Australia now has 4513 coronavirus cases.

Strict social isolation rules appear to be working as the number of new cases has dropped.

On Monday, Australia recorded 261 new cases of coronavirus.

Just two days before, on March 28, Australia had 458 new cases of COVID-19.

The latest cases are still largely from overseas.

However, NSW and Victoria have reported a growing number of COVID-19 cases from local transmission.

The graph below shows the daily increase of positive coronavirus tests in Australia from the date of the first infection on January 25.

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At 8am Tuesday, New South Wales has 2032 coronavirus cases.

Victoria has 917.

Queensland has 743.

South Australia has 305.

In the video below Chief Medical Officer, Brendan Murphy gives new hope for new COVID-19 cases in Australia.

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Western Australia has 355.

The ACT has 78.

The Northern Territory has 14.

Tasmania has 69.

The graph below shows how coronavirus cases in Australia have grown state-by-state.

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Health experts and leaders are cautiously optimistic about the slowing growth rate in virus cases.

But it could still be months before Australia can afford to lift the heavy social restrictions in place to slow the spread of coronavirus.

Gatherings of more than two people - apart from families - in public and private have been banned and older Australians have been urged to stay at home for their own protection.

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Anyone returning from overseas must now spend 14 days in hotel quarantine.

The graph below shows the rise of COVID-19 in Australia.

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So far, 18 people have died from coronavirus in Australia.

All have been aged over 68.

But young people aged 20-29 are the demographic with the highest numbers of coronavirus in Australia.

The total number of confirmed COVID-19 cases in Australia by sex and age group. Credit: Health.gov.au

NSW is expected to update the number of coronavirus cases at 8am on Tuesday.

7NEWS.com.au will continue to update this story with the new cases as they are confirmed.