Severe Covid is rare in people who have been fully vaccinated. In a paper published last month, the Centers for Disease Control and Prevention said that it had received reports of 10,262 breakthrough infections by April 30. That is just a tiny fraction of the 101 million Americans who had been vaccinated by that date, though the agency noted that it likely represented “a substantial undercount” of breakthrough infections. Of those breakthrough cases, 10 percent of patients were hospitalized and 2 percent died — and in some of those cases, patients were hospitalized or died from something unrelated to Covid-19. The median age of those who died was 82. Older adults, who are at greater risk for Covid complications, may also be more likely to develop breakthrough infections because they are known to mount weaker immune responses to vaccines. People who are immunocompromised or have other chronic health conditions may also be at increased risk.