South Australia has begun rolling out additional doses of the COVID-19 vaccine as local research confirms those who are unvaccinated face a higher risk of serious illness or death.

The South Australian Health and Medical Research Institute analysed 70,450 virus cases in SA between August and October last year.

With rising case numbers last week suggesting a new wave, the institute found the unvaccinated were about eight times more likely to be hospitalised and about five times more likely to die than those who had three or four doses.

"This research is based on South Australia's real-world data and shows just how important vaccination is in protecting against serious illness," Health Minister Chris Picton said.

"I encourage everyone to check the date of their last vaccine or infection, and make sure you're up to date with vaccinations."

From Monday, additional vaccine doses are available to anyone 18 and over who has not had COVID-19 or a booster dose in the past six months.

For some people that represents a fifth dose since the vaccine first became available.

SA reported 1720 new virus cases last week, up from 1495 the previous week, in what appeared to be the start of another wave.

Based on the latest modelling, health officials expect case numbers to climb to about 6000 a week by mid-March, at the height of the Adelaide Festival and Fringe arts events.

Chief Public Health Officer Nicola Spurrier said for many people it had been six months or more since their last vaccine or infection and their immunity "could do with a boost".

"We are expecting further waves of COVID-19 this year and winter will also be a time of greater risk," Professor Spurrier said.