SAN FRANCISCO — At Facebook on Thursday, the questions from spooked employees came thick and fast.

The evening before, the social network had disclosed that the coronavirus had been diagnosed in a contractor in its Seattle office and had said all employees in that city should work from home until March 31.

Other Facebook employees, some of whom had recently traveled for work, soon began asking their managers and one another: Who was the contractor? Had that person been near them? And what did that mean for their work?

That same alarm has now spread through other companies around the world, despite escalating efforts by many of the firms to deal with disruptions from the coronavirus outbreak that started in China. Microsoft, Amazon, Ford Motor, CNN, Citigroup and Twitter have put employees through work-from-home drills, dusted off emergency-response plans and ordered increasingly stringent safety measures to protect their workers.

Even so, the coronavirus has moved faster than their preparations. Amazon said this week that two employees in Europe, who had been in Milan, were infected with the virus and that one employee at its Seattle headquarters had tested positive for it. HSBC said on Thursday that the coronavirus had been diagnosed in an employee at its global headquarters in London. And AT&T said a retail employee at one of its stores in San Diego had tested positive.