Ella Morton at Atlas Obscura covers a few academic papers exploring what would happen to us (humanity, that is) if vampires--as seen in popular fiction--actually exist.
Mathematically influenced scholarship of vampire-human relations took off in the early '80s courtesy of Richard Hartl and Alexander Mehlmann, Austrian mathematicians with a mutual penchant for the undead. In 1982, their paper, titled "The Transylvanian Problem of Renewable Resources" was published in the operations research journal RAIRO. In it, Hartl and Mehlmann posited "optimal bloodsucking strategies for dynamic continuous vampires."
In doing so, they divided vampires into three categories: the "asymptotically satiated vampire," the "blood maximizing vampire," and the "unsatiable vampire." Regardless of the type of vampire, though, they found that bloodsuckers can't help but face diminishing resources:
"[W]e are facing a typical consumption-resource trade off. The vampire society derives utility from consumption of blood but in sucking the blood of a human being and in turning him to a vampire the resource of human beings is reduced whereas the number of vampires is increased. Both of these effects diminish the resource of humans per vampire curtailing future possibilities of consumption."
Hartl and Mehlmann further explored this vexing conundrum in a paper published in Applied Mathematical Modeling the following year. “The authors are well-aware that belief in vampires seems highly irrational to a scientist," they wrote in "Convex-Concave Utility Function: Optimal Blood-Consumption for Vampires," before launching into a proposed vampire self-sustainability model based on the Lotka-Volterra prey-predator system.