SEOUL—More than 160 South Koreans have tested positive a second time for the coronavirus, a development that suggests the disease may have a longer shelf life than expected.

Many had volunteered for re-examination after exhibiting symptoms such as coughing. Others submitted to extra testing on little more than a hunch despite not showing symptoms. So far, these patients—all of whom needed to twice test negative before leaving medical supervision—haven’t spread the virus to others, local health officials say.

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