It’s a question of simple arithmetic: As more people get vaccinated, we expect more breakthrough infections in vaccinated people. Imagine a world where 100 percent of people were immunized. In that scenario, 100 percent of infections would be in vaccinated individuals, even if their likelihood of being infected in the first place had been dramatically lowered by getting the shots.

Many people already know someone who’s tested positive for COVID-19 after being fully vaccinated. If you don’t, you likely soon will. If only 1 percent of the 165 million fully vaccinated Americans have a breakthrough infection, that’s still 1.6 million people.

In Israel, data show that vaccine efficacy may have dropped to 64 percent, down from 95 percent in clinical trials. But other data from England, India, and Canada show that efficacy against Delta is still greater than 87 percent. Even if the exact efficacy isn’t certain, one thing is: You can still get infected with coronavirus after you’re fully vaccinated. But the likelihood is low. And compared with infections in the unvaccinated, these breakthrough infections are more likely to be asymptomatic. For the people who do experience symptoms, they’ll likely have fewer of them than the unvaccinated.

Moreover—and this was a source of widespread confusion in the wake of the Provincetown outbreak—even if vaccinated people with breakthrough infections harbor as much virus as infected unvaccinated people, vaccinated people still collectively lower spread, given that they’re much less likely to get infected in the first place.