TEST and Protect took more than 72 hours to trace the contacts for more than 8,600 cases between August and October, increasing the risk of the virus spreading.
Scientists from the SAGE advisory group warned in May that “any delay beyond 48-72 hours total before isolation of contacts results in a significant impact on R” - the reproductive rate of the virus.
If contact tracing is too slow, onward transmission of the virus accelerates and outbreaks become more likely because people who have been exposed to an infected person - and who may be incubating the virus themselves - are not self-isolating.
Data from Public Health Scotland shows that in the 11 weeks from August 10 and October 25, there were 8,640 positive cases where contact tracers took more than 72 hours to track down all their known close contacts to advise them to self-isolate.
In two of the weeks - week ending September 27 and week ending October 4 - contact tracing took more than 72 hours to complete in relation to 36% of the positive cases reported to Test and Protect.
The period from August 11 to October 25 is associated with a significant upsurge in the prevalence of the virus in Scotland, from 0.9 cases per 100,000 to a peak of 24.3 per 100,000 on October 26 - according to the seven-day average.
In the past two weeks from October 26 to November 8 contact tracing has improved, with only 8% and 4% of cases taking longer than 72 hours for Test and Protect to 'close' - meaning that all close contacts have been notified.
That same two-week period has coincided with a 28 per cent decline in the average of the virus, from 24.3 per 100,000 to 17.6 per 100,000.
The Scottish Lib Dem leader Willie Rennie said: "We were promised we were going to have enough contact tracers, that it would hunt out and drive out the virus from our communities but, as we have seen, it has spread quite fast and that's why we need to make sure we get proper investment in the Test and Protect system if we are going to get on top of it."
A Scottish Government spokesman said: “While Test and Protect is working well, we are continually reviewing our approach to contact tracing, and adapt and improve the system as issues are identified.
“Our approach uses established, tried and tested contact tracing techniques. These are delivered by health protection professionals in teams within local NHS Boards with support provided by the National Contact Tracing Centre.
“Our contact tracers have successfully interviewed 94% of people who have tested positive for coronavirus.
"In the latest week (November 2nd-8th), Test and Protect completed 95.8% of cases within 72 hours – far exceeding the World Health Organisation standard of 80% - and 88.7% of cases were closed within 48 hours.”
READ MORE: Contact tracers have not spoken to thousands who have the virus
It comes after it emerged earlier this week that a 'coding earlier' had resulted in the Test and Protect performance being overstated.
The error meant that some people who had tested positive were recorded as having been notified within 24 hours when it was actually 24-48 hours.
The figures have now been updated on the Public Health Scotland website.
For outbreaks to be curtailed it is recommended that people get their results within 24 hours of being tested - assuming they go for a test as soon as symptoms emerge.
Scientists writing in the Lancet Public Health journal in July said that for conventional contact tracing to be effective at stemming the spread of the virus "at least 80 per cent of people with possible Covid symptoms must be tested, there must be no delays in testing after the onset of symptoms, and at least 80% of contacts must be identified within 24 hours of test results".
READ MORE: Glasgow and west set to be escalated to Level 4
If testing is delayed by two days, keeping the R number below one "would require contacts to be traced within 24 hours and at least 80% of contacts must be identified".
In the week ending November 8, only 56.7% of people who tested positive were notified within 24 hours of being tested.
Anyone with symptoms is asked to self-isolate as soon as symptoms emerge and until they receive their test results, but people who know they have tested positive are more likely to comply with quarantining.
Between August 3 and November 8, 3851 infected individuals waited more than 72 hours for their test results.
It has also emerged that coronavirus tracers have been unable to contact more than 3,512 Scots who tested positive for the disease since June 22.
Public Health Scotland said this was 6% of those who had tested positive, describing it as a "very small proportion" of the overall number of cases.
The First Minister said the failure was not down to the Test and Protect contact tracing system, which she said is performing to an "exceptionally good" standard.
READ MORE: Contact tracing problems caused by people 'not answering their phones'
Ms Sturgeon said the issue was people not answering phone calls or responding to text messages from contact tracers.
She stressed there is a "personal responsibility" to do this.
She said: "Test and Protect is working well, it is doing a good job and I think it is a disservice to those working in that system to suggest otherwise."
Labour health spokeswoman Monica Lennon suggested home visits could be one way of reaching coronavirus-positive Scots who refuse to answer their phones.
She said "Every effort should be made to establish contact with someone who has Covid or is potentially infectious.
"There are many factors that could prevent someone from answering the phone, including serious illness.
"If the Scottish Government is committed to doing everything possible to reach them, the option of a house visit should be included."
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