On any digital dashboard tracking the spread of Covid-19, on any graphic comparing country-by-country case curves or death tolls, they were the champs. Singapore, Hong Kong, Taiwan, South Korea—leaders there saw what was headed their way from China in the early days of the new coronavirus, before it became a pandemic. They remembered what happened two decades ago with SARS: People died, economies suffered. So they locked down their immigration hardest and soonest, deployed public health workers to follow up contacts of cases, got their hospitals shored up, and started publishing clear and consistent information and data. They flattened their curves before the rest of the world understood there would be curves to flatten. But in recent weeks, those curves have taken another chilling turn. The numbers of new cases in these places are creeping upward.

Hong Kong’s slow and steady case count started going up on March 18, and took an 84-case jump on March 28. After months of new cases barely brushing double digits, Singapore’s count jumped by 47 on March 16, and since then the city-state has had three days with more than 70 new cases each. Taiwan’s new-cases-in-a-day peaked at 5 in late January … and then jumped into the high 20s per day in, again, mid-March. South Korea had 86 new cases on April 3.

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These new case numbers are still low, especially compared with the United States, which had 983 new cases on March 16 and 29,874 new cases on April 2 … or Italy, which (hopefully) peaked on March 21 with 6,557 new cases. What’s alarming about the numbers of new cases in the would-be success-story locations is that they’re happening at all—that the numbers were going down, and now they’re creeping up. From the outside, that looks like a worst-case scenario: the return of the disease after a country eases off the measures to combat it. But that appearance is deceiving. The bad new numbers come from somewhere else—literally. And that might have lessons for the next phase of the pandemic in the US.

The real problem is that viruses don’t know what a border is. These countries are experiencing “reimportation” of the disease, infections that are the result of inbound travelers from places that aren’t winning their fight against Covid-19.

All these countries are, after all, on the same planet. In Singapore, Hong Kong, South Korea, and Taiwan, a few earlier cases from China made it through the barrier and got into the community. That resulted, throughout February, in community infections, or “unlinked local cases.” Those were worrying, but the overall spread was still slow—until the pandemic went transnational, and boomeranged back around. “There were just a small number, and then they kind of disappeared,” says Ben Cowling, an epidemiologist at the University of Hong Kong. “But at the end of February and early March we started to get more imported cases from Europe. Hong Kong got a lot from Europe, the US, and other parts of the world, and Taiwan got a lot from the US.”

Those all led to a bunch of new unlinked local cases, and the numbers started going up again. In Taiwan, for example, “they prolonged the winter break for kids by 10 days so they could prepare kids to go back to school with masks. A lot of people went to Europe for vacation, and they came back with it,” says Jason Wang, director of the Center for Policy Outcomes and Prevention at Stanford University School of Medicine and an author of a paper on Taiwan’s early successes. “We did stop all the flights from China before the WHO said we should. But then after we did that, we didn’t do too much. So it was brewing in the community, and now we have community spread. And then people started to come back from Europe, and we didn’t even think about that.”