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There were 132 confirmed or probable cases of Covid-19 in the Southern District Health Board area yesterday.
That was more than any other DHB area.
Director-general of health Ashley Bloomfield this week suggested some regions might have their Level 4 restrictions eased, depending on the spread of the virus.
Mr Hawkins said those regions forced to stay in lockdown would need extra support.
"This may be a necessary public health response, but the country can't afford to have a two-speed recovery.
"They need to be working through this now, when there's still a couple of weeks up our sleeves."
He had raised the issue with Dunedin MPs, including Health Minister David Clark, at a meeting yesterday.
"If the Government are going to keep our local economy on ice, while other areas are able to open for business, they need to either work with us on a plan to mitigate that or be honest about the fact that we'll be punished for people getting sick," Mr Hawkins said.
"I’m not disappointed that they haven’t turned their attention to this specific issue yet.
"My intention in flagging it with them was that it’s better to start thinking about that now rather than having to react to things should it get to that point."