What it does
Some illnesses pass from person to person. How far one spreads depends on three things: how many people an ill person meets each day, the chance of passing it on at each meeting, and how many days they stay ill. Multiply them and you get R0 (“R nought”), the number of people one ill person infects in a town where nobody is immune. If R0 is above 1 the illness can spread; below 1 it fades away. This page shows a town of 400 dots. Three start ill; press Play or One day and watch the illness move through the town, with a graph of how many can still catch it, are ill and have recovered.
Move the share vaccinated slider to give some people immunity before it starts. Once enough people are immune, the herd immunity threshold 1 − 1/R0, chains of infection break and even unvaccinated people are mostly protected.
It follows the school topics Class 8 Science, health (how diseases spread, prevention and vaccination) and Class 9 Biology, why do we fall ill. Germs multiply inside the body as in the microbe growth simulator simulator, and the full maths model is in the epidemic model.
How to use it
- Set the three illness sliders: people met each day, chance of passing it on and days ill. R0 is worked out under the town.
- Set the share vaccinated.
- Press Play, One day or Run to the end. Press New town to try again with a fresh town: results vary because meetings are random.
- The Level switch (Class 9 and up) adds the effective R (R0 × share who can still catch it) and the big-town prediction from the final-size equation.
Worked example
Each ill person meets 4 people a day, passes it on at 15 % of meetings and is ill for 5 days: R0 = 4 × 0.15 × 5 = 3. The herd immunity threshold is 1 − 1/3 = 67 %. With nobody vaccinated, the final-size equation z = 1 − e^(−3z) gives z = 0.94, so about 94 % of a big town catches it; most runs of the town come close, though now and then it dies out in the first days by luck. With 80 % vaccinated the effective R is 3 × 0.2 = 0.6, below 1, and only a handful of people catch it.
Check yourself
Five fresh questions: R0 from the three numbers, the herd immunity threshold, effective R, what happens below 1, and why vaccination protects others. Nothing is saved.
Tips
- Staying home when ill cuts people met; washing hands and covering coughs cut the chance per meeting. Both lower R0.
- Herd immunity needs a higher share for illnesses that spread more easily.
- Small towns are lucky or unlucky: the same settings can give very different outbreaks.
FAQ
Is this a real illness? No. The illness, the town and every number are made up. Real people do not mix at random, so real outbreaks are more complicated. Use this only to learn the ideas.
Why does it sometimes stop at once? If the first few ill people happen to pass it on to nobody, it dies out. This happens even when R0 is above 1.
Is this from NCERT? No. It is an independent study aid that follows the same school topics, with its own model and numbers.
Where the numbers come from
- Basic reproduction number R0 = contacts per day × chance per contact × days infectious, herd immunity threshold 1 − 1/R0, effective R = R0 × susceptible share, and the SIR final-size equation z = 1 − e^(−R z): standard epidemiology (Kermack and McKendrick, 1927, for the final size).
- The illness, the town and every number on the page are made up. Checked against an independent Python calculation of the final-size equation and against the average of many simulated towns.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.