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One of the cases is a woman in her 30s, from Peru. She is staying in Rotorua, and was known about yesterday afternoon but was not part of yesterday's official count.
She is at the Ibis. Everyone staying at the hotel is being tested and isolated.
The woman arrived on June 20. She tested positive following routine testing on day three of her managed isolation.
Everyone on the bus from Auckland to Rotorua is being followed up, as is the driver. They will be tested.
Director-general of health Ashley Bloomfield conceded there "may be more" Covid cases in Rotorua after yesterday's new infection and the fact that travellers were transported there on crowded buses.
The second case is a man in his 70s, who arrived in New Zealand on June 20.
The third is a man in his 30s from India.
Both these men are staying at the Commodore Hotel in Christchurch in managed isolation.
Bloomfield said he was confident that "very safe protocols" were followed on the transfer flight to Christchurch.
He also said they were satisfied appropriate protection was taken for those who had travelled alongside the infected passengers on the plane.
'Very good' relationship with Health Minister
The press conference was the first time he had faced media since a video went viral of Health Minister David Clark saying Bloomfield had taken responsibility for the border blunder as the health chief looked on.
Bloomfield today reaffirmed his commitment to Clark.
He said his relationship with the minister was "very good".
The clip was on Newshub's 6pm bulletin last night and was shared by its political editor Tova O'Brien on Twitter, where it has amassed more than 100,000 views.
Some have opined that Clark threw Bloomfield under the bus.
National leader Todd Muller called Clark's treatment of Bloomfield "a disgrace".
10,436 tests yesterday
There are now 1169 confirmed cases in New Zealand.
Yesterday there were 10,436 tests undertaken throughout the country, a record total.
There have now been 368,432 Covid tests done to date.
Testing will continue with ongoing community surveillance and those considered in high risk jobs on the border that may bring them into potential exposure with Covid.
Five of 190 guests who stayed at the Novotel Ellerslie at the same time as the sisters who returned to New Zealand from the UK are still outstanding - they are still being followed up.
Since 11pm last night, a team had been at the Auckland Airport working with Customs to get information on passenger arrivals. They were linking the passengers to those on New Zealand's NHI database.
For those without an NHI, for example if they had been living overseas for some time, they were working with local DHBs to generate one.
"I'm really pleased our team has been able to put that in place," Bloomfield said.
"At the moment it is quite a manual process ... we are working with Customs and aviation security to be able to get a data feed from when a door is closed on an aircraft and once it is landed and we can start to make that match automatically through the data system."
When asked about compassionate exemptions, Bloomfield said people were still awaiting the results of tests.
They continued to work with enforcement services to follow up one person.
But he said the person presented a "very low risk".
It was revealed this week 51 of the 55 people who left managed isolation early on compassionate leave were not tested for Covid.
Forty had returned negative virus results and 11 were not being tested, for a range of reasons.
Testing of people who have left managed isolation
Of the 2159 people who had who had left managed isolation between June 9 and 16, 1184 who had been contacted and has tested negative for Covid-19.
Eight-hundred of those were people who were tested before they left managed isolation. The remaining 384 were tested after departure; 143 people had also been referred for a test and results are pending.
"We are still in the connecting with the balance, which is 695 people," Bloomfield said, adding 168 of those had invalid numbers.
"As needed, we will refer people who we do not make contact with to finding services. They get a text first and then a number of phone calls. So it is very clear who the call is coming from and we are very keen that those people actually pick up the call."
Yesterday, the ministry gave an update on the Covid-19 case definition and removed the definition of "suspected" case to introduce a new higher index of suspicion (HIS) category.
It means not everyone who has a sore throat or cold symptoms must be tested.
Bloomfield said it was best to seek advice from their doctor or healthline whether one was needed.
Instead they could be tested as part of the wider surveillance testing programme to ensure there isn't community transmission.
And only people who meet the case definition and HIS criteria will need to be notified to the Medical Officer of Health.
Those HIS criteria are that, in the 14 days prior to their illness, they:
• Had contact with a confirmed or probable case.
• Travelled internationally.
• Had direct contact with a person who has travelled overseas (eg Customs and Immigration staff, staff at quarantine/isolation facilities).
• Worked on an international aircraft or shipping vessel.
• Cleaned at an international airport or maritime port in areas/conveniences visited by international arrivals.
• Were subject to any other criteria requested by the local Medical Officer of Health.
It comes as GPs and testing stations have seen a rush on demand due to the onset of cold and flu season combined with heightened anxiety about Covid-19.
The clinical symptoms of Covid-19 remain any acute respiratory infection with at least one of the following symptoms: new or worsening cough, sore throat, shortness of breath, a head cold, loss of smell with or without fever.