LESS than one in a thousand Scots is currently infectious with coronavirus, the Scottish Government has said

However Nicola Sturgeon refused to give into pressure to relax the 2m rule on physical distancing, or to allow separated couples to reunite in so-called ‘love bubbles’.

“Call me boring if you want, but I'm going to try to stick to the plan to get Scotland through this," she said.

Research published by the Government estimated the number of infectious people as of June 5 was 4,500 out of a Scottish population of 5.4million.

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Barely a month ago, on May 8, the official estimate was of 26,000 infectious people.

The Government’s latest modelling paper also said the R number, the rate of transmission of Covid-19, was between 0.6 and 0.8, down from 0.7 to 0.9 the previous week. 

However the numbers have not yet factored in the easing of the lockdown on May 29, when thousands met other households outdoors, took a drive, and played non-contact sports. 

At the daily briefing, Nicola Sturgeon said the latest estimates appeared to be more accurate than earlier ones, which may have over-estimated the pool of infectious cases in Scotland.

She also announced a further five people had died overnight, taking the number of laboratory confirmed fatalities to 2,439.

However the total for confirmed and suspected Codi deaths is put at more than 4000.

Ms Sturgeon said: “These latest estimates reflect the encouraging data that we've seen in the last couple of weeks and there is no doubt in looking at all of this data that we are making very real progress in combating and suppressing the virus."

She announced the construction industry in Scotland would be able to move into the next stage of its reopening plan, with workers gradually be able to return to building sites, provided they adhered to hand hygiene and social distancing measures.

This is intended to allow for a slow build-up of workforces to optimum capacity.

Work on “non-essential” sites can only be carried out with physical distancing.

The First Minister said the construction industry move was in line with the timing set out in the Scottish Government’’s route map out of the lockdown.

However she said there was still "a long way to go" before construction was back to normal.

She said: "A week today we will have further review of the lockdown restrictions.

"I am currently very hopeful that at that point we will be able to lift some further restrictions, we may not be able to do everything in phase two but I hope that we can do certainly at least some of that."

She also announced a year-long extension of the Scottish Government's help-to-buy scheme to March 2022 and financial support for students to help them through the summer.

Help-to-buy provides up to 15% of the price of buying a new-build house, was due to end in March next year.

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Ms Sturgeon said more than £11 million of support will be made available for students through their colleges or universities to help those who "most need it".

Throughout the briefing, Ms Sturgeon was pressed on whether Scotland would follow England and allow separated couples to resume physical intimacy.

Boris Johnson announced on Wednesday that single adults living alone could form a “support bubble” with another household from Saturday, including overnight stays.

However Ms Sturgeon said the Government’s plan for continued physical distancing remained in place for now, though she "totally understands the frustrations people have". 

She said: "If we are to come out of lockdown at the right pace and in a way that is sustainable, then we stick to our plan with careful and well-founded decisions." 

She added: “Call me boring if you want, but I'm going to try to stick to the plan to get Scotland through this. This is not a popularity contest. My fundamental duty as first minister is to steer the country through the biggest crisis any of us have ever lived through.”

She also said the 2m rule on social distancing remained in place, despite dire warnings from the tourism and hospitality sector that it means businesses cannot trade profitably.

However she said it was kept under review.

The Government’s route map contains no specific reference to reunited couples, and says physical distancing is expected to remain in place to Phase 4 in August.

Labour MSP Monica lennon said more close contact could be possible if there was greater antibody testing to let people know if they had already come through a Covid infection.

She said: “If we had antibody tests by now we might be more liberal about hugging. 

"With more and more concern being raised about mental health and social isolation, a hugging ban just doesn’t seem credible in the long term.”

SNP Housing Minister Kevin Stewart added: “The health and safety of construction workers and the public remains the top priority as we begin to restart the industry.

“In considering the industry’s readiness to move to the next stage, we have taken an evidence-led approach. The sector’s response to this crisis  continues to be responsible and measured, and I am satisfied that it is well-placed to progress into this next phase.  

“I must reiterate, however, that easing restrictions will not mean returning to how things were before the virus. Physical distancing, hand hygiene, and other critical behaviours will be essential in each area to ensure public and workforce confidence. I am pleased that we are now able to take this significant step in safely returning the industry to work.”

Nicola Barclay, chief executive of Building for Scotland, said: “To get confirmation that home builders can now commence the re-opening of their sites is great news that hasn’t come a moment too soon given the robust safety plans that the industry has put in place.  

“With pent-up housing demand having increased with every day that has passed, we look forward to finishing off the many homes that are already largely complete and that families are desperate to move into as well as starting to get the new homes that are so desperately needed out of the ground.

“Having the extension of the Help to Buy scheme announced at the same time is also a much required confidence booster for the housing market.”

Vaughan Hart, Managing Director of Scottish Building Federation, added: “We are delighted the First Minister has approved plans to allow the construction sector to begin a soft start on site from next week.  

“Both individual members and the industry as whole have been working tirelessly with unions, clients and professional bodies to ensure we only reopen sites when we can make it safe to do so. I believe that work has paid off and a number of sites will now be ready to begin work again on Monday.”

Scottish Conservative housing spokesman Graham Simpson said: “The First Minister's announcement is long overdue but it is good news that she has finally seen sense and agreed to allow construction sites to reopen.

“This follows sustained pressure from the Scottish Conservatives and exasperated home buyers, 6000 of whom were waiting for houses that were very nearly complete.

“The delay has been baffling and not founded on any reasoning at all, other than to be different.

“The construction industry has had safe working plans in place for weeks - now we can look forward to seeing them put into practice.”