This situation has changed completely with the appearance of Refs. 3 and 4. Starting from a dynamic control model of confrontation between vampire-predators and human-preys the authors indicate how the vampires' utility from blood intake can be optimized through sophisticated depletion of renewable human resources.
However, the problem with all these results is that the derived monotonic state trajectories and bloodsucking rates are not in accordance with empirical evidence. According to the main body of literature on vampirism research the appearances of vampires follow a typical cyclical behavior (Ref. 5). The purpose of this paper is to extend the model in such a way that more realistic cyclical bloodsucking patterns are optimal.
Another possible extension-proposed in Ref. 6-provides human beings with an intertemporal welfare trade-off by allocation of labour services between production of economic goods and of useful instruments against vampires (such as stakes, garlic or rosary beads). To a traditional vampirologist the use of optimal control theory against vampires-as exercised in Ref. 6-seems highly questionable. This is due to the fact that the application of Pontryagin's principle requires the derivation of a shadow price for vampires. Such a price is, however, nonexistent since vampires do not have a shadow.