Then came the Delta variant. Despite keeping their countries largely sealed off, the virus found its way in. And when it did, it spread quickly. In the summer, South Korea battled its worst wave of infections; hospitals in Indonesia ran out of oxygen and beds; and in Thailand, health care workers had to turn away patients.

With cases surging, countries quickly shifted their vaccination approach.

Sydney, Australia, announced a lockdown in June after an unvaccinated limousine driver caught the Delta variant from an American aircrew. Then, Prime Minister Scott Morrison, who had previously said vaccination “was not a race,” called in July on Australians to “go for gold” in the country’s inoculation drive.

He moved to overcome a supply shortage, compounded by the slow regulatory approval. In August, Australia bought one million Pfizer doses from Poland; this month, Mr. Morrison announced a purchase of a million Moderna shots from Europe.

When the Delta outbreak emerged, fewer than 25 percent of Australians over the age of 16 had received a single shot. In the state of New South Wales, which includes Sydney, 86 percent of the adult population has now received a first dose, and 62 percent of adults are fully vaccinated. The country expects to fully inoculate 80 percent of its population over the age of 16 by early November.

“There was great community leadership — there were people from across the political divide who came out to support vaccination,” said Greg Dore, an infectious-disease expert at the University of New South Wales. “It really helped us turn around a level of hesitancy that was there.”

Many governments have used incentives to encourage inoculations.

In South Korea, the authorities eased restrictions in August on private gatherings for fully vaccinated people, allowing them to meet in larger groups while maintaining stricter curbs for others. Singapore, which has fully vaccinated 82 percent of its population, previously announced similar measures.

Researchers there have also analyzed the pockets of people who refuse to be inoculated and are trying to persuade them.