Another two coronavirus-linked deaths in Southern Tasmania have taken the state's pandemic toll to 88.

A man in his 50s and a man in his 80s have died.

It follows the death of another man in his 50s - also from the South - reported on Wednesday.

Premier and Health Minister Jeremy Rockliff says fluctuations in daily case numbers are a part of living with COVID, after new infections blew out to more than 1000 a day since Tuesday.

Active cases have now risen to 5264 and 12 people are in hospital specifically for COVID, including two patients in intensive care.