Humans vs Vampires
Free vampire apocalypse simulator using the Lotka-Volterra predator-prey model. Enter human population, initial vampires, and transformation probability to see extinction year and population timelines.
About This Calculator
The Humans vs Vampires Calculator simulates a vampire apocalypse using the Lotka-Volterra predator-prey model, a mathematical framework used in ecology to model interactions between predator and prey populations. This interactive simulator lets you explore how a vampire outbreak would unfold based on population size, initial vampire count, and the probability of human-to-vampire conversion.
The model works by tracking two populations over time using differential equations. Humans (the prey) grow at a fixed annual rate of 1%, representing natural population growth. Vampires (the predators) do not reproduce naturally — instead, they grow by attacking and converting humans into new vampires. The rate of conversion depends on the encounter frequency between humans and vampires and the transformation probability you set. The simulation uses a 4th-order Runge-Kutta numerical integration method to solve these equations accurately over time.
Regional Notes
Global: This simulation is relevant worldwide — the predator-prey model applies universally regardless of geography. Default values use Earth's current population of approximately 7.9 billion people. The Stoker-King scenario uses the 1897 world population of 1.65 billion.
Educational use: The Lotka-Volterra equations are taught in ecology, biology, and applied mathematics courses worldwide. This calculator serves as an interactive demonstration of how small changes in predator-prey parameters can dramatically alter outcomes.
Frequently Asked Questions
How does the Humans vs Vampires apocalypse simulator work?
The simulator uses the Lotka-Volterra predator-prey differential equations with a 4th-order Runge-Kutta solver. Humans (prey) grow at 1% annually but are hunted by vampires (predators). Each vampire encounter can turn a human into a new vampire based on the transformation probability you set. The model tracks both populations over time to predict the outcome.
What is the Lotka-Volterra model used in this vampire simulator?
The Lotka-Volterra equations describe the dynamics between predator and prey populations. In this model, humans (prey) grow exponentially at a set rate, while vampires (predators) grow by converting humans. The interaction term (encounters between humans and vampires) drives the system. The model uses a 4th-order Runge-Kutta numerical integration for accurate simulation.
What do the transformation probability and encounter rate mean?
The transformation probability is the chance that a human attacked by a vampire becomes a vampire themselves (0-100%). The encounter rate is a fixed model parameter representing how frequently vampires encounter humans based on population density. Higher transformation probability leads to faster vampire growth and earlier human extinction.
What happens when vampires outnumber humans in the simulation?
When the vampire population exceeds the equilibrium point (where human birth rate equals vampire conversion rate), the human population begins to decline. As humans become scarce, vampire growth slows due to fewer conversion opportunities. The simulation shows whether humanity reaches extinction or both populations stabilize.
Can I share my vampire apocalypse simulation results?
Yes, all input parameters are saved in the URL when you click Simulate. You can copy the URL and share it with friends to show your exact scenario — initial population, vampires, transformation probability, and simulation years are all encoded in the shareable link.
Is this vampire apocalypse calculator scientifically accurate?
The calculator uses the mathematically rigorous Lotka-Volterra predator-prey model, which is widely used in ecology to model real predator-prey dynamics. However, it is a simplified representation — real-world factors like geography, vampire hunting, and human countermeasures are not included. It is designed for educational and entertainment purposes.
What are realistic starting values for the vampire simulation?
A realistic scenario: start with Earth's current population of about 7.9 billion humans (7900 million), 1 initial vampire, 50% transformation probability, and simulate over 100 years. You can also try the Stoker-King model scenario with 1,650 million humans (1897 world population) and 1 vampire — humanity falls in about 30.8 months.
Why do vampires grow exponentially in the simulation?
Vampires grow exponentially because each vampire can create multiple new vampires by converting humans. Unlike natural predators that have limited offspring, vampire reproduction is proportional to the number of encounters with humans. This creates a positive feedback loop where more vampires lead to more encounters and faster growth, until humans become scarce.