Data about the proportion of contacts reached by the trace and protect system should be published by authorities to show if it is working, a public health expert has said.

Professor Linda Bauld said the information was the “missing piece in the jigsaw” in the data published about the coronavirus pandemic.

She said the country will be living with test and protect “for many months” and the extra data is needed to show whether the system is working as it should be.

The Scottish Government said it expects to publish figures on the percentage of positive cases followed up by the end of August.

Speaking on BBC Good Morning Scotland, Prof Bauld said: “All we have at the moment is the number of people who have been tested and then the number of people who are contacts.

“We don’t know the proportion that have been followed up, how long it is taking to do that, though we’ve heard the First Minister give some examples, and then we don’t know what happens to those people who are followed up and we need to be able to see all those data to be confident that the system is working as it should be.”

Prof Bauld, who is professor of public health at the University of Edinburgh, said Scotland has done “extremely well” on other areas of the data but outlined the information she would also like to see published.

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“What I would like to see, these are the data we need, we need the proportion of contacts reported by index case, so that’s the person who tested positive, that have been successfully reached, so that’s that percentage,” she said.

“Also the time taken to reach the individual, that’s crucial because to shut down the chains of transmission it needs to be rapid and I’d also like to see whether follow-up occurs for those who are asked to isolate.

“Finally, and this is probably optional but would be interesting, whether cases have been symptomatic or not because there’s routine testing in care homes and in the NHS and of course those people will have contacts as well so let’s aim to be even better than the countries that are currently reporting that data and give all of that data, not just to researchers like me but to the public as well.”

Justice Secretary Humza Yousaf was questioned on why schools have reopened without data about the proportion of contacts traced being known.

He told the programme: “We would not take any gamble or any risk when it comes to young people’s education. In fact, what we’ve said from day one is that our children’s education is a priority.”

He added: “It’s not just public health data, although that’s hugely important, but also the impact that not being in school has had on children.

“There’s a number of harms we have to balance, a range of data we have to look at. And having looked at that data, we’re confident that schools can reopen.”

A Scottish Government spokeswoman said: “The Scottish Government is committed to setting out as much data as possible about the Covid-19 pandemic to help inform and improve our response.

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“We work closely with National Records of Scotland and Public Health Scotland to ensure the figures we publish are robust, and will publish significantly more information about the contact tracing process, including the percentage of positive cases followed up, time taken to reach individuals who had tested positive and time taken to reach their contacts. We expect to publish this data by the end of August.

“This will be drawn from the case management system used by all territorial health boards and the National Contact Tracing Centre, and Public Health Scotland is continuing to work with CMS users across the territorial boards to improve data quality ahead of publication.”