The first person-to-person transmissions in Australia, new positive cases and a man's death are testing the country's readiness to tackle the coronavirus.

 Biosecurity control orders could soon be imposed to direct Australians suspected of carrying the coronavirus to remain in lockdown.

Human health "response zones" could also be declared, banning people from attending places of mass gathering like schools and shopping centres.

Attorney-General Christian Porter said the laws were already used in a "limited and narrow" way at border points, if incoming travellers are suspected of being sick.

"It's very likely that these laws will get used on a larger scale," Mr Porter told ABC radio on Tuesday.

"And it's very likely that Australians will encounter practices and instructions and circumstances that they have not had to encounter before."

Mr Porter acknowledged the laws would feel "strange and foreign" to many people.

"But they will become very important, I would suspect, over the next couple of months."

Australia's efforts to contain the coronavirus have suffered a blow after the first person-to-person transmissions in the country, potentially influencing daily gestures like greetings.

The sister of an infected man recently returned from Iran and a health worker, both in Sydney, were confirmed on Monday as having the first locally-acquired infections.

These two cases, along with Tasmania's first positive report, brought the nation's confirmed cases to 33, one day after the first death from the disease.

James Kwan, 78, was the first Australian to die from COVID-19.

He and his wife were among the evacuees from the Diamond Princess cruise ship, and both fell ill after being taken to Darwin for quarantine.

As the number of virus cases grew, Chief Medical Officer Professor Brendan Murphy issued a stern warning, stating "it's no longer possible to absolutely prevent new cases coming in".

NSW Health Minister Brad Hazzard on Monday urged people to stop shaking hands and instead opt for a pat on the back.

Efforts will now focus on quickly isolating newly-infected people and dissuading or banning Australians from heading to virus hotspots.

Italy and South Korea are among the countries the government will keep a close eye on. People returning from those countries will need to monitor their health for 14 days after their arrival home.

Prof Murphy said, however, the situation in Iran was different as alarm bells had been ringing after more than 60 deaths from about 1500 cases.

Iran joined mainland China as the two countries from where arrivals will be denied entry for 14 days, except for citizens and permanent residents.

Globally there have been more than 88,500 infections and more than 3000 deaths spanning 67 countries and regions.

The health emergency has seen stock markets plunge across the world, triggering fears of a global recession.

The Australian market on Monday closed down almost one per cent, which was a vast improvement on the dive of more than three per cent in previous trading.

Prime Minister Scott Morrison intends to meet with Reserve Bank heads to discuss the impact on the economy.

"This is a health crisis, not a financial crisis, but it is a health crisis with very significant economic implications," Mr Morrison told parliament.