In a perfect world, the entrance to every office, restaurant and school would offer a coronavirus test — one with absolute accuracy, and able to instantly determine who was virus-free and safe to admit and who, positively infected, should be turned away.

That reality does not exist. But as the nation struggles to regain a semblance of normal life amid the uncontrolled spread of the virus, some scientists think that a quick test consisting of little more than a stinky strip of paper might at least get us close.

The test does not look for the virus itself, nor can it diagnose disease.

Rather, it screens for one of Covid-19’s trademark signs: the loss of the sense of smell. Since last spring, many researchers have come to recognize the symptom, which is also known as anosmia, as one of the best indicators of an ongoing coronavirus infection, capable of identifying even people who don’t otherwise feel sick.

A smell test cannot flag people who contract the coronavirus and never develop any symptoms at all. But in a study that has not yet been published in a scientific journal, a mathematical model showed that sniff-based tests, if administered sufficiently widely and frequently, might detect enough cases to substantially drive transmission down.

Daniel Larremore, an epidemiologist at the University of Colorado, Boulder, and the study’s lead author, stressed that his team’s work was still purely theoretical. Although some smell tests are already in use in clinical and research settings, the products tend to be expensive and laborious to use and are not widely available. And in the context of the pandemic, there is not yet real-world data to support the effectiveness of smell tests as a frequent screen for the coronavirus. Given the many testing woes that have stymied pandemic control efforts so far, some experts have been doubtful that smell tests could be distributed widely enough, or made sufficiently cheat-proof, to reduce the spread of infection.

“I have been intimately involved in pushing to get loss of smell recognized as a symptom of Covid from the beginning,” said Dr. Claire Hopkins, an ear, nose and throat surgeon at Guy’s and St. Thomas’ Hospitals in the United Kingdom and an author of a recent commentary on the subject in The Lancet. “But I just don’t see any value as a screening test.” A reliable smell test offers many potential benefits. It could catch far more cases than fever checks, which have largely flopped as screening tools for Covid-19. Studies have found that about 50 to 90 percent of people who test positive for the coronavirus experience some degree of measurable smell loss, a result of the virus wreaking havoc when it invades cells in the airway.

“It’s really like a function of the virus being in the nose at this exact moment,” said Danielle Reed, the associate director of the Monell Chemical Senses Center in Philadelphia. “It complements so much of the information you get from other tests.” Last month, Dr. Reed and her colleagues at Monell posted a study, which has not yet been published in a scientific journal, describing a rapid smell test that might be able to screen for Covid-19. In contrast, only a minority of people with Covid-19 end up spiking a temperature. Fevers also tend to be fleeting, while anosmia can linger for many days. Translating theory into practice, however, will come with many challenges. Smell tests that can reliably identify people who have the coronavirus, while excluding people who are sick with something else, are not yet widely available.