Vampire Apocalypse Calculator
How long would humanity last against a vampire outbreak? This calculator models three populations - humans, vampires, and vampire slayers - using the same Lotka-Volterra differential equations that ecologists use to study predator-prey dynamics. Choose a scenario inspired by Dracula, Interview with the Vampire, or Twilight, or dial in your own parameters, and see whether humans survive, reach equilibrium, or go extinct.
The predator-prey model behind the simulation
This calculator uses a modified Lotka-Volterra system, the same family of differential equations ecologists apply to wolf-deer or shark-fish dynamics. Three coupled equations drive the simulation. The human population grows at a natural rate k1 but shrinks whenever vampires attack, captured by the term -a1*y where a1 is the aggression rate and y is the vampire count. The vampire population grows when attacks convert humans (b1*a1*x) but is reduced by slayer activity (-c*z). The slayer population grows at rate k2 but is depleted by vampire counter-attacks (-a2*y). Because no closed-form solution exists for the full coupled system, the calculator advances time in 2,000 small steps using the Euler method, accumulating the population changes at each step.
How to read the results
The primary result is the outcome label: whether humanity survives, is extinguished, or reaches a prolonged stalemate. The population chart traces humans (blue), vampires (red), and slayers (yellow) across the chosen time window. Pay attention to the peak vampire count, which marks the most dangerous phase of the outbreak. The time-to-parity figure tells you when vampires first outnumber humans, which is often the tipping point for an extinction cascade. Increasing the slayer population is usually the most effective lever: even a small organized resistance can break the exponential vampire growth curve and let the human birth rate recover.
Why the math is based on real science
The Lotka-Volterra predator-prey model was proposed independently by Alfred Lotka (1925) and Vito Volterra (1926) to describe oscillating fish populations in the Adriatic Sea. It has since been applied to ecology, epidemiology, chemical kinetics, and even economics. A vampire outbreak maps naturally onto the model: humans are prey, vampires are predators, the conversion probability parallels disease transmission, and slayers act as a control agent analogous to a predator on the predator. Physicist Dominik Czernia formalized this exact framework in a 2019 paper in the Journal of Geek Studies, using the fourth-order Runge-Kutta method for higher numerical accuracy. This calculator uses a simplified Euler integrator that is fast enough to run in the browser while preserving the qualitative behavior of the model.
Limitations and assumptions
The model assumes homogeneous mixing: every vampire has an equal chance to encounter any human, which underestimates geographic clustering effects. Parameters are held constant throughout the simulation, whereas a real outbreak would trigger behavioral changes, quarantine measures, and evolving vampire tactics. The model ignores age structure, so it cannot represent the fact that children and elderly people are attacked and converted at different rates. Slayers are assumed to operate independently and do not benefit from coordination or technology upgrades over time. Despite these simplifications, the model correctly captures the key qualitative transitions: exponential vampire growth, population collapse when the prey base is exhausted, and the stabilizing effect of a growing slayer population.
Vampire scenario presets
| Scenario | Aggression (a1) | Conversion (b1) | Slayer kill rate (c) | Typical outcome |
|---|---|---|---|---|
| Classic horror (Stoker / King) | 0.0008 | 50% | 0.0015 | Extinction in decades |
| Restrained predators (Rice) | 0.0003 | 20% | 0.0010 | Long conflict |
| Coexistence (Twilight) | 0.0001 | 10% | 0.0005 | Humanity survives |
| Dusk of humanity | 0.0020 | 80% | 0.0010 | Rapid extinction |
| Custom | User set | User set | User set | Variable |
Parameters are annual rates. Aggression is per 10,000 per year. Conversion is the fraction of attacks that create a new vampire.
Frequently asked questions
What is the Lotka-Volterra model?
The Lotka-Volterra model describes how two or more interacting populations change over time. In the classic two-species version, prey grow naturally but are consumed by predators; predators grow when they find prey but decline in its absence. This creates the oscillating boom-bust cycles seen in real ecosystems. The vampire calculator extends the model to three populations: humans (prey), vampires (predator), and slayers (predator on the predator).
What does the conversion probability represent?
When a vampire attacks a human, the outcome can be death or transformation into a vampire. The conversion probability is the fraction of attacks that result in a new vampire rather than a dead human. A rate of 100% means every attack creates a new vampire (as in many zombie-adjacent fiction tropes); a rate of 0% means vampires kill but never recruit, which brings the vampire population toward eventual collapse once enough humans die.
How do slayers affect the outcome?
Slayers reduce the vampire population at a rate proportional to both the slayer count and the vampire count. Even a small number of effective slayers can prevent the exponential vampire growth phase from running away. The slayer population itself grows over time (representing recruitment and training) but shrinks when vampires attack back. There is a critical slayer-to-vampire ratio below which slayers cannot keep pace with vampire reproduction, so timing matters: a small early slayer force is far more effective than a large late one.
Why do some scenarios reach equilibrium instead of extinction?
When the vampire aggression and conversion rates are low relative to human birth rates and slayer kill rates, the system can settle into a stable oscillation or a low-level coexistence state. This mirrors real predator-prey systems: if wolves reproduce and hunt faster than deer can breed, deer go extinct and wolves starve. But when rates are balanced, the two populations cycle indefinitely. The Twilight preset demonstrates coexistence, where vampires feed selectively and avoid mass conversion, allowing the human birth rate to compensate for losses.
Is this based on actual scientific research?
The underlying Lotka-Volterra differential equations are among the most studied models in mathematical biology, applied in thousands of peer-reviewed studies since the 1920s. The specific application to a vampire outbreak was formalized by Dominik Czernia in a 2019 paper in the Journal of Geek Studies, which is a real open-access journal dedicated to applying rigorous scientific methods to fictional scenarios. The equations and numerical approach used here follow that paper.
What happens when I set slayers to zero?
With no slayers, the third equation drops out and you have a classic two-population predator-prey system. In most scenarios this leads to either extinction (if vampire aggression is high) or sustained oscillation (if aggression is low and the human birth rate can compensate). The dusk-of-humanity preset with zero slayers will almost always produce rapid human extinction because the conversion rate is high enough to overwhelm natural birth rates before any equilibrium can form.