A number of other countries have introduced such measures.
Melbourne, Australia is the latest city to fine people who fail to comply, after it experienced an increase in Covid-19 cases which caused the states of New South Wales and Victoria to close their borders.
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TCD Professor Luke O'Neill believes we may have to follow suit.
"Many countries have made it mandatory, not just in shops, but outside.
"In Melbourne, it's mandatory anywhere now, on the streets you have to wear a mask. On the sport fines if you don't. We may be heading in that direction."
