SYDNEY, Australia — One case. One young security guard at a quarantine hotel who tested positive for the coronavirus and experienced minor symptoms.

That was all it took for Perth, Australia’s fourth-largest city, to snap into a complete lockdown on Sunday. One case and now two million people are staying home for at least the next five days. One case and now the top state leader, Mark McGowan, who is facing an election next month, is calling on his constituents to sacrifice for each other and the nation.

Shannon Romano, a molecular biologist, came down with Covid late last March, about a week after she and her colleagues shut down their lab at Mount Sinai Hospital. A debilitating headache came first, followed by a fever that kept rising, and then excruciating body aches. “I couldn’t sleep. I couldn’t move,” she said. “Every one of my joints just hurt inside.”

It was not an experience she wanted to repeat — ever. So when she became eligible for the Covid-19 vaccine earlier this month, she got the shot.

TORONTO — As frustration mounts in Canada at the leaden weight of lockdowns and the glacial pace of vaccinations, a consortium of some of the country’s largest companies has launched a rapid testing program with the aim of protecting their 350,000 employees and publishing a playbook for businesses across Canada on how to reopen safely.

The program is believed to be the first of its kind among the Group of 7 industrialized nations, and has already attracted the attention of the Biden administration.