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Scott Morrison has rejected trying to wipe out coronavirus with a longer lockdown as he claims it would be against Australia's way of life.

The Prime Minister announced on Thursday that the country would stay at stage three restrictions for another four weeks, then review relaxing them.

He was asked why he had ruled out following New Zealand in trying to eradicate the virus as the number of new cases plummeted to just 34.

Scientists have predicted this could be slashed to zero by the middle of June if the lockdown persisted for another two months. 

Modelling from the Universities of Sydney (orange) and Melbourne (green) shows Australia can get to zero new cases within 90 days of lockdown. The current trend in recorded cases (yellow) is already ahead of this

But Mr Morrison said the economic and social damage that would cause was 'not a wise trade-off' and he didn't want to 'copy' New Zealand.

'Eradication pathway involves an approach which would see even more economic restrictions that are currently in place,' he said.

'The policy we have been following for a month has sat well in the groove of Australia's ethos and how we live.

'It is rubbing at the edges a bit in parts of the country and that is understandable. We like our freedom and being able to do what we want to do. 

'We like to have the barbecue we like going out, we are very sociable beings, Australians, and we miss it.

'We miss our kids being able to get together and go to school and be with their friends, we miss all of that.'

Mr Morrison said Australia would stick with the suppression strategy that tries to limit the spread of the virus to what the health system can manage.

Scott Morrison rejected trying to wipe out coronavirus with a longer lockdown as he claims it would be against Australia's way of life

Chief medical officer Brendan Murphy said Australia may eradicate coronavirus with the current plan anyway

Chief medical officer Brendan Murphy said at the same press conference that Australia may eradicate coronavirus with the current plan anyway.

'It is quite possible we could eradicate the virus in some parts of the country. Some states have had no cases for days or a small number of imported cases,' he said.

'We are on the same trajectory of New Zealand which is aiming for eradication.

'The difference [is] that we don't feel the need to hold the country very seriously locked down until we have no cases. If that happens with the measures we are doing now, that would be fantastic.' 

Travel bans, closed borders, and business shutdowns have slashed the number of new cases a day by up to 90 per cent in less than a month.

The country only recorded 34 new cases on Wednesday, compared to 460 on March 28, raised the total number to 6,449 with 63 deaths.

Stage three restrictions on gatherings and leaving the house brought in on March 31 are expected to crush the curve further over the rest of April.

Australia's measures have been so successful that Mr Morrison and state premiers next month will begin planning how to wind back the lockdown.

However, a collection of scientists believe Australia's local transmission cases could be reduced to zero if the restrictions are kept in place another two months.

'We like to have the barbecue we like going out, we are very sociable beings, Australians, and we miss it,' Mr Morrison said in defending his strategy

Scenes like this one in Melbourne where a family is told to go home from St Kilda beach under stage thee lockdown need to continue for another two months

Analysis by the Grattan Institute concluded that the country would not need a tougher lockdown to achieve this, but to extend stage three a little longer.

'A successful elimination strategy would give most Australians a good chance of resuming a near-normal life well before the end of the year,' authors Stephen Duckett and Jonathan Nolan wrote.

They pointed to separate recent modelling by two Australian universities predicting a 90-day lockdown would result in no new cases by mid to late-June.

Dr Jason Thompson at the University of Melbourne said his modelling showed local transmission of coronavirus would be eradicated by June 19 on average across states.

His model assumed 85 per cent of Australians followed social distancing rules 85 per cent of the time and 90 per cent of those told to self-isolate did so.

Analysis by the Grattan Institute of these models concluded that the country would not need a tougher lockdown to achieve this, just extending stage three a little longer

Dr Jason Thompson at the University of Melbourne said his modelling showed coronavirus would be eradicated by June 19 on average

James Jansson at the University of Sydney came to the same conclusion, writing that if Australia tried to eliminate transmission of the virus, the 'pain would be measured in months, rather than years'.

'This can give both business and citizens the strength and determination to stick to the lockdown and be ready to exit the other side with all pistons firing,' he wrote.

Dr Ducket and Dr Nolan said this strategy was being employed in New Zealand with its even harsher lockdown with great results - and Australia could do even better.   

'The prospect of 90 days of stage three restrictions is daunting, but there are good reasons to believe we could bring cases down to zero earlier than that,' they wrote.

The pair wrote that Australia's new cases have been halving every 4.2 days for the past week, far less than the 16 days employed by the models.

'Even if that trend slows over the next few weeks, there's a real prospect that many states could begin easing spatial distancing as early as May, with a clear plan in place by Anzac Day,' they wrote.

Australia has made significant progress in the fight against coronavirus, with a clear flattening of the curve on the graph that measures the daily infection rate

Manly Beach in Sydney is shut down to stop the spread of coronavirus. Big beaches could be reopened soon but scientists argue they should stay shut another 2 months

Knocking out that last few cases and preventing them from starting new outbreaks would be the hardest part, requiring every patient to be locked down fast. Testing centres like this one in Bondi will be a key part of that effort

Knocking out that last few cases and preventing them from starting new outbreaks would be the hardest part, requiring every patient to be locked down fast.

Australia is already gearing up for this by ramping up contact tracing abilities with an army of health workers tracking down everyone an infected person had contact with.

The government is also floating the idea of digital tracking of the individual's movement via mobile phones, as used in Singapore and Taiwan. 

The app, which will be optional, would require at least 40 per cent of the population to be on board for it to be effective, according to the ABC.

However, the trade off is that international travel would be off limits for many months to come, to prevent Australians contracting it abroad and bringing back, restarting local transmission.

The downside of Australia's relatively few cases is the lack of herd immunity, leaving locals vulnerable to any new flare-up.

Dr Thompson said there are means to regulate international travellers, such as requiring them to be certified as virus-free before arriving, being quarantined for two weeks upon return as they are now, or both.

'Wouldn't we all prefer to at least have unrestricted movement within our own country in the meantime?' he wrote.

Borders could also be opened to individual countries as they got the virus under control, such as New Zealand which is on track to stop their transmissions. 

Grattan Institute said this strategy was being employed in New Zealand with its even harsher lockdown with great results - and Australia could do even better

Overseas travel would be off limits for some time, but could be relaxed if arrivals were quarantined in hotels, like this woman at Sofitel Wentworth in Sydney

Australia's policy had been to flatten the curve of the rate of infection to prevent a spike in pressure on hospitals rather than introduce the most stringent methods to eliminate transmission.

Chief medical officer Brendan Murphy said the country's peak of cases could be as late as November based on current modelling.

Under this suppression method, stage three restrictions could be relaxed within weeks but others may have to remain for far longer.

'Unless herd immunity is achieved, a significant proportion of the community will continue  to be susceptible and illness and death will result, albeit at a lesser rate than in the 'let it rip' scenarios,' Dr Thompson wrote.

'Significant social and economic restrictions will still need to continue for an unknown duration.'

State and federal leaders will meet on Thursday to discuss when restrictions on travel and gatherings of people can be relaxed.

Mr Morrison has stressed that a premature relaxation of all restrictions risked a rise in infections, but said the government was ready to discuss plans to gradually re-open the economy.

'That's what we're working on as a National Cabinet,' he said.

'We will be considering further plans about how we can chart that way back to get the economy operating at a much higher level than it is now so it can support people's incomes.'