A person in their 20s is among the latest positive cases of coronavirus detected in Tasmania, taking the state tally to 42.

Authorities said three of the six new cases are from Northern Tasmania, two are from Southern Tasmania and one case is from the north-west.

In a statement, Director of Public Health Dr Mark Veitch said "two of the cases are aged in their 70s. One is aged in their 60s, one in their 50s, one in their 30s, and one is in their 20s. Four of the cases are women, two are men".

"Two of the cases have recently been on cruise ships. One case is a close contact of a previously confirmed case, and three have recently travelled to Tasmania from overseas," Dr Veitch said.

"[There is no evidence of community transmission in Tasmania, as all the cases are directly or indirectly linked to overseas travel," he said.

Public Health Services is contacting the cases to identify and contact any of their close contacts so that these people can be placed in self-quarantine.

As of Wednesday, Tasmania has conducted 1,272 tests.

Early end to school term

The Tasmanian school term will end four days early to give teachers time to plan to provide home learning delivery for students.

Tasmania COVID-19 snapshot Confirmed cases: 226

Confirmed cases: 226 Deaths: 13, 12 in north-west What do I do if I think I have coronavirus? If you think you might have COVID-19 phone your GP or the Tasmanian Public Health Hotline on 1800 671 738. Need an interpreter? Phone the Translating and Interpreting Service on 131 450 and tell them your language. For more information and factsheets: Visit the Tasmanian Government's coronavirus page here.

Tasmanian Premier Peter Gutwein said while schools remained open for now, they would close to students after Friday next week.

From the 6th to the 9th of April schools would be student-free.

Mr Gutwein said the student-free days would: "enable schools and teachers to complete the professional learning required to finalise the delivery of a home and online model from the beginning of the new term post the holidays".

"In term two, schools will remain open for students of essential workers and parents who wish their children to attend an education setting.

"We will support other students in their home, through either online or through other resources."

But the Australian Education Union (AEU) called for the student-free days to start a week earlier from Monday, March 30.

AEU Tasmanian president Helen Richardson said teachers and support staff felt abandoned by Mr Gutwein.

"Tasmanian private schools have already announced student-free days this week, others have closed, allowing their teachers to prepare for online learning from Monday," she said.

"Public schools are being left further and further behind in terms of preparation time and resourcing."

Several independent schools in Tasmania — St Michael's Collegiate and the Friends School in Hobart and Scotch Oakburn College in Launceston — have either announced plans to transition to online learning or have done so already.

The Hutchins School in Hobart on Wednesday said it would move to an online learning model for the rest of the term, with the last school day on Thursday and remote learning commencing on March 31.

Harsher policing of border controls

At his Wednesday press conference, Mr Gutwein also promised harsher policing of borders from today, with more aggressive contact tracing and policing of self-isolation.

"I expect that community transmission will occur at some stage," he said.

"These measures will give us a fighting chance to control it.

"They will give us a fighting chance not to go into an economy wide shutdown."

From today, additional police officers will help biosecurity staff manage non-essential travellers arriving in the state.

Those with nowhere to stay will be charged a fee to self-isolate in government-provided accommodation.

The Health Minister Sarah Courtney said there was still no evidence of community transmission, with all confirmed cases linked to international travel or cruise ships.

Police Commissioner Darren Hine said people in self-isolation would be subjected to random police checks and those flouting the rules would face penalties.

"We do not want to put our police officers or our community at risk by having to arrest people," he said.

"But if people need to be given that harsh message that if you don't obey there is a significant fine of over $16,000 up to six months' imprisonment if you do not obey."

No-one has been charged at this stage.