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Contact-tracing systems still require work and epidemiologists say the population needs to be prepared for mass mask-wearing.
"We need a greater sense of urgency in getting prepared, because so many countries that were enjoying success in controlling Covid-19 are now struggling with relapses," University of Otago epidemiologist emeritus professor Sir David Skegg said.
"No-one wants us to have to return to a lockdown for several weeks."
The Southern District Health Board is not satisfied it can trace contacts quickly enough.
"We are continuing to build up our capacity to meet the contact-tracing targets as required by the Ministry of Health," SDHB medical officer of health Susan Jack said.
"We are fairly close to meeting the targets but we are taking a little more time to ensure we have a robust scaling up which is sustainable for our staff."
The SDHB is running pop-up Covid-19 testing clinics to lift testing rates to an effective level.
Officials were delighted with the response to pop-up testing in Queenstown this week when they had aimed for 300 tests but more than 1000 people turned up.
About a third of the tests had been processed by yesterday afternoon and came back negative for the Covid-19 virus.
A pop-up clinic will be run in Milford today.
"Covid-19 testing rates have been lower than we would like across the Southern district, outside of pop-up testing," Dr Jack said.
"We would still aim for around 400 tests per day for the region to have reasonable surveillance and assurance we do not have Covid-19 circulating undetected in our district."
She encouraged anyone who might have Covid-19 symptoms to make an appointment with their GP and be swabbed. Patients are not charged for this.
Dr Jack reminded people of how they could help contact-tracing efforts.
"We would encourage all businesses to use the Ministry of Health QR codes that are readily visible to customers to use."
University of Otago Wellington campus epidemiologist Michael Baker said there was not yet a culture of wearing masks in New Zealand but preparing the population to take that measure, if necessary, could make a decisive difference.
"That may make a difference in having to go into lockdown or not."
He suggested the region could run a pandemic exercise, where people would wear masks for a day while indoors.
Sir David said community spread of Covid-19 could depend on the effectiveness of the public health response and the Australian state of Victoria showed how easily things could go wrong.
"This virus spreads at an alarming rate," he said.
"In Victoria, the capacity for testing and contact-tracing got completely overwhelmed, so that a rigorous lockdown became the only feasible option.
"Here in New Zealand, we are enjoying a life of relative normality, but it is vital that we don’t become complacent.
"We should be using this lull in the battle to prepare for the next challenge."
The testing clinic at the Milford Sound Fire Station will start at 8am. Appointments are not required.