Poultry giant Sanderson Farms Inc. last week reported the first case of a worker at a major U.S. meat producer testing positive for coronavirus. The employee and six more from the McComb, Mississippi, plant were sent home to self-quarantine, with pay, but operations continued as normal.

A few days later Smithfield Foods Inc., the world’s biggest pork producer, confirmed a positive case at its Sioux Falls, South Dakota, facility. In all likelihood, the numbers will keep going up at meat plants, farms, warehouses and packaging factories across the globe.

The infections speak to a growing threat to the world’s food supplies. Massive operations where workers pick berries together, cut meat side-by-side on a production line or load warehouse trucks in sometimes close proximity risk slowing down. Some facilities may have to shutter for cleaning and worker quarantines. Produce could end up rotting in fields if there aren’t enough healthy workers.

“If we can’t flatten the curve, then that is going to affect farmers and farm laborers — and then we have to make choices about which crops we harvest and which ones we don’t,” said Al Stehly, who operates a farm-management business in California’s North San Diego County, growing about 250 acres of citrus crops, 250 acres of organic avocados and 60 acres of wine grapes. “We hope no one gets sick. But I would expect some of us are going to get the virus.”

To be clear, the food from a plant where infection pops up doesn’t pose health concerns because by all accounts COVID-19 isn’t a food-borne illness. Supplies from a farm or a production plant with a confirmed case can still be sent out for distribution.

And it’s important to note that so far there’s been no major interruptions to food supplies. Inventories are still ample, and major bottlenecks have not yet developed in the supply chains, which tend to react quickly to changing situations.

Still, there is a risk to continued production. When a worker gets sick, the employee and every person they’ve come into contact with has to be quarantined. That could mean limited impact in some cases, like at the Sanderson factory, where the infected individual’s work was contained to one small processing table. But the more employee mingling there is, the bigger the threat to production.

“One of our beef plants feeds 22 million people per day, so it’s vital that these plants stay open,” Dave MacLennan, chief executive officer of Cargill Inc., the world’s largest agricultural commodities trader, said in a recent Bloomberg Television interview.

At many meat-processing plants, workers are “essentially elbow to elbow,” said Thomas Hesse, president of United Food and Commercial Workers Union Local 401, the largest private sector union in Western Canada that represents 32,000 members, mostly in food processing and retailing. Though employees are usually wearing protective gear, the risk of contagion is difficult to completely eliminate.

“There’s underlying tension, there’s fear and there’s anxiety,” Hesse said, calling on employers to act more diligently to keep workers safe, including by increasing the space between work stations.

Moves like that would likely hamper output though. It’s a tricky balance for producers who are prioritizing worker safety but also trying to meet the huge surge in demand that the virus has unleashed. Grocery store shelves across the world are running empty as consumers load their pantries in anticipation of long lockdown periods.

Just about every major agricultural and food producer is stepping up its sanitary procedures to keep workers from getting infected. Companies are enforcing hand washing, spraying down plants and break rooms and wiping down door knobs. Workers are covered in head-to-toe protective gear, shifts are staggered and lunch breaks are taken alone.

In Sabah, the state that churns out about a quarter of Malaysia’s palm oil, the local government ordered plantations and factories in three districts to shut after some workers tested positive for COVID-19. To avoid further disruption, the country’s industry is in a desperate bid to “starve the virus,” disinfecting tractors, providing workers with antibacterial body soap and distributing face masks to employees and their families, said Joseph Tek, CEO of palm-oil producer IJM Plantations Bhd.

It’s hard to say if all that will be enough. Given the real possibility of an illness-driven labor crunch, some companies are stepping up hiring now to prepare.

Steve Cahillane, CEO of Kellogg Co., said bringing in additional workers is part of the company’s “mitigation plans,” without specifying how many employees have been added.

“We’re going to see some creative solutions where folks that are being laid off are going to be able to find new opportunities that continue to support the essential critical infrastructure,” said Mary Coppola of the United Fresh Produce Association. Many food companies will be trying to aggressively hire, including in distribution centers and in retail stores, she said.

But it may not be that easy to lure people into the field. For all their import, these are not glamorous jobs.

Think of the back-breaking work of tomato pickers, the dangerous conditions at slaughter houses and what many would consider the unpalatable environment of large livestock-feed operations. The wages are often low, benefits meager and contributions hidden from the public eye: How many social-media posts have you seen bursting with appreciation for the grain-export inspectors?

Now they’re putting their health at risk by keeping food flowing. Not surprisingly, there’s been some backlash. Unions in South America have threatened to strike over safety concerns. And some poultry workers in the U.S. recently walked off the job.

Food companies are ramping up efforts to make sure employees feel appreciated. Cargill, Maple Leaf Foods Inc., Campbell Soup Co., Mondelez International Inc., Kraft Heinz Co. and Hormel Foods Corp. are among those paying bonuses or premiums to workers.

In some places, more unusual solutions are being deployed.

Dairy producers in Vermont recently put out a call through social media, asking for volunteers to come milk cows if farmers start falling ill. A day later, more than 80 relief milkers had signed on as standbys.

“It started when we got a couple of calls from dairy farmers who were super worried they might get sick and wouldn’t be able to milk their cows, and that would be it — they’d lose their farms,” said Kim Mercer of the Northeast Organic Farming Association of Vermont, which posted the online plea. “We now have people everywhere all across the state who are ready to go.”