The authors, led by Justin Kurland of the University of Southern Mississippi, used the number of positive cases not just from the counties where the 32 N.F.L. teams play, but also from surrounding counties to track the spread among fans who may have traveled to games from farther away. After adjusting the figures to eliminate potential false positives and days when counties did not report cases, they found surges in infection rates in the second and third weeks following N.F.L. games that were played with more than 5,000 fans in attendance. The study does not prove a causal link between fan attendance and Covid-19 cases, but suggests that there may be a relationship between the two.

“The evidence overwhelmingly supports that fan attendance at N.F.L. games led to episodic spikes” in the number of Covid-19 cases, the researchers wrote.

Jeff Miller, the N.F.L.’s executive vice president for communications, public affairs and policy, said in an interview that public health officials in cities and states where N.F.L. teams play found no “case clusters” following the 119 games held with fans in attendance. Miller added that a study done by researchers at the M.I.T. Sports Lab, which was unpublished and independent, found no notable increases in Covid-19 infection rates “in the appreciable time frame following the games.” That study also looked at Covid numbers from surrounding counties but compared them to “synthetic” data used as a control group and found little difference between the two sets of numbers.