Frequent screening of healthy, vaccinated people will pick up even the mildest infections. How much testing is too much?On Sunday, officials announced that two players on South Africa’s soccer team had become the first athletes to test positive for the coronavirus inside Tokyo’s Olympic Village. The next day, news broke that an alternate on the American women’s gymnastics team, training outside of Tokyo, tested positive.Another cluster of cases has reportedly popped up on the Czech men’s beach volleyball team. There will be more.“The Olympic Village isn’t the type of lockdown bubble that you saw in the N.B.A.,” said Zachary Binney, a sports epidemiologist at Oxford College of Emory University. “So I think you are going to continue to see cases pop up, including among vaccinated people.”It is too early to judge what impact, if any, the Olympics will have on the Covid-19 pandemic writ large — or if the Games may ultimately fuel larger outbreaks.But the discovery of isolated cases, even in vaccinated athletes, is entirely expected, scientists say, and not necessarily a cause for alarm. “This isn’t really that much of a surprise,” said Angela Rasmussen, a virologist at the Vaccine and Infectious Disease Organization at the University of Saskatchewan.Still, these cases do raise thorny questions about how to design testing programs — and respond to test results — at this phase of the pandemic, in which the patchy rollout of vaccines means that some people and communities are well protected from the virus while others remain at risk.As Dr. Rasmussen put it: “When does a positive test really indicate that there’s a problem?”Counting casesCovid-19 tests, which were once profoundly limited, are now widely available in most of the developed world, making it possible for organizations — including private employers, schools, professional sports leagues and the Olympics organizers — to routinely screen people for the virus.Vaccination is not required for Olympic participants, and officials are relying heavily on testing to keep the virus at bay in Tokyo. Those headed to the Games must submit two negative tests taken on separate days within 96 hours of leaving for Japan regardless of vaccination status, according to the Olympic playbooks, or manuals.At least one of the two tests must be taken within 72 hours of departure. Participants are again tested upon arrival at the airport.Athletes, coaches and officials are also required to take daily antigen tests, which are less sensitive than P.C.R. tests but are generally quicker and cheaper. (Olympic staff and volunteers may be tested less frequently, depending on their level of interaction with athletes and officials.) If a test comes back unclear or positive, a P.C.R. test is administered.“Each layer of filtering is a reduction in the risk for everybody else,” Brian McCloskey, the chair of the Independent Expert Panel of the International Olympic Committee, told reporters this week, adding that the number of confirmed infections so far are “lower than we expected.”But when you look that hard for infections — especially in a group of people who have recently flown in from all over the globe and have had varying levels of access to vaccines — you’re all but destined to find some.“The bottom line is there’s still just a lot of SARS-CoV-2 around the world that’s spreading,” Dr. Rasmussen said, referring to the virus that causes Covid-19.Tennis practice at an empty Ariake Tennis Park on Tuesday.Chang W. Lee/The New York TimesSo far, 75 people with Olympic credentials have tested positive for the coronavirus, including six athletes, according to Toyko 2020’s public database. That number does not include those who tested positive before their departure to Japan. Little information has been released about the severity of most of these cases, though public reports suggest that the athletes are generally experiencing mild or no symptoms.It is also unclear how many of these athletes have been fully vaccinated. The I.O.C. said that it expected 85 percent of athletes, coaches and team staff staying in the Olympic Village to be vaccinated.The vaccines provide strong protection against severe disease, but they are not an impenetrable shield. There have been concerns, in particular, about the effectiveness of China’s Sinopharm and Sinovac vaccines, which some Olympic participants may have received.Some breakthrough infections are inevitable, even with the best vaccines. And these infections, which tend to be mild and rare, are more likely to be caught — and reported — when they crop up in Olympians.“You’re hearing about cases particularly among famous people and athletes because they’re well known, and they’re being tested frequently,” Dr. Binney said. It’s not just Olympians. Last week, six Yankees players tested positive for the virus, at least three of whom were fully vaccinated. It was the second breakthrough cluster on the Yankees. Five fully vaccinated state lawmakers from Texas also tested positive for the virus after racing to Washington last week in an effort to stop the passage of a restrictive state voting rights bill.As expected, most of these cases were apparently mild or even entirely asymptomatic. But P.C.R. tests can detect even minute traces of the virus.“You’re going to pick up on these low-grade infections, and the players are going to be quarantined and out of competition,” said John Moore, a virologist at Weill Cornell Medicine in New York. “And they’re probably not going to be ill, because they’re young, healthy athletes.”According to the Olympic playbooks, athletes with positive P.C.R. tests are to be isolated at designated facilities, though the location and length of isolation vary depending on the severity of the case. Japan’s health authorities require a 10-day quarantine at facilities outside the Olympic Village, and multiple negative P.C.R. tests before discharge, an I.O.C. official said in an email.Some athletes who have been flagged as close contacts of positive cases have also been moved into isolation or quarantine, although they may be allowed to continue training or competing on a case-by-case basis.Those who are cleared to compete may have to adhere to “enhanced countermeasures,” the I.O.C. says, such as eating meals alone, training at a safe distance from others and taking daily P.C.R. tests.Changing courseA testing area of the