whatNine hundred people and one unchanging disease: it crosses each contact at a fixed rate, the sick recover after a fixed time, and everyone averages six contacts. Only the wiring changes. Click to rewire the same crowd three ways: a lattice of neighbours, a small world with a few shortcuts, and a scale-free web where a few hubs know dozens. Bursts are the sick, hollows the recovered, crosses the vaccinated; the chart keeps each wiring's epidemic curve, and every outbreak's final toll lands as a tick on the lower chart.

whyThe claim: identical R0, wildly different fates. Measured here, the same disease took a tenth of the lattice slowly, a third of the small world, and two thirds of the scale-free web in half the time, with a peak fourteen times higher, because the average R0 hides the hubs. And the lever: vaccination is topology, not arithmetic. Protecting the best-connected twelve percent cut the scale-free toll to under one percent; the same number of doses at random left it at half the population.

howSIR with per-edge transmission and fixed recovery, seeded with three cases each outbreak; outbreaks repeat, and the herd threshold emerges as the knee where toll ticks collapse. Hub vaccination sorts by degree; the caption toggles it against random. The three wirings share one mean degree, so the naive R0 truly is identical. One integer seeds the wiring and every infection.