Big Chinese corporations and wealthy individuals have been donating, many generously. But they also try to keep low profiles for fear of offending a government that is eager to take credit for any success and quick to suspect outside groups of challenging it.

Those gaps are evident on the front lines of the outbreak, where workers have lacked the proper equipment to keep themselves safe. Doctors and nurses wear disposable raincoats instead of protective gowns. They wear ordinary, and inadequate, surgical masks while conducting dangerous throat swab tests. They wear adult diapers because, once they take off their one-piece protective suits, the suits will have to be thrown away. They get only one per day.

The authorities said on Monday that over 3,000 medical workers had been infected, though not all got it from work.

Ordinary Chinese people have set up social media groups to help patients find hospital beds, get volunteers to drive them to hospitals and scavenge the world for protective gear. In coordination with the government, they could do much more.

“We’re just a small boat with very limited capacity,” said Panda Yin, a designer in Beijing who organized a WeChat volunteer group of about 200 people to help find protective supplies for front line medical workers. “People came to us because they know the highway that’s supposed to move fast has a big black hole on it.”

That “big black hole” is the Red Cross Society of China. Unaffiliated with the Red Cross elsewhere, the Red Cross Society is one of two government-controlled organizations through which Beijing monopolizes philanthropy. The Wuhan government has insisted that all donations go through the local chapter.

The Red Cross Society is notorious for corruption and inefficiency. The Chinese media have reported on many of its scandals, including one nine years ago when a person who reportedly held a senior position there shared pictures of her opulent lifestyle online.