Labs across the country are facing backlogs in coronavirus testing thanks in part to a shortage of tiny pieces of tapered plastic.

Researchers need these little disposables, called pipette tips, to quickly and precisely move liquid between vials as they process the tests.

 The number of people infected with the coronavirus in different parts of the United States was anywhere from two to 13 times higher than the reported rates for those regions, according to data released Tuesday by the Centers for Disease Control and Prevention.

The findings suggest that large numbers of people who did not have symptoms or did not seek medical care may have kept the virus circulating in their communities. The study is the largest of its kind to date, although some early data was released last month.

“These data continue to show that the number of people who have been infected with the virus that causes Covid-19 far exceeds the number of reported cases,” Dr. Fiona Havers, the C.D.C. researcher who led the study, said in an email. “Many of these people likely had no symptoms or mild illness and may have had no idea that they were infected.”

In the heated debate over reopening schools, one burning question has been whether and how efficiently children can spread the virus to others.

A large new study from South Korea offers an answer: Children younger than 10 transmit to others much less often than adults do, but the risk is not zero. And those between the ages of 10 and 19 can spread the virus at least as well as adults do.

The findings suggest that as schools reopen, communities will see clusters of infection take root that include children of all ages, several experts cautioned.

“I fear that there has been this sense that kids just won’t get infected or don’t get infected in the same way as adults and that, therefore, they’re almost like a bubbled population,” said Michael Osterholm, an infectious diseases expert at the University of Minnesota....