The chief of the nation’s largest pork producer raised an alarm about food supplies in announcing the indefinite closure of its massive slaughterhouse in Sioux Falls this weekend, but plenty of other plants remain open with nearly a half million pigs arriving at them daily.

Smithfield Foods Inc. on Sunday said its Sioux Falls plant, shuttered last Thursday initially for three days, would remain closed after a count of COVID-19 cases among its 3,700 workers jumped from 80 to nearly 300.

The company’s chief executive, Kenneth Sullivan, said reduced meatpacking capacity is “pushing our country perilously close to the edge in terms of our meat supply. It is impossible to keep our grocery stores stocked if our plants are not running.”

The disruption is an unfolding disaster for hog farmers, who made decisions months ago about how many pigs to raise. Hog prices have plunged in recent weeks as demand for pork, notably bacon, dropped because so many restaurants closed as part of the effort to slow the spread of the virus.

The same dynamic is playing out in the beef market, with some plants closing or cutting production.

But experts in the food supply chain say it’s premature to worry about availability for consumers. Most processing plants are operating at full strength. And the decline in restaurant dining means that more food is available to be sold through groceries. Additionally, for pork, supplies in cold storage have risen recently.

The Smithfield facility, for decades a Sioux Falls landmark under the John Morrell name, is the nation’s ninth-largest by capacity, processing about 19,500 hogs a day. It is the second-largest in Smithfield’s U.S. operations, behind one in Tar Heel, N.C., that processes 34,500 hogs a day and is the country’s biggest. Smithfield is owned by China’s WH Group Ltd., which has pork operations around the world.

A half-hour away from Sioux Falls, the JBS plant in Worthington, Minn., the country’s third-largest processing site, has not had a single case of COVID-19 among its workers, said Matt Utecht, the president of United Food and Commercial Workers Local 663, which represents 1,850 workers at the plant.

“One of the reasons there hasn’t been a positive test is the employer was one of the first to implement taking temperatures of all workers,” Utecht said. “We had gloves, surgical masks, face shields, overcoats — these things came out quicker than in some other facilities.”

Despite those measures, he said, “We all know that it’s going to come eventually, but the longer we can hold it off and perhaps limit the number of positive cases would be great.”

That’s the challenge facing food processors around the country, said Lee Schulz, a livestock economist at Iowa State University.

“It’s unknown,” he said. “That’s part of the concern here. It’s so widespread and unknown, just all the implications,”

In Worthington, JBS is now building an 8-by-40-foot structure — “almost like a tunnel,” Utecht said — for workers to undergo temperature screenings before entering the plant. If a worker has a temperature, he or she will be referred to a nurse.

The union has four people working full time at the plant to educate workers about social distancing, hand-washing and hygiene. The largest group of workers there is Hispanic, but more than 56 languages are spoken by workers at the plant.

“It’s just not always possible to social distance there because it’s shoulder-to-shoulder, but they’re putting in plastic barriers between employees now in those areas,” Utecht said.

A JBS spokesman said its large pork plants in Marshalltown and Ottumwa, Iowa, and Beardstown, Ill., are operating.

Triumph-Seaboard, a pork plant in Sioux City, Iowa, which slaughters 21,000 animals a day, is operating at full capacity, a company spokesman said. So are two other plants that Seaboard Foods is involved with — similarly sized facilities in St. Joseph, Mo., and Guymon, Okla.

Sleepy Eye, Minn.-based Christensen Farms, which raises 3 million hogs for slaughter per year in five states, is part-owner of the plants in Sioux City and St. Joseph.

Beef plants in Pennsylvania, Illinois, Iowa and Colorado have closed for various periods of time, in a situation that’s “very similar to pork,” said Karin Schaefer, executive director of the Minnesota Beef Council.

When plants operate at reduced capacity, farmers who raise cattle are seeing less demand for their livestock.

“They’re just not buying cattle right now, or they’re trying to process a bare minimum to keep their orders and give their employees space and time off,” Schaefer said. “That’s a huge bottleneck in our industry right now.”

Cattle prices have dropped about 17% since late February. Hog prices have dropped about 28% over the same period.

Slaughterhouses butcher 510,000 pigs a day in the U.S. Because the market, including exports, consumes that many hogs a day, another 510,000 will be ready for slaughter tomorrow, and the day after that, and the day after that.

Supply won’t change for several months since the decision to raise a hog is made nine months before it goes to the slaughterhouse.

“The hog industry under normal circumstances is a well-oiled machine,” said Schulz, the livestock economist. “But when you do have these bottlenecks and backlogs, that becomes a very challenging situation, because there isn’t much flexibility.”