"Modelling warfare between vampires and humans: who wins?" by Samuel Cuthbertson and Mark Ian Nelson
We adapt the Lanchester combat model to represent conflict between vampires and humans. It is assumed that vampires attack humans during the hours of darkness whilst humans attack vampires during the hours of light. The right-hand side of the differential equation model therefore depends upon the hour of the day. A key insight is that to answer the question ‘who wins’ it is not required to ‘stitch together’ the solutions to the differential equation over many days. Rather, the number of combatants surviving at the end of each day can be cast as a difference equation in terms of the num...
Source: uow.edu.au