The National Clinical Director’s comments came as Scottish Covid-19 cases reached a record high over the festive weekend – reaching its peak on Boxing Day.
Christmas Day recorded 8,252 cases with a further 11,030 confirmed on Boxing Day and 10,562 more yesterday (Monday).
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In an interview with BBC Good Morning Scotland on Tuesday, Prof Leitch said the case numbers were “depressingly predictable" with numbers having quadrupled in the past three weeks.
He said: “Case numbers going down is a very difficult piece of information to give.
"The modelling suggests that the peak of the Omicron wave in the United Kingdom will be somewhere between mid to late January, maybe even pushing into February.
"But that will depend quite a lot on human behaviour and what we do now.
"We may not want the peak early because if this is an enormous wave we may want to draw it out over a longer period because you might then get more people vaccinated."
On potential further restrictions in Scotland, Prof Leitch said he hoped the country could ‘get away without anything too dramatic.’
New restrictions are now in place across Scotland, with capacity limited at outdoor and indoor events and curbs such as table service and social distancing now in place at hospitality venues.
Mr Leitch said: “Our advice is really clear, don’t move to break the rules in the place you are already in.”
He added “big case numbers” would not be recorded for another two or three weeks with people urged to get “boosted by the bells” and regularly take home tests.
Prof Leitch earlier said he expected the wait for PCR test results to return to normal after some people reported waiting over four days to receive their results.
This morning, he added the large amount of people who went to test over Christmas led to the delays and that the backlog “has now been cleared”.