Among the more than 75 million people fully vaccinated against COVID-19 in the United States by the second week of April, there were only 5,814 reports of coronavirus infections — a staggeringly low number that shows just how effective the shots are.

Because the vaccines aren’t 100 percent effective, some breakthrough infections were inevitable and expected. Still, the Centers for Disease Control and Prevention is watching them closely. Studying those cases will help experts make sure the vaccines are working as expected and understand any factors that make it more likely that a vaccinated person would get sick.

Currently, the CDC has a national database where state health departments can send reports of any cases of COVID-19 in people who have been vaccinated. Because COVID-19 is a notifiable disease, which means every case has to be reported to the CDC, the agency will eventually use a different system, called the National Notifiable Diseases Surveillance System (NNDSS) to find breakthrough infections. Right now, it’s working to make sure that states can include vaccination history in NNDSS reports.

Almost a third of the breakthrough infections reported to the CDC were asymptomatic. Only 396 people were hospitalized, and a third of that group was in the hospital for a reason other than COVID-19 — that is, the disease was not the reason they were seriously ill, they just happened to also test positive for the virus.

“Most of those have been mildly symptomatic or asymptomatic. That’s exactly what we were hoping for,” Tara Smith, a professor of epidemiology at the Kent State University College of Public Health in Ohio, told NBC News.

Two new reports from the CDC published today gave more details about outbreaks of COVID-19 in vaccinated people. One described a Kentucky nursing home where 90 percent of residents and around half of staffers were fully vaccinated. After an unvaccinated staffer came down with COVID-19, a total of 46 people tested positive for the virus. Four cases were in fully vaccinated staffers and 18 were in fully vaccinated residents.

Notably, the Kentucky outbreak was linked back to a variant form of the coronavirus referred to as the R.1 lineage. It has a number of mutations in common with the variant viruses first identified in South Africa and Brazil, which experts think might partially evade antibodies produced by the vaccines.

The infections by the R.1 virus found in vaccinated people support some of those concerns, the CDC said in its report. But the vaccines still worked: unvaccinated nursing home residents were three times as likely to get infected during the outbreak as vaccinated residents. During this outbreak, the shots were around 87 percent effective against symptomatic COVID-19, the report found.

The second report tracked infections in vaccinated people at 75 Chicago nursing homes. Across nearly 8,000 vaccinated residents and 7,000 vaccinated staffers, there were only 22 coronavirus infections. Fourteen were asymptomatic and five had only mild symptoms. None of the 22 people appeared to pass the infection on to anyone else. That shows how important high levels of vaccination can be in settings like nursing homes, the report noted. Even if a vaccinated person gets sick, they’re not likely to set off a chain of infections that could spread through a facility.

That’s key in stopping the spread of disease overall. People who have their shots might still get sick, even though it happens very rarely, but they probably won’t pass the virus to anyone else.

Vaccinated people who get COVID-19 may find the experience disorienting, but the close investigations into the circumstances around these cases highlight just how powerful the vaccines are. Over half of adults in the US have had their first dose of a COVID-19 vaccine. As more and more people get vaccinated, the pool of people who will catch COVID-19 steadily shrinks, and less of the virus will circulate around a community. And when levels of the virus drop, vaccinated and unvaccinated people alike are less likely to be exposed to it and less likely to catch it themselves.