WUHAN, China — The Lunar New Year festivities were just hours away, but instead of helping to prepare a joyous family banquet, Chen Yanming stood anxiously outside a hospital where her father was being tested for a dangerous new virus.

“Today should be the Chinese people’s happiest day,” Ms. Chen, 47, said here in Wuhan, the riverside city of 11 million in central China where the outbreak began. “But this sickness has destroyed that feeling. It came suddenly and unexpectedly. We should have been better prepared.”

The emergence of the mysterious coronavirus could hardly come at a worse time for China, turning its biggest holiday into a time of deepening fear, restrictions and frustration.