How did they do the eradication of smallpox?

Vaccination: Smallpox eradication was achieved through a massive worldwide vaccination program.

Circles of vaccine: The virus is never asymptomatic and has no animal or insect hosts and the vaccine is heat stable, not needing a cold chain. At the end, as each case in asia or africa was discovered, all of the people around the index case were immunized.

Because smallpox: Only affects humans, there were no vectors (reservoirs) that needed to be addressed. There is no carrier state for smallpox. The world health organization (who) initiated the global smallpox eradication program which used a combination of identification of cases, vaccination & quarantine which led to the who’s declaration that smallpox was eradicated in 1979.