An imperfect test for a virus can Be worse than No test at all.

This note studies the effect of the availability of a test for a virus on the public health of a population. It is shown by example that the existence of a freely available and moderately informative test for a virus may lower society's welfare in comparison to the case where no test exists or access to the test is restricted. In this setting, any test provided to any subset of agents who would find it optimal not to isolate absent the test improves welfare.