Olympic media center in Tokyo on Tuesday.Loic Venance/Agence France-Presse — Getty ImagesGiven these kinds of disruptions, some experts say that the benefits of routine testing of asymptomatic vaccinated individuals may not be worth the costs..css-1xzcza9{list-style-type:disc;padding-inline-start:1em;}.css-3btd0c{font-family:nyt-franklin,helvetica,arial,sans-serif;font-size:1rem;line-height:1.375rem;color:#333;margin-bottom:0.78125rem;}@media (min-width:740px){.css-3btd0c{font-size:1.0625rem;line-height:1.5rem;margin-bottom:0.9375rem;}}.css-3btd0c strong{font-weight:600;}.css-3btd0c em{font-style:italic;}.css-w739ur{margin:0 auto 5px;font-family:nyt-franklin,helvetica,arial,sans-serif;font-weight:700;font-size:1.125rem;line-height:1.3125rem;color:#121212;}#NYT_BELOW_MAIN_CONTENT_REGION .css-w739ur{font-family:nyt-cheltenham,georgia,’times new roman’,times,serif;font-weight:700;font-size:1.375rem;line-height:1.625rem;}@media (min-width:740px){#NYT_BELOW_MAIN_CONTENT_REGION .css-w739ur{font-size:1.6875rem;line-height:1.875rem;}}@media (min-width:740px){.css-w739ur{font-size:1.25rem;line-height:1.4375rem;}}.css-9s9ecg{margin-bottom:15px;}.css-uf1ume{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-box-pack:justify;-webkit-justify-content:space-between;-ms-flex-pack:justify;justify-content:space-between;}.css-wxi1cx{display:-webkit-box;display:-webkit-flex;display:-ms-flexbox;display:flex;-webkit-flex-direction:column;-ms-flex-direction:column;flex-direction:column;-webkit-align-self:flex-end;-ms-flex-item-align:end;align-self:flex-end;}.css-12vbvwq{background-color:white;border:1px solid #e2e2e2;width:calc(100% – 40px);max-width:600px;margin:1.5rem auto 1.9rem;padding:15px;box-sizing:border-box;}@media (min-width:740px){.css-12vbvwq{padding:20px;width:100%;}}.css-12vbvwq:focus{outline:1px solid #e2e2e2;}#NYT_BELOW_MAIN_CONTENT_REGION .css-12vbvwq{border:none;padding:10px 0 0;border-top:2px solid #121212;}.css-12vbvwq[data-truncated] .css-rdoyk0{-webkit-transform:rotate(0deg);-ms-transform:rotate(0deg);transform:rotate(0deg);}.css-12vbvwq[data-truncated] .css-eb027h{max-height:300px;overflow:hidden;-webkit-transition:none;transition:none;}.css-12vbvwq[data-truncated] .css-5gimkt:after{content:’See more’;}.css-12vbvwq[data-truncated] .css-6mllg9{opacity:1;}.css-qjk116{margin:0 auto;overflow:hidden;}.css-qjk116 strong{font-weight:700;}.css-qjk116 em{font-style:italic;}.css-qjk116 a{color:#326891;-webkit-text-decoration:underline;text-decoration:underline;text-underline-offset:1px;-webkit-text-decoration-thickness:1px;text-decoration-thickness:1px;-webkit-text-decoration-color:#326891;text-decoration-color:#326891;}.css-qjk116 a:visited{color:#326891;-webkit-text-decoration-color:#326891;text-decoration-color:#326891;}.css-qjk116 a:hover{-webkit-text-decoration:none;text-decoration:none;}“Many places are still continuing to asymptomatically screen fully vaccinated individuals, which isn’t something that the C.D.C. guidance recommends,” said Dr. Amesh A. Adalja, an infectious disease expert at Johns Hopkins Center for Health Security. “It lends itself to all of these kind of pseudo outbreaks that you might see with a bunch of asymptomatic infections.”Testing remains vital for people who have symptoms of Covid-19, he noted. But it no longer makes sense for those who feel fine and have been fully vaccinated, particularly with one of “the big four” vaccines — Pfizer, Moderna, Johnson & Johnson or AstraZeneca — for which there is the most data, he added.But officials may not always know who has been vaccinated and what vaccine they have received, Dr. Rasmussen noted. In those instances, they “really have no choice” but to use testing and contact tracing to minimize risks.Moreover, questions about transmission remain unsettled. Vaccinated people with asymptomatic or breakthrough infections may still be able to pass the virus on to others, but it is not yet clear how often that happens.Until that science is more definitive, or until vaccination rates rise, it is best to err on the side of safety and regular testing, many experts said. At the Olympics, for instance, frequent testing could help protect the broader Japanese population, which has relatively low vaccination rates, as well as the support staff, who may be older and at higher risk.“It’s those folks I’m most worried about, really,” said Dr. Lisa Brosseau, a research consultant at University of Minnesota’s Center for Infection Disease Research and Policy.Not only can they contract the virus, adding strain on the Japanese health care system, but they can also become sources of transmission: “Everybody’s at risk, and everybody could potentially be infected,” she said.According to the Tokyo 2020 press office, all Olympics staff and volunteers have been offered the opportunity to be vaccinated, though officials did not provide data on how many had received the shots.Instead of testing less frequently, officials could rethink how they respond to positive tests, Dr. Binney said. For instance, if someone who is vaccinated and asymptomatic tests positive, he or she should still be isolated — but perhaps close contacts could simply be monitored, rather than being placed into quarantine.“You’re trying to balance the disruptive nature of what you do when somebody vaccinated tests positive against any gains at slowing or stopping the spread of the virus,” Dr. Binney said.Organizations and officials could also adjust their testing protocols, depending on the vaccination rates in a given group and local virus transmission levels. If most people are vaccinated and the virus is circulating at low levels, officials and managers could decide to test less often or use a less sensitive test, said Andrew Pekosz, a virologist at the Johns Hopkins Bloomberg School of Public Health.At this stage of the pandemic, there is room to be more strategic about testing, said Michael Mina, an epidemiologist at Harvard T.H. Chan School of Public Health who called for widespread rapid testing when the virus hit last year.“I think testing is never going to go away as a way to know what’s happening with the virus,” he said, noting that it remains particularly important as a strategy for controlling outbreaks.“We can do the frequent testing when we need to, but only when we need to, because people are tired,” he added. “And it can be considered a very dynamic process.”