MACHIPONGO, Va. — Health officials on Virginia's Eastern Shore are increasingly worried that clusters of coronavirus tied to two poultry plants may overwhelm the one local hospital, even as the Trump administration insists such facilities remain open to keep the country fed during the crisis.

The chicken plants, one operated by Perdue Farms, the other by Tyson Foods, have continued operating as the number of cases linked to them climbed in the past week, according to health officials. Hospital officials said Tuesday that there are nearly 100 cases of Tyson employees or people who came in contact with them contracting covid-19, while the Perdue plant has about 80 such cases.

The concerns about chicken-processing facilities in Virginia come amid a larger national debate about the safety of workers in the meat industry, which has seen eruptions of coronavirus and tensions between health officials who have ordered some sites closed to prevent further infection, and industry officials who say they need to stay open to feed the country.

The coronavirus numbers on the Eastern Shore are small compared with big cities, but in rural areas it does not take nearly as many cases to overwhelm local health-care facilities.

“Something needs to be done to reduce the spread of the infection,” said Michael Dacey, president and chief operating officer of Riverside Health System, which operates the only hospital in Accomack County, where the two chicken plants are located.

That hospital, Riverside Shore Memorial, has 52 beds, six of them for patients in the intensive care unit. On Tuesday, five of those six beds were in use, and the hospital had already sent about 10 patients to a larger hospital hours away.

“We’re quite concerned,” said Dacey. “My worst fear of what could happen is running out of resources in the middle of the night or anytime you can’t quickly backstop medical resources, whether it’s people or equipment or physical space.”

Dacey wrote to state health officials last week urging “decisive action” to contain the spread. Both Perdue and Tyson have declined to say how many of their employees at the facilities have covid-19, the disease caused by the coronavirus, but said they are taking extra precautions to try to prevent its spread. On Friday, Tyson closed the facility for a three-day cleaning, and employees were back at work on the line Monday, officials said.

The two facilities combined employ more than 3,000 people, and the covid-19 cases linked to those plants make up a majority of the cases in the county, according to health officials.

Meat-processing plants in other parts of the country have been coronavirus hot spots, and health experts suspect that is in part because workers operate in proximity to each other in enclosed spaces. At least 20 meatpacking plants have closed in recent weeks because of the outbreaks, and at least 17 workers have died of covid-19.

Industry leaders have warned the nation’s meat supply is in danger. “The food supply chain is breaking,” John H. Tyson, chairman of Tyson’s executive board, wrote in a full-page newspaper ad published in The Washington Post, the New York Times and the Arkansas Democrat-Gazette on Sunday.

In response to such warnings, President Trump signed an executive order Tuesday mandating that meat production plants remain open to stave off a food shortage.

Trump invoked the Defense Production Act, which classified the meat plants as essential infrastructure that must remain open. The federal government will provide additional protective gear for employees as well as guidance.

Sen. Charles E. Grassley (R-
Iowa) praised the president’s decision, raising the specter of riots if there was a lack of meat in the country, and saying the federal government should give meat industry workers protective gear and testing.

Tyson spokesman Gary Mickelson said the company’s “top priority remains the safety our team members and plant communities while we work to continue fulfilling our role of feeding families across the country.” The company said it is in regular contact with local health officials about their concerns.

Perdue spokeswoman Diana Souder said the company has “fully implemented incremental safety measures,” including face masks, temperature checks and temporary partitions between workers. “Perdue continues to regulate strict preventive safety and sanitation standards in all our facilities,” she said. “We continue to look for additional protective measures we can employ to protect our associates in our essential role to help keep our country fed.”