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There have been ten detected cases of Covid-19 since mandatory hotel and quarantine testing began in the quarantine facilities on 26 March, according to Niamh O'Beirne, the HSE's National lead for Covid-19 Testing and Tracing.
She said 413 people have been swabbed.
Ms O'Beirne said since 31 March, contact tracers have been asking additional questions to index cases, who were noted to have contracted the virus through community transmission.
She said of the 3,476 cases in the last week, it was indicated to do close investigation on 787 of those cases.
She said about 60% of those cases resided in Dublin.
Ms O'Beirne said when people were asked where they had been over the previous seven days "a high number" (over 55.8%) said they had been in supermarkets and petrol stations.