Recently seven states struck a deal to jointly purchase three million antigen tests, which look for viral proteins and return results in minutes. To detect infection, they require that more of the virus be present than P.C.R. tests do, but, Mina says, they may be able to “capture the vast majority of people at risk of spreading it at the time that they’re taking it.” He adds, though: “It doesn’t mean you’re not going to be positive tomorrow or that you weren’t positive yesterday.”

To filter out enough asymptomatic carriers to reduce overall infection rates, such rapid tests would need to be given every few days, focusing first, when supplies are limited, on groups with the highest risk of spreading the virus. “Imagine that you go to the airport and check your bags and then you spit in a tube,” Larremore told me. If your test is positive, you can’t fly and are sent for a diagnostic follow-up. A system like that, he says, even if set up by individual companies or schools, would reduce spread and free up more P.C.R. tests for people with symptoms: “Every little bit helps here.”

Compared with a diagnostic test, a screening test would give the taker no definitive health information; being identified as infected would incur costs like lost wages. But, Larremore says, we shouldn’t underestimate the value of giving information to someone that “allows you to protect people around you.” If we could act on that knowledge immediately, testing positive, instead of being the frightening news it often is now, could actually be, Larremore says, “really empowering.”