Zombie Invasion Calculator — Outbreak Spread Simulator

Formula

How this is calculated

The calculator uses a discrete-time SI (Susceptible–Infected) epidemic model with an optional removal term for human defences. On each simulated day, the number of new infections equals the bite rate β multiplied by the current zombie count I times the fraction of the population still human (S/N). This mass-action mixing term is the same kernel used in real epidemiological models for diseases without recovery — once bitten, you stay a zombie, matching the classic movie trope. A defence rate δ removes a fixed percentage of the zombie horde every day, representing organised human counter-attack.

At the start of an outbreak, when nearly everyone is susceptible (S ≈ N), the zombie population roughly multiplies by (1 + β − δ/100) each day. With a bite rate of 2 and no defence, that means tripling every day — a city of 500,000 reaches 50% infection in about 12 days. The growth slows dramatically as the pool of susceptibles shrinks, producing the characteristic S-curve of logistic growth. If the defence rate is high enough that δ/100 > β, the horde shrinks every day and humanity eventually wins; the calculator reports the day the last zombie falls.

This is a fun, educational demonstration of exponential and logistic growth — the same mathematics that describes real disease outbreaks, viral marketing, and adoption curves. The model ignores geography, zombie decay, supply chains, fortified buildings, and many other real-world complications. Treat the results as intuition-building, not a genuine emergency plan.