Patients 19 and 20 who have tested positive for Covid-19 are Waikato residents who returned from overseas this month.

A woman in her 20s arrived from Sydney on March 8 and a man in his 70s arrived from Europe on Sunday.

Their flight numbers are still to be released by the Ministry of Health in an effort to trace close contacts on those flights.

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It comes as the Avantidrome at Cambridge closed today after a person with coronavirus symptoms was at the cycling centre, and a staff member at Hamilton City Council is in self-isolation awaiting Covid-19 test results.

It's believed none of the Waikato cases have required hospitalisation.

Hamilton mayor Paula Southgate said Hamilton City Council was urgently identifying "creative ways" to help minimise the economic impact of Covid-19 on the city.

"Our key focus right now is on following public health guidelines and making sure we do our part of help stop the spread the virus.

"But we know the potential economic impacts mean this is a really worrying time for people," Southgate said.

Southgate said a city-wide rates freeze was not on the cards but the council would focus on a more targeted approach to helping those people and businesses most likely to struggle.

"We need to be sensible, we need to be considered and we need to target any potential help where it is most needed and where it will deliver most benefit."

Options on the table included working with central government and other Waikato councils to look at stimulus projects which could generate economic activity.

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She said councillors expresses support for a hardship fund.

"We also have an existing rates remission and rebates scheme which we could look at extending or adjusting, so these are all options."

Around the city and district, sports competitions were being cancelled today.

Athletics in Cambridge, Waikato's junior touch rugby competitions in Hamilton, and Northern Districts Cricket all notified schools and individuals of the premature season ends.

At least one retirement home, Resthaven in Cambridge, was in lockdown.

It follows an announcement this morning by Ryman Healthcare to stop non-essential visits and that visitors sign health declarations or be turned away if they had recently travelled from overseas.