Definition
An S-curve is the sigmoid trajectory traced by most diffusion, adoption, and catch-up processes — a slow start while only a few adopters get on board, a rapid middle where the majority joins, and a plateau as the remaining laggards or natural limits cap the total.
Vaccination coverage, contraceptive use, literacy, mobile-phone subscriptions, electricity access, female labour-force participation — all of these trace S-curves when plotted against time within a country.
Why it matters
How it works
The mathematical shape arises from a simple feedback: each new adopter slightly raises the probability that the next person adopts (network effect, social proof, falling cost), and each remaining non-adopter is harder to convert than the last (cost rises near the ceiling, the holdouts are by definition the resistant). Multiply those two forces and you get the sigmoid.
To recognise an S-curve in real data, look for three signs: a defined upper limit (you cannot have more than 100% of children vaccinated), evidence of a feedback that accelerates uptake, and at least one comparable case that has already completed the curve. Once you have all three, both flat early data and rapid middle data become legible — they are two stops on the same trip.
The corrective Rosling stresses is to ask, every time you see a rising line: "What is the ceiling, and where on the curve am I?" If the ceiling is real, the extrapolation must bend.