Data on the spread of the disease will be monitored closely in certain counties over coming days. Officials told The Irish Times they are particularly concerned about counties Louth, Donegal, Waterford, Kildare, Offaly and Wicklow.
In Louth, the 14-day incidence rate of the disease now stands at 102 cases per 100,000 people. In counties Donegal and Waterford, the rate is at 97 and 94 cases respectively.
In comparison, when local restrictions were imposed in Co Kildare in early August, the 14-day incidence of Covid-19 stood at 130 cases per 100,000 – in counties Laois and Offaly the incidence rate was at 70 and 90.
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In the North, Belfast and surrounding areas are also seeing a high rate of infection – the city council area has an incidence rate of 123 cases per 100,000 people over the most recent fortnight.
The council areas for Derry, Strabane, Newry and Armagh are also seeing increasing rates of transmission and confirmed cases. All have incidence rates above 100.
New restrictions will be imposed across the North from Tuesday night. There will be no mixing of households indoors with some exceptions, and no more than six people from two households can meet in a garden.
The move followed an urgent meeting of the Northern Executive on Monday afternoon.
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Dublin continues to have the highest incidence rate of coronavirus in the country, with the numbers expected to continue to rise over the coming days.
The infection rate in the county now stands at 138 cases per 100,000 people over the last two weeks, almost double the national average at 70 cases per 100,000.
Dublin is now in Level 3 of the Government's Covid-19 plan. Level 3 restrictions mean the city is subject to tighter rules than the rest of the country.
Within the city itself, infection rates vary. Dublin North West, an area that includes Smithfield, Phibsborough, Finglas and Blanchardstown, has the highest rate currently, with 205 cases recorded per 100,000 people over the last fortnight.
Dublin South, which encompasses Blackrock, Dún Laoghaire, Stillorgan and Shankill, has a rate of 63 cases per 100,000.
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Sources familiar with discussions between public health experts and political decision-makers say the Government is in a “waiting game” to see if the number of infections in Dublin stabilises by the middle of next week.
If not, further restrictions are likely to be considered for the capital, according to The Irish Times.
This comes as the chief executive of the HSE, Paul Reid, said he was "very concerned" about the number of people in hospital with Covid-19.
There have been 14 new admissions to Irish hospitals with Covid-19 in the last 24 hours, the highest daily figure since the end of May.
There are now 94 people in hospital due to the virus compared to 23 a month ago, with 17 cases in intensive care.