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"The team member was tested and self-isolated as soon as they started to show symptoms and will now be treated by local healthcare authorities," McLaren said in a statement.
"The team has prepared for this eventuality and has ongoing support in place for its employee who will now enter a period of quarantine. The team is cooperating with the relevant local authorities to assist their investigations and analysis."
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Mercedes driver and reigning F1 champion Lewis Hamilton had earlier said it was "shocking" that the F1 opener was going ahead, at the same time as countless sporting events were being cancelled across the globe and US President Donald Trump had closed his country's borders to travellers from the EU.
"I am really very, very surprised we are here," Hamilton told reporters at the Albert Park media centre on Thursday, a day before the cars roll out for the first free practice sessions at the circuit.
"It is great we have races but for me it is shocking that we are all sitting in this room. There are so many fans already here today. It seems like the rest of the world is reacting, probably a little bit late.
"But already this morning we've seen (U.S. President Donald) Trump shutting down the borders from Europe ... we're seeing the NBA has been suspended yet Formula One continues to go on."
A general view of the start lights before the F1 Grand Prix of Australia at Melbourne Grand Prix Circuit on March 17, 2019 in Melbourne, Australia
Image credit: Getty Images
News of McLaren's withdrawal will naturally invite questions as to whether the whole opening race should be cancelled.
Over 12,000 people have signed a petition asking for the race to be postponed.
Several staff from the Haas and McLaren teams have been placed in quarantine. However, tests on four Haas team members who had been quarantined due to the outbreak came back negative, a spokesman said.
The Chinese Grand Prix, which was scheduled for April, has already been postponed while the Bahrain race on March 22 will go ahead without spectators.
Doubts have also grown about next month's race in Vietnam due to its quarantine measures.
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