4 ideas
Instead of vaccinating an entire population, you identify each active case, then vaccinate everyone who had contact with that case and their contacts, building an immune 'ring' that starves the virus of new hosts. This works because smallpox spreads slowly and visibly, so containing known transmission chains is more efficient than achieving universal coverage.
Eradication failed where programs chased high vaccination percentages but succeeded where they invested in finding and reporting every case fast. A disease can persist in unvaccinated pockets even at 90% coverage, so the binding constraint is detection speed, not the total number of shots administered.
Smallpox was eradicable because it had no animal reservoir, produced visible symptoms that made cases easy to identify, conferred lifelong immunity, and had a stable vaccine requiring no cold chain in some forms. A disease must possess specific biological vulnerabilities for eradication to be technically possible — strategy must be matched to the organism's actual properties.
The final naturally occurring case was Ali Maow Maalin, a hospital cook in Somalia in 1977, traced through aggressive contact-tracing and contained before further spread. The endpoint of a global campaign reduced to a single identifiable individual demonstrates how eradication is achieved person-by-person at the margins, not through abstract population statistics.