How this calculator works
The model borrows the shape of a predator and prey system. Each month, vampires kill a fixed number of humans, a share of those victims becomes new vampires, surviving humans reproduce, and a share of the human population joins the slayers. Slayers then remove vampires. The three numbers feed back into each other: more vampires means more deaths and more recruits to the slayers, and more slayers means fewer vampires next month. A delicate balance can hold for a long time or collapse quickly, which is the point of the simulation. It is deterministic, so the same inputs always give the same curve, and it is fiction rather than epidemiology.
Formula
Each monthly step: humans killed = the smaller of the human population and vampires x annual kill rate / 12. new vampires = humans killed x transformation share. vampires slain = the smaller of the vampire population and slayers x annual slayer kills / 12. new slayers = humans x annual recruitment share / 12. Humans next month = humans + humans x annual growth / 12 - humans killed, and vampires next month = vampires + new vampires - vampires slain.
Worked example
A million humans, ten vampires and no slayers, with a 1 percent annual growth rate, 12 kills per vampire per year and half of victims turned, start from a tiny vampire population. In the first month the vampires kill 10 humans, 5 of whom turn, while about 830 humans are born, so the humans still grow. The vampires gain about five members a month at first, but that gain is proportional to the vampire count, so it accelerates while human births grow only with the human population. The chart shows the crossover where vampire kills overtake human births. Removing the transformation share entirely leaves the vampire count flat, which is why it is often the deciding input.
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Frequently asked questions
Is this a realistic model?
No. It is a deterministic toy model for exploring feedback, not a forecast. Real populations have age structure, geography, behaviour and random events, none of which are represented.
Why does the human count sometimes grow while vampires attack?
Human births can exceed deaths when the vampire population is small. Growth and predation run in parallel, and the balance point depends on the growth rate, the kill rate and the transformation share.
What happens if humans reach zero?
The model clamps the population at zero and continues to run the vampire and slayer dynamics. Once humans are gone, recruitment and births stop, so the vampires eventually decay only if slayers remain.
Why do the chart lines look smooth?
The model has no randomness, and the sampling thins long runs to keep the chart readable. The underlying simulation still steps every month; only the plotted points are spaced out.