The number of big households with Covid-19 cases has doubled in the last month, but overall they make up a falling proportion of the households caught up in the Delta outbreak.
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The latest figures show about 270 of the more than 2000 households that have had cases have eight or more people.
Ninety-five had 10 or more people, but the ministry said some of them are large family groups spread across a couple of homes.
In the first two months of the outbreak, one in five households with cases had eight or more people.
Delta is highly infectious, so when one person tests positive, almost everyone they live with gets it.
But the Ministry of Health said vaccinations appear to be stopping some of that onward transmission.
Director of Public Health Caroline McElnay said there have been vaccinated people in some households who have not got the virus, while the unvaccinated have.
But she said they are taking a closer look at what is happening.
"In a household situation, that's where you're going to get the most transmission and at a high level you do see breakthrough infections in households, but equally we are seeing the protection the vaccine gives, even in those settings."