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  • About 60 min
  • 8 steps · 2 quizzes

How Epidemics Spread — R, Curves and Herd Immunity

An interactive first look at how infectious diseases spread through a population — and what stops them.

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8 steps · 2 quizzes · about 60 minutes · open any step

  1. One case becomes manyStart hereEvery outbreak starts with one sick person. The key number is R: how many people, on average, each sick person infects. Try it: pick R = 3 and press Next generation four times. Then try R = 0.8 and R = 1.InteractiveHands-on · 6 min
  2. A town full of contactsReal people don't infect a fixed number of others — it happens by chance, when they meet. Here 200 people wander around a town. A sick person (red) can infect anyone they touch; after 9 days they recover (green) and are immune.InteractiveHands-on · 6 min
  3. The epidemic curveScientists tell the same story with three numbers over time: people not infected yet, sick and recovered. This is the classic SIR model. R₀ ("R-nought") is R at the very start, when nobody is immune.InteractiveHands-on · 6 min
  4. Check: R and the curveQuiz · 4 questions
  5. Vaccination breaks the chainsImmune people are dead ends for the virus: a chain that reaches them stops. Vaccination makes people immune before the virus arrives. Try it: run the town at 0%, 30% and 60% immune. Compare your runs at the bottom.InteractiveHands-on · 6 min
  6. How many need to be immune?To stop growth, each case must infect fewer than one person. If each case would infect R₀ people, at least 1 − 1/R₀ of everyone must be immune. Try it: slide R₀ from 2 up to 15.InteractiveHands-on · 6 min
  7. Bringing R below 1Without enough immunity, we can still lower R by giving the virus fewer chances: fewer close contacts, masks and fresh air, finding and isolating cases early. Try it: switch measures on one at a time. How many do you need to get R below 1?InteractiveHands-on · 6 min
  8. Hidden spreadIsolating sick people only works if you know who is sick. For some diseases, including flu and COVID-19, people can pass it on before they feel ill — and some never feel ill at all. Try it: move the day symptoms start, and the share who never get symptoms.InteractiveHands-on · 6 min
  9. What models can — and can't — tell usEvery model rests on assumptions. Ours assumed that everyone mixes evenly, that everyone is equally likely to catch it, that immunity lasts forever and that people never change their behaviour. Real life breaks all of these.InteractiveHands-on · 6 min
  10. Final checkQuiz · 6 questions

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