In Britain, researchers said the disease had advanced so fast that it was already pointless to use survey results to steer tests for the virus; rather, the results are helping pinpoint where ventilators and mobile intensive-care units should be positioned, according to Tim Spector, a professor of genetic epidemiology at King’s College, London.

“I liken this to a radar,” he said. “Two weeks before the bombs get dropped, you can actually work out what’s going to happen — not based on what happened in China, but actually seeing what’s happening on the ground here. That’s what’s going to save lives: the fact that you can plan where to put your mobile I.C.U.s.”

Dr. Spector, the director of the TwinsUK Registry, a nationwide research cohort of 15,000 twins, rolled out the British survey to that group on March 24, and it spread by word of mouth. Within five days, he said, the tally of unique participants had surpassed two million, with the “Covid Symptom Tracker” app jumping to the No. 1 health-related download in Britain's Apple Store and the No. 4 app of any kind.

The survey is popular, but not as evenly distributed as health experts might like. People over 70 years old are underrepresented, which is not a surprise, given the app-based distribution. And women are participating at roughly twice the rate of men. “They are more altruistic, in the U.K.,” Dr. Spector said, laughing.

Over all, he said, the respondents in Britain are acting out of concern for the National Health Service and “a feeling that they’re doing something for the community.” But he also said that people who reported already having tested positive for the virus seemed to grasp at the survey as “a way to express their symptoms.”

“If they don’t go to hospital, nobody seems to care about them,” Dr. Spector said.

Surveys are not the only unconventional way that scientists are trying to detect the spread of the virus: A maker of smart thermometers says it is tracking the contagion in real time by mapping fevers in American households.