NSW Health will step up coronavirus testing in some of Sydney’s wealthiest suburbs and other areas across the state after evidence of local transmission of the deadly virus.

NSW’s coronavirus hotspots include the local government zones of Waverley, which takes in Bondi in the city’s east, and neighbouring Woollahra, which is home to some of Sydney’s ritziest suburbs.

Other areas of concern include Manly in the city’s north, Dee Why and Ryde. Outside of Sydney, they include Lake Macquarie and Port Macquarie, Nowra and South Nowra and Broken Hill.

• See coronavirus cases in NSW, by local government area, here

NSW Health executive director Dr Jeremy McAnulty said coronavirus testing had dropped off at the weekend, but it would be increased again in communities with evidence of local transmission.

“We want to encourage increased testing in those communities where we have seen even a few local cases of transmission,” he said.

“We are extending testing and encouraging patients who have got symptoms…of acute respiratory infection, a cough, shortness of breath, sore throat or fever,” he said.

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NSW had 2637 confirmed coronavirus cases on Monday, and the state’s death toll rose to 18 after men aged 85 and 86 died in Liverpool Hospital on Sunday.

The latest figures include 595 infections locally acquired from known cases, while 397 were locally acquired from unknown contacts.

NSW Health said on Monday the state had recorded 57 new cases. That was a drop on Sunday’s growth – partly due to fewer tests at the weekend.

There are 40 people in intensive care units, 22 of them on ventilators.

Tweet from @WaverleyCouncil

Dr McAnulty said case numbers in recent days had been “really hopeful” and it seemed contract tracing and social distancing measures were working.

“But it’s too early to make too many assumptions; we need to keep a very close eye on these figures,” he said.

NSW Premier Gladys Berejiklian welcomed the fall in new cases but said those acquired through community transmission remained a concern.

Elsewhere, Western Australia’s toll rose by one, with the death of a man in his 80s at Royal Perth Hospital.

Victoria’s coronavirus fatalities rose by two on Monday – a man in his 50s died at home and a woman in her 80s died in hospital. The state had 1158 confirmed cases on Monday, up 23 from Sunday.

Victoria has 88 confirmed cases of COVID-19 acquired through community transmission and the state has carried out more than 57,000 tests.

There are 45 coronavirus patients in hospital in Victoria, including 11 in intensive care.

The state has expanded its criteria for virus testing as the number of community-transmitted case has risen.

“The number of community acquired cases contracted from an unknown source are continuing to rise – the expansion of the testing criteria will allow us to get a clearer picture of how much the virus is circulating,’ chief health officer Professor Brett Sutton said.

Victoria’s coronavirus cases are also concentrated in wealthier areas. Stonnington, which covers Toorak and South Yarra, has the most. Banyule, in Melbourne’s north-east, is next, and then Boroondara, in the city’s inner-east.

Queensland’s cases are concentrated in Brisbane, on the Gold and Sunshine coasts and in Cairns.

Another 14 cases of coronavirus were confirmed in the state on Monday, taking its total tally to 921.

Queensland has also broadened testing criteria after 32 cases where authorities could not determine where the virus was acquired.

“I think this is pre-emptive, ahead of local transmission, so I don’t see there’ll be a big increase in numbers,” Queensland chief health officer Dr Jeannette Young said said.

“Once we do see increased community transmission outside those areas – Gold Coast, Brisbane and Cairns – we’ll increase the testing there as well.”