LONDON — The U.K. Department of Health and Social Care says 67% of those who tested positive for COVID-19 have provided details of their recent contacts to the new test and trace program.

The department says 5,407 out of 8,117 people who tested positive provided details from May 28 to June 3. Of the 31,794 contacts who were identified, 26,985 were reached and advised to self-isolate.

The efforts of the program are being closely watched in the U.K. as a way to ease the nation out of its lockdown while still controlling the virus. Britain has the second-highest confirmed virus death toll in the world — over 41,000 — behind only the United States.

The head of the program, Dido Harding, said “we’re not at the gold standard yet that we want to be” of identifying and contacting all ties to new cases within 48 hours "but you can absolutely see the path of how we’re going to get there.”