There are concerns people who travel from Auckland while sick could be putting the rest of the country at risk.
It follows a person on a flight from Auckland to Queenstown being taken straight to hospital by ambulance upon landing, after exhibiting flu-like symptoms on Monday.
University of Otago epidemiologist Prof Michael Baker said people should only be travelling inter-regionally for exceptional reasons, and not travelling at all if they were sick.
While people might assume it was self-evident that people who were unwell should not travel, it needed to be enforced in a systematic way, he said.
Dunedin had received a large influx of students in recent weeks, including many from Auckland.
That also posed a risk to the community in terms of transmission, he said.
''I know the guideline is that you take your Level 3 restrictions with you, so they should be carrying on down there as though they are in Auckland.''
While they were expected to self-isolate, there was a chance that the lure of Orientation events might have proved too strong.
''I know it's challenging to think of the virus of a lethal threat for some people, and the social pressures of mixing and enjoying themselves, so I think it is a real risk.''
Southern District Health Board medical officer of health Dr Susan Jack said all patients presenting at Southern emergency departments were screened for Covid upon arrival.
Patients identified as higher risk were treated in isolation from others and tested.
She reminded people travelling from Auckland not to do so if they were unwell.
WellSouth's call centre had an increase in call volumes as more people sought testing, she said.
Extra staff were added to meet increased demand.
There were 121 swabs taken in the South on Sunday and 810 taken on Monday. In comparison, there were 332 swabs taken on Monday last week.
Air New Zealand chief operational integrity and safety officer Captain David Morgan said it reiterated Ministry of Health guidelines at several communication touch points for customers before travel.
''Our website states that if customers have cold or flu-like symptoms, they should stay at home, and this message is also visible on our check-in kiosks at airports.
''We have a number of flexibility options that customers can take advantage of should they need to change their travel dates.''
On board, crew followed a standard procedure for dealing with unwell passengers which involved seeking medical advice before deciding on the next course of action.
A Ministry of Health spokesman said the most common reason for travel across the Auckland boundary was for business or work.
Some personal reasons for travel were also allowed, such as health appointments or moving house.