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The vaccines will be administered by appointment at three central hubs located at Westmead, RPA and Liverpool hospitals, Ms Berejiklian confirmed on Wednesday morning.
Anyone who receives the vaccine will need a second dose a few weeks later.
NSW Chief Health Officer Kerry Chant said the priority was to protect workers at greatest risk of coming into contact with the virus.
An estimated 10,000 to 15,000 workers across the quarantine system will be covered in the first three weeks. The balance will target other health workers.
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“We think this is a healthy number to have vaccinated in the next three weeks to cover us, but obviously the more you do, the better,” Ms Berejiklian said.