WASHINGTON — Earlier this month, the conservative radio host Dennis Prager announced he had contracted the coronavirus. This was, as far as he was concerned, good news. The unvaccinated Prager had hoped to protect himself against COVID-19 the old-fashioned way: by getting sick.

“It is infinitely preferable to have natural immunity than vaccine immunity,” Prager said, echoing an anti-vaccine argument echoed by Florida Gov. Ron DeSantis and other pro-Trump figures who have turned coronavirus vaccination into a culture war that, public health officials say, could prolong the pandemic for everyone.

Prager is wrong, suggests a new study published on Friday by the Centers for Disease Control and Prevention that finds that