthy humans could help—the standard “hole up in a basement somewhere and hope the zombie hordes don’t find you” approach employed in classic zombie horror films. We’ve seen how (in)effective that strategy can be onscreen, and Smith?’s numbers back up those observations. However, another study by an Italian scientist named Davide Cassi implies that hiding out at the mall (à la Dawn of the Dead) could vastly improve one’s chances of survival. Cassi wasn’t analyzing zombies specifically, but his version of a predator/prey model applies to any kind of “predatory random walker”: organisms (like zombies!) that stumble around without any obvious purpose or direction, destroying any human that comes into their path. The larger and more complex the structure—such as a large mall with many twists and turns—the lower the chances that the predator will stumble upon the prey.
Alternatively, we can quarantine the zombies by herding them into some sort of holding pen, but if we don’t isolate enough of them fast enough, once again, the zombies will win. Both options are rather passive strategies, and most likely will only postpone the inevitable annihilation of the human race.
Smith? and his students suggest that our only hope is an “impulsive eradication” scheme. A series of fierce, concentrated attacks could sufficiently cull the number of zombies over time so that the outbreak would finally die out. “The most effective way to contain the rise of the undead is to hit hard and hit often,” the paper concludes. “As seen in the movies, it is imperative that zombies are dealt with quickly, or else we are all in a great deal of trouble.”39 Enter the Bennett sisters and respective paramours, with their wild, weapon-wielding ways, to make quick work of any rampaging zombie hordes.
Applying epidemiological modeling to a zombie invasion might seem silly, but it is not very different from modeling the spread