Strict measures to limit the virus, such as quarantining 1200 workers and shutting two Burnie hospitals, are showing positive signs, Premier Peter Gutwein declared on Tuesday.

A probe into the source of the outbreak, which makes up more than half of Tasmania's overall cases, and how it spread is ongoing.

"We know that there were a number of staff who had symptoms when they were working over the time of the outbreak, often relatively mild symptoms," Public Health Director Mark Veitch said.

"We think that is probably an important factor."

Dr Veitch said hospital staff mixing in handover rooms where it is impossible to maintain social distancing could also have been a factor.

"We also know there were some unrecognised cases in patients that could have contributed to transmission," he said.

"At the very start of it, we know there were two people who were admitted as infections arising from the Ruby Princess."

Eight people have died from the virus in Tasmania. The first three were elderly people who had been passengers on the ill-fated cruise ship.

A fresh case was recorded in the northwest on Tuesday evening.

The local man aged in his 90s had been a patient at the North West Regional Hospital.

The latest case has taken the region's tally to 127 and the state's overall figure to 201.

Of those, 113 are linked to the outbreak that has infected 72 healthcare workers and 23 patients.

The daily number of cases peaked around the Easter weekend, with 15 recorded statewide last Tuesday, but numbers have been in single digits the past four days.

"What we have noticed is the number of cases associated with that outbreak seems to be trailing off," Dr Veitch said.

The outbreak forced the closure of Burnie's private and public hospitals on April 13 although emergency department services have returned amid an ongoing deep cleaning of the facilities.

Despite case numbers falling, Mr Gutwein said he was taking a cautious approach to easing social restrictions, which are broadly in place until at least May 15.

However, strict retail restrictions in the northwest, which closed all non-essential businesses for a fortnight, are due to be lifted on Sunday night.

Mr Gutwein said any decision to ease those restrictions would be guided by medical evidence and whether there are further outbreaks.

In the meantime, police will not let up on enforcing stay-at-home rules.

Mr Gutwein urged all Tasmanians to download the federal government's tracing app once it becomes available, brushing aside privacy concerns.

Australian Associated Press