Zombie Invasion Calculator

How to use the Zombie Invasion Calculator

What this calculator does

This calculator runs a fictional population simulation in one-day steps. It estimates how the number of humans and zombies changes when zombies attack, some humans flee, the rest fight, human casualties may transform, defeated zombies may resurrect, and – if you enable it – zombies may starve. The model is intended for mathematical exploration and entertainment, not for real emergency or public-health forecasting. Real infectious-disease models use carefully estimated parameters and uncertainty analysis; the CDC overview of infectious-disease transmission models explains how real models connect assumptions about contacts and transmission to population outcomes.

When to use it

Use the simulation to compare an aggressive fighting strategy with a flee-first strategy, test how sensitive the outcome is to faster zombies, see how transformation or resurrection changes the growth of the horde, or explore why small early differences can produce very different paths in a stochastic population model.

How to calculate

1. The calculator opens with a complete demonstration scenario, so the results, chart, schedule, and a validated example XLSX are ready immediately.
2. Replace the population values and choose the human and zombie behavior presets. Percentage fields accept ordinary decimal notation such as 80 for 80%; attack frequency accepts a decimal such as 0.8 attacks per zombie per day.
3. Read the live outcome, then use the line chart to inspect the trajectory and the schedule to audit each day's deaths and new zombies.
4. Select Download Excel to export the exact current inputs and model rows. Select Reset to clear the demonstration data; after Reset, export remains disabled until every required field is complete and valid again.

Input guide

Initial number of humans is a required whole-number starting population from 1 to 100,000,000; 10,000 is the demonstration value. Larger populations usually lengthen the contest, but the direction also depends on attack and survival assumptions. Avoid decimals or separators other than standard comma grouping. Human defense stance is required: Fight sends 20% of attacked humans into escape attempts, while Flee sends 80%. More fleeing reduces direct fights but exposes more people to the zombie-speed escape-failure probability. Human fighting skills is required and selects the probability that a human wins a fight; the demonstration uses the Ellie-style 70% preset. A higher value lowers fight casualties and increases defeated zombies.

Initial number of zombies is a required whole number from 1 to 100,000,000; the demonstration begins with 10. Transformation probability is a required 0 – 100% rate; 80 means four out of five human deaths are expected to create new zombies before stochastic rounding. Zombie attack frequency is required and measures attacks per zombie per day, from 0 to 20; 0.8 is the example. The model also caps total daily attacks at five per current human. Zombie resurrection rate is required from 0 – 100%; the 20% example means some zombies defeated in fights stand back up, reducing effective zombie deaths.

Zombie speed is required and maps a preset to the chance that a fleeing human is caught: Slow shambler 25%, Shambler 50%, Runner 85%. Can zombies starve to death? is required. Choosing Yes enables Zombie starvation rate, a required 0 – 100% daily rate applied to zombies left without a human casualty to feed on; choosing No disables that effect. Do not enter scientific notation or decimal-comma text such as 1,5; ambiguous formats are rejected instead of being silently reinterpreted.

Output guide

Simulation outcome states which population reaches the stopping threshold first, or whether the 365-day horizon is reached. Days passed is the exact number of simulated daily steps. Number of humans and Number of zombies are the final integer populations. Peak zombie population is the largest zombie count reached anywhere in the run. The Population path by day chart plots humans and zombies against the same day axis and population scale, while the Daily simulation schedule gives Day, Humans, Zombies, Human deaths, New zombies, and Zombie deaths for every step. A zero final population is a modeled extinction event; a high peak indicates rapid growth under the chosen assumptions. The three live summary pills at the top repeat the current outcome, elapsed days, and final human count for quick scanning.

Worked example

With 10,000 humans, the Flee stance, 70% human fighting skill, 10 zombies, 80% transformation, 0.8 attacks per zombie per day, 20% resurrection, 50% zombie speed, and no starvation, the seeded stochastic simulation reaches the human extinction threshold after 34 days. The final modeled population is 0 humans and 5,517 zombies. For each day, attacks are the smaller of zombies × attack frequency and humans × 5. Flee attempts equal attacks × 80%; fights are the remainder. Human deaths combine failed escapes and fights won by zombies; new zombies are transformed human deaths; zombie deaths come from fights won by humans after resurrection is allowed. Fractional event counts use reproducible stochastic rounding derived from the input set, so the same inputs produce the same workbook and chart while still representing the small-number variability discussed in this peer-reviewed primer on stochastic epidemic models.

Learn more

For a playful academic example of applying disease-model mathematics to fictional zombies, see the University of Hawai'i-hosted paper Mathematical Modelling of an Outbreak of Zombie Infection. It uses a different model than this calculator, but it is useful context for why population compartments, transition rates, and intervention assumptions matter.