Australia has been urged to remain calm and stop buying toilet paper, despite grim predictions that “millions” of citizens could be infected with the killer coronavirus in coming weeks.

The Prime Minister has also flagged a billion-dollar stimulus package to protect the economy from the prospect of a coronavirus recession, as well as a major taxpayer-funded advertising campaign to give families practical information about the threat.

The nation’s chief medical officer Professor Brendan Murphy made the grim prediction of millions of infected Australians at a press conference in Canberra on Thursday. But he cautioned the outbreak in Australia was under control and contained, compared to elsewhere in the world.

“We are looking at scenarios from the most benign through to some millions of people being infected over a period of several weeks,” he said.

“We think our health system is well able to cope with that, but we are making sure. The parameters have been very clear to us: That we need to be sure that we plan for every eventuality, and build capacity where we think it may be under pressure if we have one of the worst-case scenarios.”

Empty shelves at a Sydney supermarket. Photo: AAP

• Related: Diamond Princess evacuees head home as quarantine finally ends
• Related: Treasury boss warns on full hit from virus epidemic

But Scott Morrison said he did not want to scare the community by releasing the government’s predictions of how many people will be infected.

“We’ve been careful not to be speculative about this in the public domain,” he said.

“What we have done all the way through this global health crisis, I think, to be very candid and up front and we will continue to do that.

“But what we won’t do is be speculative, because we’re not in the position of creating unnecessary anxiety. But the modelling at this stage relies on a lot of data, some of which is being sourced from experiences we are seeing overseas, where you have to have a degree of scepticism about a lot of the assumptions.”

Mr Morrison confirmed a new travel ban will be introduced for travellers from Korea, along with enhanced screening for people arriving from Italy.

Professor Murphy also said there was no reason to panic-purchase toilet paper.

“The most important thing, and I say this every time I talk to the media, is that any return traveller from any part of the world where there is a COVID-19 outbreak who develops symptoms should isolate and seek medical attention,” he said.

“That is the most important way we can deal with and stop spread in Australia.

“But at the moment, there is no reason to put a mask on when you are walking around the shops, there is no reason to stop going to football matches or community activities, there is no reason to denude the shelves of lavatory paper in the supermarkets.

“We should continue a normal activity.”