Both patients were dairy workers whose illnesses were mild. Investigators are continuing to evaluate the contacts of a Missouri patient who had no exposure to animals.

Two more people were diagnosed with bird flu this week, even as scientists in Missouri continued to investigate a possible cluster of infections in that state, federal health officials said at a news briefing on Friday.

In California, two farmworkers who were exposed to infected dairy cattle at different farms tested positive for the virus, called H5N1, state health officials said on Thursday. Those cases bring the total this year to 16, not including those under investigation.

The cases do not come as a surprise, because the number of infected herds in California has risen to 56 from 16 two weeks ago, said Dr. Nirav Shah, the principal deputy director at the Centers for Disease Control and Prevention.

“As there are more herds that test positive, there are more workers who are exposed, and where there are more workers who are exposed, the chances of human infection increase,” he said. The risk to the public remains low, he added.

Still, experts said that the appearance of H5N1 in multiple states was worrisome.

Flu viruses are adept at acquiring new abilities by swapping their genes. As the flu season swings in, even one person who becomes infected with both bird flu and the seasonal flu virus could help H5N1 to gain the ability to spread as readily among people as seasonal flu does.

Given the many variables, it’s difficult to gauge the true risk of the virus mutating into a more contagious form, said Jesse Bloom, an evolutionary biologist at the Fred Hutchinson Cancer Center in Seattle.

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