Hilltops mayor Brian Ingram is urging residents living in Young, Harden and Boorowa to only travel if they have to, and follow updates from health experts regarding the coronavirus.
Mr Ingram on Monday said people need to take the government's health safety measures seriously.
The first case of coronavirus was confirmed in the Murrumbidgee Local Health District on Sunday evening, in the Border region.
"I think the seriousness of this is starting to hit home," Mr Ingram said.
"We're not sure when it's going to finish and that brings uncertainty and it's understandable that people are on edge.
"I read something on social media this morning and it said the longer it takes people to practice social distancing the longer we'll have do it, and that's really it.
"It's a strange time, we're in uncharted waters."
With school holidays approaching and NSW Premier Gladys Berejiklian on Monday encouraging parents to keep their children home, rather than attend school, Mr Ingram has asked that people and families living in the the Hilltops to limit travel outside the region.
"I'll ask the community to take charge of the situation. Don't take unnecessary travel or holidays. Keep it local, keep an eye on your neighbours and the elderly. As a community we will get through this," he said.
"Look after each other. Do the right things. Everyone has a phone these days and we can get immediate updates. Keep checking. We can't stop it but we can keep it to a level that our health workers can manage it."
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Thousands of jobs across the nation were slashed on Monday as pubs, clubs, restaurants and cafes closed their doors at midday. Some cafes and pubs have temporarily closed across the Hilltops while others are adjusting to operating in take-away systems.
Mr Ingram says there needs to be immediate economic support for businesses and individuals impacted by the virus.
"Whatever side of politics you're on we know the federal government is doing all they can. They have announced another stimulus package on Sunday. My only worry is, like the drought and bushfire funding, they were too slow in getting it to the people who needed it. I hope the federal government and states can get it to the people who need it now. This could be months before things change," Mr Ingram said.
On Tuesday, Hilltops Council announced further closurses:
- Hilltops Council's Administration Building in Young.
- Council's Customer Service Centres in Boorowa, Harden and Young.
The Customer Service Team will be available over the phone, online via Council's webpage and via email only.
Council staff will remain working at this time to support ongoing service delivery.
There will be no changes to household waste collections and Waste and Resource Recovery facilities will remain open.
Previous measures announced by Council include:
- Council operated libraries in Boorowa, Harden and Young will be closed until further notice
- Council operated Visitor Information Centres in Boorowa, Harden and Young will be closed until further notice
- Council requires sports clubs, schools and any organisation that utilise Council sports fields to cease competitions until end of April 2020 at this stage. Council also encourages sporting and social clubs on private facilities to suspend activities until the end of April
- Council requires all community/social/cultural organisations that use Council facilities, to suspend meetings and gatherings until the end of April 2020
- Council encourages all sports clubs, schools and other organisations on non-Council facilities to suspend their activities until the end of April 2020
- Swimming pools in Young, Boorowa and Harden will be closed for the remainder of the season