Could he just get a few bottles?

All around the world, hand sanitizer has become a precious commodity, the sought-after emblem of the daily fight to contain the coronavirus’s spread. In Italy, the epicenter of the European outbreak, that commodity is referred to by its brand name, Amuchina. And as demand soars, its producer is racing to churn out a $4 product that was once as ordinary as lip balm or shampoo.

“I’ve never seen anything like this,” said Tito Picotti, a plant director at Angelini, the sprawling pharmaceutical company that makes Amuchina. “Our lives have changed completely.”

Behind the security gates of a production plant near Italy’s eastern coast, during a frenetic period that an executive likened to a “hurricane,” the company has held one emergency meeting after the next and ramped up Amuchina production from 12 hours daily to 24. It has asked shift workers to step in on weekends. It has altered the packaging to improve efficiency. It has cranked out so many bottles — five times the rate from the same period a year ago — that one of its plastic suppliers couldn’t keep pace. So Amuchina switched from red bottle caps to white.

But even that hasn’t been enough.

At full speed, the production line in Ancona churns out 40,000 bottles a day; another smaller facility near the Swiss border contributes 5,000 daily. Executives estimate it would take more like 200,000 to meet demand.

Italians swap messages about the stores that might have Amuchina briefly in stock. Internet memes suggest that it’s better to show up at a dinner party with Amuchina than wine. The government has asked that hand sanitizer be made available in public buildings, as a way to contain the coronavirus crisis.

The company itself has not raised prices to distributors, and pharmacies have largely kept prices steady as well, as long as they have the hand sanitizer on their shelves. But some bottles have popped up in online marketplaces at astronomical markups — 100 euros or more.

Nothing drives up demand, of course, like scarcity and a sense of danger, and though the company doesn’t sell directly to consumers, Angelini executive Enrico Giaquinto said distributors now seem to be mirroring the behavior of regular Italians, stockpiling and asking for more than what they might really need.

As the number of Italian coronavirus cases this week surged toward 4,000, many stores were getting only a portion of what they asked for, with Angelini giving priority to more urgent requests, like government orders.

“Until we have a tool to fight this,” like a vaccine, Giaquinto said, “the only two things that can help are social isolation and hygiene.”

And most Italians would pick hygiene over isolation.

The company responsible for Amuchina is a massive family-run enterprise, Angelini Holding, which makes everything from diapers to Brunello wines. The biggest share of its business comes from pharmaceuticals, like painkillers and anti-depressants. Amuchina, in normal times, is just a fraction of that business, about 4 percent, and the company was quick to point out that other products have a much higher profit margin.

The company’s production facility in the port city of Ancona reflects that. There is no stand-alone hand sanitizer factory — blending and bottling happens in just a few rooms within a sprawling facility otherwise dedicated to pharmaceuticals.

The setting has the feel of an enlarged airplane cabin, with the dull background noise of whirring machinery, and curved-edge windows offering glimpses into hyper-sterilized areas that are off-limits to visitors. The rooms are tended only by a small crew of workers in hairnets and white smocks, four workers per shift. The components used for the gel are vacuumed into a silver vat and mixed for five hours. Aside from the packaging, machines do much of the rest of the work.

And it is the machines, not the people, that dictate the limit of how much can be produced.

During a tour this past week, Picotti pointed to a silver machine with a nozzle, filling the gel into bottle after bottle on a conveyor belt.

The machine had been turned to the highest speed. It could go no faster.

“You can order a new machine,” Picotti said, “but you will see it in 12 months.”

The company has requested emergency government approval to get another factory online, run by a supplier, and by next month, Angelini hopes to be producing more than 55,000 bottles per day. The shortages, though, would continue.

Several days ago, a satirical Italian political show, Propaganda Live, invited a chemist onstage to make his own version of Amuchina. Mixing various fluids, warning about the flammability of the alcohol involved, he cautioned Italians against becoming home pharmacists. Some of the techniques he described, he said, were used in “theaters of war.”

The show’s host, Diego Bianchi, interjected, mentioning a northern Italian town, Codogno, at the center of the outbreak.

“Now we have Codogno,” Bianchi said, “as a theater of war.”

At the factory, the daily coronavirus news scrolls on a television above the reception desk, and some employees say they’ve never before felt such a sense that their work inside the plant will influence the country.

“We have to produce,” said Giaquinto, the baggy-eyed chief industrial operations officer who has been working 17-hour days.

Giaquinto always considered himself good at separating work and family, coming home calm no matter the issue. But he said it has been hard to compartmentalize lately. The factory is in a region one ring from the epicenter of the outbreak that has itself seen 155 cases and four deaths. He keeps thinking about his elderly father, who lives in Umbria and uses a respirator. When they parted after a recent visit, Giaquinto told him that they might not see one another again for months.

“If he gets the virus,” Giaquinto said, “I think he will not survive.”

This is Italy right now: social life turned upside down, with no assurances about what things will look like even next week. All people can do is take basic steps to limit their exposure.

For Giaquinto, precautions start at the factory entrance, where he refused to shake hands with newly arrived visitors this past week.

But he made an exception after lunch, after walking past the coffee bar and pressing a communal supply of hand sanitizer into his hand.

“Take some, too,” he said.

In a moment of normalcy, he offered a handshake.

“We are Amuchina-treated,” he said.

Correction: A photo caption on an earlier version of this story misidentified Franco Bellagamba as Enrico Giaquinto.