BEIJING—Before going to bed, George Gao, the head of the Chinese Center for Disease Control and Prevention, typically completes his 10,000 steps for the day and then checks the news online.

When he scanned his feed on Dec. 30, he was stunned. Two leaked local-government notices warned about cases of unexplained pneumonia in the Chinese megacity of Wuhan. It was the first he’d heard of the outbreak, according to people close to him.

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