How this instrument works
This novelty calculator applies the standard exponential-growth curve — the same equation behind compound interest, bacterial cultures and radioactive decay's mirror image — to a zombie-outbreak scenario for entertainment. Enter how many are infected on day zero, a daily growth rate, and how many days have passed; the instrument multiplies the starting count by e raised to the growth rate times days, the textbook form of unconstrained exponential growth.
Because that raw formula grows without limit, the instrument caps its output at a total population figure you supply, so an aggressive growth rate can't report more zombies than there are people available to infect. Below the cap the raw and capped numbers match exactly; once the raw estimate would exceed the population, the reported count saturates at the population size instead.
This is deliberately a toy, not a disease model: real epidemiologists studying outbreaks (zombie-themed or otherwise) use compartmental models like SIR — tracking susceptible, infected and removed populations separately, with terms for transmission, recovery, and in zombie-fiction versions, things like human counter-attacks. This instrument skips all of that and uses one plain exponential term, which makes it fast and easy to play with but not a real forecasting tool.
- Enter Initial number of zombies — how many are infected at day zero, before any spreading begins.
- Set Daily growth rate as a decimal (0.3 means the infected population grows 30% per day, compounding).
- Enter Number of days elapsed to project the outbreak forward in time.
- Set Total population as the growth cap — the number of people available to be infected, which the result can never exceed.
- Read Estimated zombies for the capped figure; Uncapped exponential estimate shows the raw number before the population cap kicks in.
Worked example — one zombie, 30% daily growth, 20 days
Enter 1 for Initial number of zombies, 0.3 for Daily growth rate, 20 for Number of days elapsed, and leave Total population at 1,000,000. Uncapped exponential estimate = 1 x e^(0.3 x 20) = e^6 = 403.4288.
Because 403.4288 is well under the 1,000,000 cap, Estimated zombies reports the same value: 403.4288. So a single patient zero, spreading at a 30% daily growth rate, becomes roughly 403 zombies after twenty days in this simplified model — a demonstration of exponential blowup, not a prediction about how any real or fictional outbreak would actually play out.
Questions
Is this a real epidemiological model of a zombie outbreak?
No — it's a single exponential-growth equation, the same one used for compound interest or bacterial growth, repurposed here purely for entertainment. It has no infection-radius mechanics, no human counter-attack or removal terms, and no dependence on any particular film, show or game's zombie rules. Academic researchers who've modeled zombie outbreaks 'seriously' use multi-compartment SIR-style equations with several interacting terms; this instrument intentionally uses just one, for speed and simplicity, not rigor.
What does the 'daily growth rate' number mean?
It's the fraction by which the infected population compounds each day, entered as a decimal — 0.3 means 30% growth per day, applied continuously through the e^(rate x days) term rather than as one lump addition. Small changes to this rate produce very different outbreak sizes once you project more than a couple of weeks out, which is the whole point of exponential math: growth accelerates faster than intuition expects.
Why does the estimate stop growing once it reaches my Total population?
The uncapped exponential formula has no ceiling and will report more zombies than there are people on the planet if you run the days out far enough. The Total population field caps that: once the raw estimate would exceed it, Estimated zombies locks at exactly the population number instead of an impossible figure.
Has anyone actually modeled a zombie outbreak with real math?
Yes — a well-known 2009 paper, 'When Zombies Attack!: Mathematical Modelling of an Outbreak of Zombie Infection' by Munz, Hudea, Imad and Smith, applies a proper SIR-style compartmental model (with terms for infection, human counter-attacks and 'quarantine') to a hypothetical zombie scenario for teaching purposes. It's a genuinely more sophisticated approach than the single exponential term used here, and is worth a read if this topic interests you.
Can I model a slow-building outbreak instead of a fast one?
Yes — enter a small Daily growth rate like 0.02 (2% per day) rather than a large one. The same formula works at any rate; a low rate simply means far more days elapse before the estimate approaches your population cap, letting you compare a gradual 'slow burn' scenario against an explosive one using the same instrument.