Sorry this has taken me so long but I have a definite answer to your question.

Drinking age people (19-24) have a far higher incidence than school age people (15-18).

And honestly, the question is well-worded because alcohol has a definite role in that. /1 https://twitter.com/VixFinlay/status/1317452334105055233
These are the official 7-day incidences per 100,000 presented in the Daily Briefings.

Week 40:

19-24: 174.2
13-18: 63.2

Week 41:

19-24: 303.7
13-18: 127.3

Young adults with a far higher rate than teenagers.
This doesn't fully answer the question asked though, because this shows you 13-18 vs 19-24.

The question is 15-18 vs 19-24.

That can be calculated through combining a few pieces of information given at the October 22nd press conference, it just took me a while :)
The first piece of information is the 7-day incidence in the 19-24 age bracket is ~400.0 per 100,000 for Week 42.

Week 42 is week ending October 18th.

From that, we know the 14-day incidence for 19-24 for the period October 5th to October 18th is ~703.7 per 100,000.
We now have enough information to break down the 15-24 age group.

Because we know the incidence 19-24 and we know the population 15-18 from the 2016 Census.

First, the entire age bracket:

October 5th to October 18th, 15-24:

Cases: 2,985
14-day incidence: 518.2 per 100,000
So we have 518.2 per 100,000 across the 15-24 age band but 703.7 per 100,000 across 19-24.

Applying that, here's what you get:

October 5th-18th:

Total cases 15-24: 2,985

Cases 15-18: 657
Cases 19-24: 2,328
By knowing the 14-day incidence 19-24, it's easy to calculate the cases in 15-18.

So I can then take those 657 cases in 15-18 and calculate the incidence using the 15-18 population.

You get this:

14-day incidence per 100,000:

19-24: 703.7
15-18: 268.2
I had to tediously go through the 2016 census line-by-line because the HSE uses the census to calculate their figures and I needed to know the numbers to do this.

For anyone interested, I'll just give the population in those age brackets in the census.
This is the population for older teenagers in Ireland:

15 male 31,483, female 30,160 = 61,643
16 male 31,183, female 29,806 = 60,989
17 male 31,540 , female 29,778 = 61,318
18 male 31,183, female 29,911 = 61,094

Population 15-18: 245,044
Young adults:

19 male 29,319, female 28,253 = 57,572
20 male 28,508, female 27,829 = 56,337
21 male 27,407 , female 26,990 = 54,397
22 male 27,326, female 27,026 = 54,352
23 male 27,272, female 26,663 = 53,935
24 male 27,071, female 27,544 = 54,615

Population 19-24: 331,208
So the rate of infection in young adults 19-24 is 2.6 times higher than teenagers.

One factor in this is obviously alcohol.

15-17 year-olds don't go to pubs or house parties to get locked as much as 19-24, as their parents usually have something to say about that i.e. NO.
Another factor is mobility.

19-24-year-olds tend to get around more than teenagers.

If you remember your life at 15, it's very centered around school and home, and relying on parents for a few bob.

At 19-24, you've got college, work - some money! - pubs, restaurants etc.
I know some were thinking that secondary schools were behind the large 15-24 case rates but that isn't supported by any of these numbers.

Both the positivity rates and case rates are far lower in teenagers and the vast majority of cases in the 15-24 age band is in 19-24.
That tends to reflect a few of the above factors, such as alcohol and mobility.

What it also reflects is excellent work done in schools, both by teachers and parents, in creating a safe environment and safe behavioural patterns for children of all ages to learn.
I know 2009 feels like a lifetime ago - but people forget Irish schools were decimated during the Swine Flu pandemic.

We don't see it in 2020.

In 2009, hundreds were affected in a single school from Kerry to Donegal and basically everywhere in between. https://www.rte.ie/news/2009/0810/120538-swineflu/
The reason we are not seeing that again is due to the great work of teachers and parents.

There's still a lot of scope for teenagers to mix less with each other, though.

I've anecdotally seen a group of 20 teenagers outside Spar - nothing good is going to come from that.
Overall, the 19-24 age band has, by a considerable distance, the highest rate of infection in the country.

If anyone you know is in that age category, remind them young people are not invincible and Covid19 can kill.

We have to get those rates down so it doesn't.
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