While there have been no confirmed cases of the virus in Australia yet, in Queensland Premier Anna Bligh has activated the state's pandemic plan after 16 people presented with suspected cases of the disease.
There are 10 suspected cases under investigation in NSW.
”The frontline defences are our airlines and airports and what's critical is that not only government but also employers and industry, Qantas and other airlines, appropriately put systems in place to make sure we minimise the risk both to the workforce, Australian community and air passengers right across this country,” TWU national secretary Tony Sheldon said.
Mr Sheldon said the union had received calls from about 20 members around the nation expressing concern about Qantas' lack of action on swine flu.
”What is particularly of concern to us is that we've received numerous phone calls across the country that the company has not got a comprehensive strategy, they have not informed the workforce of potential symptoms, they've not notified the workforce of the potential of infecting others and it's critically important that the company deals with this in a very swift and appropriate way,” he said.
”This is the third occasion in the last decade that we've had a potential epidemic. We've had bird flu, we've had SARS and now we've got swine flu.
”We're saying to Qantas ‘you really need to get your act together’ and other airlines to have a proper, efficient and right response to this present challenge.”
Mr Sheldon said the union would not rule out taking action over the issue.
The World Health Organisation (WHO) has urged tourists to continue with their travel plans despite warnings from the European Union about visiting places affected by the outbreak of swine flu.
“WHO did not recommend any travel restrictions, we need to be very clear on that,” said Gregory Hartl, the organisation's spokesman in Geneva.
However, EU Health Commissioner Androulla Vassiliou urged people to avoid non-essential travel to flu-affected areas.
The Department of Foreign Affairs and Trade has also refused to issue a travel warning for Mexico, but says anyone who travels there should see a doctor immediately if they develop flu-like symptoms.
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