There’s been a spike in coronavirus cases at meat plants in the U.S., with hundreds of reported infections in just the last week.

That’s adding to questions over the fragility of the food-supply chain and raising concerns over worker safety.

As many as 50 people at a JBS SA beef facility in Colorado’s Weld County tested positive, adding to more than 160 cases at a Cargill Inc. meat-packaging plant in Pennsylvania, union officials said on Friday.

South Dakota Governor Kristi Noem on Friday reported 190 cases at a Smithfield Foods Inc. pork facility, the Associated Press said. The Cargill and Smithfield plants are being shuttered, while JBS said it will continue operations.

Workers are also starting to die. Two more deaths were reported by union officials on Friday, one at the Greeley, Colorado meat plant and one in Pennsylvania. Both those facilities are owned by JBS SA, the world’s top meat producer, which didn’t confirm the deaths.

“As our communities and our country collectively face the coronavirus challenge, JBS USA has had team members impacted by COVID-19,” the American unit of the Brazilian meatpacker said in an emailed statement. “We are offering support to those team members and their families. Out of respect for the families, we are not releasing further information.”

While it’s unclear whether the deaths and other cases have anything to do with the workplaces, the news exposes the vulnerability of global supply chains that are needed to keep grocery stores stocked after panic buying left shelves empty.

President Donald Trump and Vice President Mike Pence both addressed the sudden jump in cases at meat plants when speaking to reporters on Friday.

Mr. Pence said as many as 300 people have been “impacted” by the coronavirus at the Colorado meat plant. It’s unclear what that figure was referring to, whether it was people who have been quarantined, or possible cases.

Trump also referred to the outbreak at Colorado meat plants on Friday. Neither Pence nor Trump specified exactly which plant they were talking about.

Plants across the U.S. are starting to reduce output or idle as cases spread from the main cities to rural America.

Laborers have, in some cases, staged walk-outs to protest working conditions.

In meat plants, stations on processing lines can be close together, creating challenges for social distancing. Workers share break and locker rooms.

The deaths reported Friday bring the total reported for JBS employees to three.

On Tuesday, the Retail, Wholesale and Department Store Union, which represents thousands of poultry workers, said two of its members working at a Tyson Foods Inc. plant in Camilla, Georgia, died from the virus.

Smithfield said it will close its South Dakota plant for three days. The company will suspend operations in a large section of the plant on April 11 and completely shutter on April 12 and April 13. The facility has 3,700 employees.