By Andrew Williams --
As many children and partygoers prepare to dress up as the undead for trick-or-treating fun or Halloween-themed parties, the scientific community is taking the potential of a Zombie attack more seriously. A group of mathematicians at the University of Ottawa and Carleton University (also in Ottawa) have prepared a paper for the up-coming book "Infectious Disease Modelling Research Progress," in which they have not only introduced and refined a basic model for zombie infections, they derive conditions under which Zombie eradication can occur. Dr. Robert Smith? (below), who is an assistant professor in the Department of Mathematics and Statistics and on the Faculty of Medicine, who should not to be confused with the lead singer of the The Cure, compares the modeling of a zombie attack to the modeling any new disease. "We refined the model again and again to say . . . here's how you would tackle an unfamiliar disease," explains Dr. Smith? (see "The zombies are fictional: the science is real"). And, in case you were wondering, the question mark is not a typographical error -- according to records in Australia, it is actually part of Dr. Smith?'s name (see "Welcome to the homepage of Robert Smith?").
For those who are not familiar, a zombie is defined as "a reanimated human corpse that feeds on living human flesh" (see Munz, P., et al., "When Zombies Attack!: Mathematical Modelling of an Outbreak of Zombie Infection," in Infections Disease Modelling Research Progress (Tchuenche and Chiyaka, eds., 133 (2009)), citing Brooks, Max, 2003 "The Zombie Survival Guide – Complete Protection from the Living Dead" (Three Rivers Press, pp. 2-23)). Dr. Smith? and colleagues chose to model their zombies after the slow moving and cannibalistic undead of classical pop-culture, rather than the faster moving and smarter zombies of recent films (id. at 134-35). The basic model includes three classes, Susceptible, Zombie, and Removed (those that have died, either through attack or natural causes) (id. at 135). New zombies can only result from (1) the resurrected humans from the Removed class, or (2) members of the Susceptible class that have lost an encounter with a zombie (id.). In addition, members of the Zombie class can only be moved to the Removed class by decapitation or destroying the brain of the zombie (id.). The basic model, therefore, looks like this:
where δ is the rate of Susceptibles that become deceased through natural causes, ζ is the rate of humans in the Removed class that resurrect and become zombies, β is the rate of Susceptibles that become Zombies through an encounter with a zombie, π is the birth rate, and α is the rate of Zombies that are destroyed (id. at 135-36). Of course, this model had to subsequently be revised to include a latent class of infected individuals, because as everyone knows, there is an approximately 24-hour period between a human getting bit by a zombie and succumbing to the wound (id. at 137). The other models also took into account the effect of a partial quarantine of zombies, the possibility of the quick development of a zombie cure, and the results of impulsive eradication (id. at 140-46).
The researchers conclude that "a zombie outbreak is likely to lead to the collapse of civilization, unless it is dealt with quickly" (id. at 146). They found that even though it may be possible to eradicate the infection with aggressive quarantine, it is likely that only sufficiently frequent attacks with increasing force will result in eradication (id.). And this is only if the timescale of the outbreak is short -- if the timescale increases, human births and deaths would provide the zombies with a limitless supply of new bodies (id.). Therefore, the researchers warn, "if zombies arrive, we must act quickly and decisively to eradicate them before they eradicate us" (id.). Dr. Smith? and his colleagues do recognize that a zombie attack is unrealistic, but the scenarios that they provide are instructive to help develop mathematical models for unusual infectious disease outbreaks (id.). Their work helps demonstrate how mathematical modeling can be used to respond to a wide variety of "biological" challenges. Regardless, I, for one, will sleep better tonight knowing that Dr. Smith? and others are on the forefront of both infectious disease modeling, as well as zombie eradication.