On the first Sunday in February, as the San Francisco 49ers were in the middle of blowing a lead in the Super Bowl, a small group of doctors in the Bay Area was too busy to care about a football game. They were dealing with the region’s first cases of coronavirus.

They had no time to waste as they raced to bring the University of California San Francisco’s Covid-19 command center into operation. They worked overnight and had it running by the next morning—when two patients confirmed with the virus were transferred to UCSF’s...