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Two of the people had been in managed isolation in Christchurch and caught the charter flight to Auckland with another person who later tested positive for Covid-19.
The family travelled to Taupō last Friday, where they joined 18 others from Bay of Plenty, Wellington, Christchurch and Hamilton.
There are now a total of 35 close contacts linked to the family. Eight have returned negative test results and the remaining have been or are in the process of being tested, but all were now self-isolating, according to the Ministry of Health.
The ministry has published an extended list of shops and tourist businesses visited by the family, and says anyone who was at the same place during the relevant timeframes is considered a "casual contact", with a low risk of exposure.
If anyone becomes unwell, they should phone Healthline and stay home.
Three additional community testing centres have been stood up, one in Taupō and two in Rotorua.
The National Contact Tracing team has so far issued 15 exposure notices through the COVID Tracer App yesterday.
Locations of interest in relation to recent cases:
• McDonald's Frankton, Frankton, Sunday 20 September, 8.20pm-9pm
• Subway, Robert St, Taupō, Sunday 20 September, 5pm-5.15pm
• KFC Taupō, Robert St, Taupō Sunday 20 September, 5pm-5.15pm
• Z Turangi Service Station - Cnr State Highway 1 and Pihanga Road, Turangi Sunday 20 Septembr, 11am-11.12am
• Taupō Tandem Skydiving, Taupō Airport, Saturday, 19 September, 2pm-3.15pm.
• DeBretts Hotsprings, Taupō, Friday, 18 September, 2.40pm-6.45pm
• McDonald's Tokoroa, Tokoroa, Friday 18 September, 9.30pm-9.44pm
• Kmart St Lukes, Westfield St Lukes, Auckland, Thursday 17 September, 5pm-7.20pm and Monday, 14 September, 6pm-8pm
• Farmers St Lukes, Westfield St Lukes, Auckland, Thursday 17 September, 5pm-7.20pm
• Mountain Warehouse, Westfield St Lukes, Auckland, Thursday 17 September, 5pm-7.20pm
• Just Cuts, Westfield St Lukes, Thursday 17 September, 4pm-5pm
• Dress Smart Outlet Shopping (Jacqui E, Max, Fila, Puma), Onehunga Auckland, Wednesday 16 September, 2.45pm-5pm
• Lotus supermarket, Mt Roskill, Auckland, Saturday 12 September, 7pm-8pm
• Briscoes St Lukes, Morningside, Auckland, Saturday 12 September, 4.30pm-6pm
• Christchurch Airport - departures, Harewood, Friday 11 September, 9.30am-1.30pm