COVID-19 infections have been reported in just a tiny fraction of Americans who have been fully vaccinated against the disease, according to a survey Tuesday by the U.S. Centers for Disease Control and Prevention.

The study looked at so-called vaccine breakthrough infections reported to the CDC from January 1 through April 30. The CDC defines vaccine breakthrough infections as detection of the coronavirus in respiratory samples taken from a person two weeks or more past the final vaccine dose.

With more than 101 million Americans fully vaccinated as of April 30, the survey found 10,262 reports of breakthrough infections among the immunized across 46 U.S. states and territories, which comes to 0.01%.

“Even though FDA-authorized vaccines are highly effective, breakthrough cases are expected, especially before population immunity reaches sufficient levels to further decrease transmission,” the study said. “However, vaccine breakthrough infections occur in only a small fraction of all vaccinated persons and account for a small percentage of all COVID-19 cases.”

The report said 63% of the breakthrough cases were in women. The median patient age was 58.

Of the breakthrough cases, preliminary data indicated that 2,725, or 27%, were in people showing no symptoms of COVID-19, the study said.

A total of 995 of the infected, or about one in 10, were hospitalized, but 289 of them, or 29%, were asymptomatic or hospitalized for a reason unrelated to COVID-19, the study said.

A smaller number of the patients, 160, or 2%, died, with a median age of 82. But the study said that 28 of them, or 18%, were asymptomatic or died from a cause unrelated to COVID-19.

CDC spokeswoman Martha Sharan said many states were not able to collect symptom status for all cases, “which makes it challenging to determine relatedness or causality.”

“Therefore, we only eliminated the proportion of cases that were known to be unrelated to COVID-19,” Sharan said. “We cannot say what proportion of the cases are specifically due to COVID-19.”

The report said data on variants of the coronavirus were available for 555, or 5% of the reported cases, and that 356, or 64% of those, were identified as “variants of concern.” Those included 199 of the B.1.1.7 variant first discovered in the United Kingdom; 88 of the B.1.429 and 28 of the B.1.427 variants, both of which were first recognized in California or the West Coast; 28 of the P.1 variant that came to life in Brazil; and 13 of the B.1.351 variant widespread in South Africa. The study said the proportion of those variants of concern reflects their presence in the U.S.

The report comes as the vaccines have become widely available to anyone in the U.S. who is 12 years and older, and as demand for the shots has softened, prompting federal, state and local officials try to encourage more people to get vaccinated to reach a level of “herd immunity” where the virus has difficulty spreading.

Today more than 130 million U.S. residents, or 39% of the total population, are fully vaccinated, and 164 million, or 49%, have received at least one dose. In California, more than 16 million, or 42% of the total population is fully vaccinated. The Pfizer and Moderna vaccines require two shots three to four weeks apart, while the other authorized vaccine by Johnson and Johnson requires one shot.

The CDC noted that the number of reported COVID-19 vaccine breakthrough cases “is likely a substantial undercount” of all infections among fully vaccinated persons because the national surveillance system “relies on passive and voluntary reporting,” and many with vaccine breakthrough infections, especially those who are asymptomatic or who experience mild illness, might not seek testing.

But Sharan said the study still demonstrates the value of vaccination in reducing COVID-19 risk.

“While the number of cases reported to CDC is likely an undercount, vaccine breakthrough cases are very rare, and severe outcomes like hospitalization and death are even more rare,” Sharan said, adding that data reported to CDC about such cases provide a snapshot and help scientists identify patterns. “Importantly, there have been no concerning patterns detected among reported cases.”