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The NHSX app, which is being trialled on the Isle of Wight, allows people to log their symptoms anonymously with their data only to be used by NHS staff.
Other app users would then be sent an alert if they have been in contact with the person who suspects they are infected with Covid-19.
Shapps told Sky News’ Sophy Ridge said the app will be a “fantastic way” to stop a second peak of the outbreak, but 60% of people in the UK will need to to download for it to be effective.
“The idea is that we will encourage as many people to take this up as possible,” he said.
“This is going to be a huge national effort and we need for this to work 50-60% of people to be using this app.
“Not everybody has a smartphone, and I appreciate that for various reasons not everybody will download it but it will be the best possible way to help the NHS.”
Shapps said data from the app would be used by the NHS but it would be completely confidential.
Asked how many of the 18,000 contact tracers the government has pledged have been hired, Shapps said he did not know.
He added: “It’s not an issue because the app isn’t going to be available for some time yet, a few weeks yet, but when it is there we will have the people in place.”
On when schools would reopen, Shapps said it was “also the case we are still working with teachers” to figure out “what would be safe and when”.
It comes amid reports the primary school children will be able to return on June 1.
Boris Johnson will set out details of a “roadmap” out of the lockdown on Thursday, but Shapps stressed Britain will not return to “business as usual”.
He said: “I don’t think we should expect us to go from this situation that we have at the moment of social distancing back to where we were in February – that’s clearly not going to happen and I don’t think anyone imagines that for one moment.
“The most important thing is that the absolute focus of what the prime minister will be announcing later in the week is that what we do do going forward doesn’t undo the brilliant work people have been doing to get that R number below 1 – the all-critical reproduction rate doesn’t come back up because that’s when we’d see a second spike.
“So no I’m afraid it is definitely not going to be business as usual but we do want to make sure that people understand where the routemap lies.”