Texans love to brag that everything is bigger in their state. The land, the food and, this year, the size of the crowds at Dallas Cowboys games.

The team’s five home games have drawn a total of 128,750 fans, by far the most of any N.F.L. team and nearly 20 percent of the entire league’s reported attendance. The team counted 30,048 fans at AT&T Stadium in Arlington, Texas on Thursday, when the Cowboys, as they have nearly every year since 1966, played at home on Thanksgiving, this time against the Washington Football Team.

To control the spread of the coronavirus, state rules limit attendance at the stadium to half its capacity of over 100,000, and no game has approached that limit. Still, attendance has grown, hitting a high of 31,700 on Nov. 8, when the Pittsburgh Steelers were in town. Jerry Jones, the team owner, plans to keep selling tickets even as the number of coronavirus infections surges in Tarrant County, where the Cowboys play home games.

“My plan was to increase our fans as we went through the season and move the number up, and we followed that plan,” Jones said last week on Dallas sports talk radio. “I see a continued aggressive approach to having fans out there. And that’s not being insensitive to the fact that we got our Covid and outbreak. Some people will say maybe it is, but not when you’re doing it as safe as we are and not when we’re having the results we’re having.”

Local and state authorities have ultimate authority over whether fans can attend games, and the rules in Texas are more permissive than in states like California and New Jersey, where teams have played without spectators this season.

But Jones’s “aggressive approach” runs counter not just to what other N.F.L. teams have done in recent weeks, but to what medical experts say is prudent public health. The number of cases in the county has jumped more than fivefold since the start of the regular season in early September, when there was an average of 1,500 confirmed infections a day. The number of people hospitalized with the coronavirus has more than tripled over that period.

And last week, health officials in Tarrant County said that eight residents who tested positive for the virus told contact tracers that they had recently attended Cowboys home games. It is unclear whether they were infected before, during or after the games. The actual number may be higher because of how difficult it is for contact tracers to determine the source of an infection where the virus is spreading rapidly.

The increasing number of cases locally, coupled with more people indoors in the colder weather, prompted the Tarrant County health director, Dr. Vinny Taneja, to warn residents against attending large gatherings.

“Whether it’s a sporting event, whether it’s a demonstration or any other large public gathering, there’s always somebody there who has Covid,” Taneja said at a briefing last week. “No matter how hard you try, people are people. They’re there to celebrate, they’re there to have a good time. You’re going to have some spread occur.”

Some N.F.L. teams that had opened their gates to fans have reversed course as cases of the virus skyrocket. The Denver Broncos, for instance, got clearance in October from the Colorado Department of Public Health and Environment to have around 5,700 spectators at Mile High Stadium, but the team said last week that rising cases in the area forced them to go back to playing home games without fans. Other teams like the Baltimore Ravens, facing a team-wide outbreak that shut down practices on Monday and Tuesday, stopped admitting fans altogether, at least temporarily.

Fourteen of the N.F.L.’s 32 teams, from the Buffalo Bills to Seattle Seahawks, have not had spectators this year. Another 10 teams have allowed no more than 10,000 fans at a game, and some have welcomed fans for only one or two games. The Houston Texans, who face similar capacity limits as the Cowboys and are subject to the same state orders, have averaged 12,400 fans at their games, half as many as there are at Cowboys games.

To determine whether to permit fans in the stadiums, the N.F.L.’s chief medical officer, Dr. Allen Sills, said the league and its teams, along with local authorities and the league’s infectious disease consultants, review data on positivity rates, the number of people hospitalized with Covid-19, the disease caused by the coronavirus, and deaths from the virus in the regions where the teams play.

“We do that not just for Dallas,” Sills told reporters last week. “We try to look at the data in each point in time and make what we think is the safest decision. That’s a collaborative decision that’s not made strictly by us in the central New York office.”

But absent any prohibition from a local government, the decision ultimately rests with team owners.

Jones said his team has taken steps to reduce the chance of infection. The air conditioning in AT&T Stadium, which is domed, pulls in fresh air from outside and all air filters in the stadium were replaced and upgraded before the season. The giant doors behind the end zones have been open every game so a breeze can blow through. The retractable roof has been open the past two games and was open on Thursday.

Similar to measures other teams have been taking to minimize contact, fans in Dallas must sit in small groups, or pods, with friends and family, and wear masks except when eating or drinking. Concession stands no longer accept cash and paper tickets have been eliminated. Cars parked in lots designated for tailgating must have an empty space on either side, and parties should not commingle.

But the team has not set a limit on attendance as long as it doesn’t exceed 50 percent of the stadium’s capacity, and the number of fans at each game depends on how many season ticket holders decide to come and how many single-game tickets are purchased.

Dr. Sonja Bartolome, a critical care doctor and an infectious disease specialist at the University of Texas Southwestern Medical Center in Dallas, called attending games in large stadiums a medium risk relative to the parties, weddings and funerals in indoor venues to which she has traced positive cases. “We’re lucky the stadium is huge because it allows them to put people at a safer distance and there’s a lot of air circulation,” she said.

Still, with another 17,000 projected deaths among Texans between now and March 1, other experts were more skeptical.

“Maybe they’re not looking down the line enough and not understanding what’s in store for Dallas,” Dr. Peter Hotez, the dean of the National School of Tropical Medicine at Baylor University, said of the Cowboys. “If they were, they’d stop it because it’s going to get a lot worse. I understand football is like religion, but this is not the time to be having fans at games.”