Tasmania has confirmed eight more cases of coronavirus, bringing the state's tally to 36, and another college has suspended classroom teaching, citing "mixed and uncertain medical health advice within the community and from various public health authorities".

Key points: A Hobart school has ceased face-to-face classes and is moving to online learning

A Hobart school has ceased face-to-face classes and is moving to online learning Non-essential travel is now banned on the Spirit of Tasmania

Non-essential travel is now banned on the Spirit of Tasmania Tasmania's coronavirus tally moves to 36

In a statement, the Department of Public Health said seven of the cases were from Southern Tasmania. The other case is from Northern Tasmania.

The department said it had "commenced contacting these people to investigate their movements, and to identify and contact any of their close contacts so that these people can be placed in self-quarantine".

Six of the newly diagnosed people had been on cruise ships ad the other two on planes while returning from trips abroad.

None of the newly confirmed cases were a result of local transmission.

Authorities are investigating the movements of the newly diagnosed people to identify and contact those they have been in close contact with in order to get them to self-quarantine.

Tasmania has conducted 1139 tests for COVID-19.

On Tuesday, a Hobart girls' school announced it was moving to online lessons, with parents notified by letter of the "extraordinary situation" due to the continuing coronavirus crisis.

St Michael's Collegiate principal Adam Forsyth sent out the notification today that the independent Anglican school was "suspending all co-curricular activities until the end of term one".

A message on the school website stated "our school wishes to support the slowing of the spread of COVID-19 and maintain a healthy school community".

A program of online learning will be fully implemented by this Thursday, the school said.

"We are all in this extraordinary situation together and I thanks those who have supported us in our decisions to date," Mr Forsyth wrote.

On Tuesday evening, another school sent out a notification it was also "transitioning to distance learning", citing the "mixed and uncertain medical health advice within the community and from various public health authorities".

An email from the Friends' School in North Hobart said it "accepted a recommendation from the school's senior management" to cease face-to-face classes, as of Monday.

Launceston's Scotch Oakburn College, which was the first college to end classroom teaching, plans to continue with e-learning until at least the end of this term.

'Do not come. We will turn you around', travellers told

Non-Tasmanians have been told if they arrive on the Spirit of Tasmania thinking they can complete a period of self-isolation in their caravan or motorhome, they will be "turned around and told to go back".

Speaking at his daily press conference earlier on Tuesday, Premier Peter Gutwein said non-essential travel on the Spirit of Tasmania would no longer be allowed from Tuesday.

"Do not come. We will turn you around and ask you to go back," he said.

Mr Gutwein said Tasmanian was in "stage one" of coronavirus measures and a "hard lockdown" was being considered.

"I think people are very familiar with what's been occurring overseas, total lockdown would mean only essential services would continue to be provided," he said.

Today, TT-Line, the operator of the Spirit of Tasmania ferries, has begun contacting all bookings of caravans and motorhomes of non-Tasmanian residents to inform them that they cannot self-isolate in their camping vehicles.

Mr Gutwein said today that the state now had police compliance teams (PCT) on the beat to force businesses and individuals to follow measures introduced to stem the spread of COVID-19.

"They [the PCT] will be working closely with Public Health to ensure that where people are asked to self-isolate, that they do so. To do anything other [than that] is to put people's lives at risk."

He said while most in the community were complying with the rules, some were not.

"Stop deliberately putting people's lives at risk, abide by the rules … there are penalties and we will apply them," he said.

Tasmanian Government minister in isolation

Mr Gutwein also revealed his minister for Sport and Recreation Jane Howlett was in self-isolation.

He said Ms Howlett had travelled to Townsville with her chief of staff, who was last night informed by Queensland Health that they had been a close contact of a confirmed case of COVID-19.

"She [Ms Howlett] is going into self-isolation today and will not be in the Parliament," he said.

The Premier said Ms Howlett had not been tested for COVID-19 because she did not have any symptoms.

Questions over coronavirus testing

When asked whether testing would become more widespread, Tasmania's deputy director of public health Scott McKeown said the state had "already expanded the testing criteria to respond to our local situation".

Most tests are carried out on people who have been overseas or in contact with a person who has been overseas and are showing symptoms.

However, Dr McKeown said "there have been circumstances in Tasmania where we have decided for particular cases or circumstances, whether a more complex case of a person in hospital or an illness in a health care worker or a person in the community who presents to their GP with a history that we think testing is required, we have been doing that testing and none of those circumstances … have confirmed coronavirus "

Tasmania has 28 cases of coronavirus, 17 infections were acquired overseas and 11 on cruise ships.

Three have recovered and been released from isolation.

Mr Gutwein said yesterday was a very difficult day for Tasmanians, with tens of thousand of them losing their jobs.

"It breaks my heart to have had to take the steps that we took yesterday, and to all of you who have lost your jobs I am so very, very sorry," he said.

He further addressed all Tasmanians, urging them to let their sacrifices "mean something".

"Abide by the rules, take the appropriate steps," he said.

Tasmanians abroad plead for help

Tom Tully and Leanne Matthews (left) with other Australians in Cape Town who fear they will become stranded when commercial flights cease. ( Supplied )

Meanwhile, Tasmanians stuck overseas are worried they will be stranded.

Tasmanian couple Tom Tully and Leanne Matthews have spent the past two days on a cruise ship docked at Cape Town.

South Africa plans to lock down on Thursday.

The couple were due to fly home on Tuesday morning, but after arriving at the airport, discovered their flights had been cancelled.

About a hundred other Australians were in the same situation.

Mr Tully said neither the Australian High Commission nor the Department of Foreign Affairs and Trade had offered to help.

They are planning to go to Johannesburg where they're hoping to get on one of the two booked out Qantas flights to Australia.

"Our only hope is to try and get there and get on a wait list and just see if there are any cancellations.

"Because at the moment we've been told that we will have to find our own way home and we're not going to get any assistance from anyone." Mr Tully said.