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.

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.”

Until then, Singapore, Hong Kong, and Taiwan had all been able to maintain diligent containment within their own borders, following every infection—or nearly every infection, as it turned out—back through its chain of contacts and isolating all those people from the general population. Taiwan had linked its immigration database to its national health system. Singapore had instituted harsh fines for anyone breaking social distancing and published detailed data on every case and cluster. “The problem is, you don’t pick up every single person, especially when the people with mild symptoms know if they get tested they’re going to be isolated, and their friends and family are going to be isolated,” says Cowling. “There’s a disincentive.” That’s especially bad with Covid-19, which seems to spread in part because of a few days of pre-symptomatic infectiousness before the onset of heavy illness.

Other nations couldn’t hold containment, or didn’t try. In Europe and the United States, governments dithered about whether and when to institute draconian but necessary measures like social distancing, school closures, and shelter-in-place orders. Now those same governments and public health researchers have to figure out how long to maintain them. They’re destructive to people’s psyches and the economy, but letting people swirl back into close contact with one another allows the disease to spread again.

In epidemiological terms, this tension is about taking control of what’s called the reproductive number, the number of people a contagious person goes on to infect. At the top of the curve in Wuhan, where Covid-19 started to spread, that number was something like 2 or 2.5—as it might now be in parts of the US and Europe. After the Chinese government quarantined Wuhan and forced everyone to stay home, it went down to perhaps as low as 0.3. In China, those rules went into effect in January; the government may lift them this week.

The virus’s apparent return will spur different kinds of containment measures in different places. Hong Kong’s were already strict, though they’d relaxed somewhat in the first weeks of March. Now, Singapore, Hong Kong, South Korea, and Taiwan have all instituted even stricter social distancing rules and immigration controls. Nationals who are allowed in can expect 14-day quarantines, in Hong Kong and Singapore monitored by smartphone app, though those apps’ efficacy may be doubtful. (Singapore’s numbers do seem to look better since officials started quarantining everyone coming in, rather than people from specific countries.) Singapore is also closing all schools and most workplaces.

Despite the resurgences, these places are all still roughly in the containment phase of dealing with the pandemic, tracing individual cases and contacts—or some transitional phase that combines containment and the next step, mitigation, including social distancing measures, school and workplace closures, and canceling mass gatherings. The US and Europe are well into mitigation, riding the exponential curve upward. “Right now they’re in different parts of the graph,” Wang says. “When it’s near the peak, and you have to manage it, you start to do as much of the mitigation strategy as possible, so you flatten the curve. Then you try to wait and see where you are, and if you lift it too early, you get a resurgence.”

For the US, that’s a scary warning. The peak numbers could be terrifying, and they’ll certainly vary across hot spots. But once the peak is passed? Hundreds of millions of people can’t stay socially distanced forever. Despite the new cases, Singapore, Hong Kong, and Taiwan are still keeping their reproductive numbers around 1—a slow enough spread to follow cases and contain flare-ups. “That may be the long-term strategy for the US and Europe,” Cowling says. “There’s two approaches, maybe. One is test, test, test. Identify cases, isolate them, stop transmission of them into the community. But it’s always difficult to catch every infection, especially the mild ones. So the other approach that is necessary, really important, is to maintain some social distancing.”

The nice thing about this goal—get that number hovering down to 1—is that it might actually make for a more pleasant country. Schools could reopen, but only with better ventilation and smaller class sizes. Polling places for the election would have to be plentiful enough, and big enough, to give everyone room and make sure they aren’t packed into queues. Stores and restaurants could reopen. People’s work hours would have to be flexible enough that offices and factories wouldn’t be packed, and commute times would be smeared out to prevent crowded buses and subways. A good blood test for Covid-19 antibodies could determine who’s immune and could help everyone else get back to a more normal life.

“For the second wave, what we would like to happen is, if there is a growth, it’s much slower,” Cowling says. “Coronavirus is not going away. We’re not going to eliminate it. We’re going to have to face the prospect that it is always going to be around, but hopefully in small numbers until we can identify an effective treatment or vaccine.” It’s a hopeful idea—that doing all the things that slow the virus enough for a public health system to fight it also builds a world even better than the one everyone fled.