Vampire stories hide a neat piece of population biology. Vampires are predators, humans are their prey, and – unlike wolves and rabbits – every successful attack can create a new predator. Without anything to stop them, vampires grow exponentially until the prey runs out. Add vampire hunters who prey on the vampires and you get a three-level food chain, the same family of models (Lotka–Volterra) that ecologists use for lynx and hares.
This calculator lets you play with that system. Pick a ready-made scenario – a single vampire with nobody to stop it, a discreet coven that keeps its numbers low, hunters and vampires circling each other in slowly fading cycles, hunters who quickly reach a stalemate, or the dusk of humanity when hunters are overwhelmed – or build your own world with custom numbers.
The model tracks humans, vampires and hunters together and solves the equations with the fourth-order Runge–Kutta method. The chart (linear or logarithmic) shows all three populations, and the results report the outcome, the peak number of vampires and when humanity disappears, if it does.
How to use the Humans vs Vampires Calculator
- Scenario
- Initial humans
- Annual human population growth
- Initial vampires
- Chance a bitten human becomes a vampire
- Vampire feeding (aggression toward humans)
- Vampires restrain themselves (avoid killing, keep ≥ 1,000 humans per vampire)
- Initial hunters
- New hunters recruited per hunter per year (when the threat is high)
- Vampires destroyed per hunter per year (when vampires are easy to find)
- Attacks on hunters per vampire per year
- Chance a bitten hunter becomes a vampire
- Hunters retiring or dying of other causes
- Limit the hunters’ organisation to 0.1% of humans
- Simulation length
- Time unit
- Chart scale
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Each day vampires feed f times a year per vampire, spread over humans, hunters and fellow vampires. A bitten human turns with probability c, otherwise dies (or, for a restrained coven, usually survives). Hunters destroy vampires but find them hard to track when vampires are rare, recruit new hunters while the threat is high, retire at a steady rate and can themselves be bitten and turned.
Worked example
In the lone-predator scenario one vampire feeds 12 times a year and half of the victims turn. Each vampire then creates about 6 new vampires a year, so the number grows roughly like e6t while humans are plentiful. Reaching one million takes about ln(1,000,000) ÷ 6 ≈ 2.3 years, and with the feeding slowing as humans become scarce the simulation shows humanity wiped out after about 3 years and 4 months – with roughly 510,000 vampires left and nothing to eat.
What the scenarios show
| Scenario | Typical outcome over 40 years |
|---|---|
| Lone predator | Humans gone after about 3 years 4 months |
| Discreet coven | Stable: about 1,000 humans per vampire |
| Fading cycles | Vampires peak near 440 after about 4 years, then swing in fading cycles towards about 290 |
| Quick stalemate | Hunters hold vampires near 110 for decades |
| Dusk of humanity | Humans gone after about 1 year 3 months |
Formula
dH/dt = r·H − bites·(c + k) − recruits · dV/dt = bites·c + q·A − K · dS/dt = recruits − A − δ·S · bites = f·V·H/(H + S + V), K = κ·S·V²/(V² + 300²), A = α·V·S/(S + V + 1), recruits = ρ·S·V/(V + 300)
Worked example
Inputs — Scenario: Lone predator – one vampire, nobody to stop it; Simulation length: 5; Time unit: Years; Chart scale: Linear.
Results — Outcome = Humanity is wiped out after 3 years and 4.1 months.; Time until humanity is wiped out = 3 years and 4.1 months; Humans at the end = 0; Vampires at the end = 509,572; Hunters at the end = 0; Peak number of vampires = 509,572.
Key terms
- Lotka–Volterra model
- Coupled equations for predator and prey populations that can cycle.
- Runge–Kutta method
- A numerical method that advances differential equations in small, accurate steps.
- Refuge effect
- Predators struggle to find prey when prey is scarce, which stabilises the system.
- Carrying capacity
- The largest population an environment (here, the human food supply) can sustain.
Frequently asked questions
How fast would vampires take over the world?
With one vampire who feeds once a month and turns half of its victims, the vampire population doubles roughly every six weeks; a city of one million is gone in about 3 years and 4 months in this model.
Why can't vampires exist mathematically?
The classic argument (Efthimiou and Gandhi, 2007) shows that unchecked vampires grow exponentially and would have run out of humans within a few years – stories need restraint or hunters to stay plausible.
What makes the populations oscillate?
When hunters are many, vampires decline; with fewer vampires, recruitment of hunters drops and they retire, letting the vampires recover. That feedback loop produces predator–prey cycles.
Why do the cycles fade in some scenarios?
Hunters find rare vampires hard to track (a "refuge" effect), which damps the cycles and leads to a stable balance.
What does the logarithmic scale show?
It spreads small and large numbers evenly, so 20 vampires and 1,000,000 humans fit on one chart.
Is this a real epidemic model?
It uses the same mathematics as predator–prey and SIR epidemic models, but the numbers are playful assumptions, not data.