Older children are more likely to spread COVID-19 within a household than younger children and adults, according to a new study of 5,706 coronavirus patients in South Korea.

The researchers traced and tested nearly 60,000 people who had contact with the infected people and found that, on average, 11.8 percent of household contacts tested positive for COVID-19, according to the early release of a study published on the U.S. Centers for Disease Control and Prevention website.

For people who lived with patients between the ages of 10 and 19, 18.6 percent tested positive for the virus within about 10 days after the initial case was detected — the highest rate of transmission among the groups studied. Children younger than 10 spread the virus at the lowest rate, though researchers warned that could change when schools reopen.

The study comes on the heels of an intensifying debate about whether, when and how schools should resume classes. Working parents around the world have been struggling to balance their own remote work with the added complication of school closures. There is intense pressure on political leaders. In the U.S., the Trump administration has threatened to withhold federal funds for local school districts that fail to reopen.

At the same time, virus rates have been rising again, even in places that thought they’d extinguished their outbreaks, and many teachers are wary of returning to the classroom. State data suggests the infection rates among children could also be far higher than the 2 percent reported by the CDC.

The South Korean study suggests that older children may be particularly contagious, although the researchers point out that household contacts could have contracted the virus elsewhere. Still, given the high rates of infection within families, the study called for more research to understand how to limit the spread of the virus at home.