Customers can continue to shop at Woolworths' Wellington Street store despite the man who tested positive to coronavirus visiting there on Sunday night.
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The 40-year-old Iranian man who tested positive to coronavirus visited the store between 10 pm and 10.15 on Sunday on his way to self isolation.
A Woolworths spokesperson said following advice from Tasmanian Public Health they have contacted employees who were working at the time.
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"As per Tasmanian public health advice, customers and team members should be assured they can continue to shop at our supermarket with confidence," they said.
Woolworths have however put a cap on the amount of toilet paper customers can buy.
"The purchase limit of four packs per transaction applies in-store and online, and will help shore up stock as suppliers ramp up local production in response to higher than usual demand," said a spokesperson.
Shoppers have been clearing supermarket shelves as panic over coronavirus ramps up.
Woolworths said customers could experience some stock shortages but the vast majority of products will remain available.
A spokesperson for Coles said they will continue to work with suppliers to improve the availability of popular items such as long-life food and healthcare items.
"While there may be some temporary stock shortages, the vast majority of products in our stores and via Coles online remain available for customers," they said.
They have not followed Woolworths lead in limiting the amount of toilet paper customers can buy.