So in some sense, we actually have an appropriate control for your assertion that its down to population density.
In general, the data does not support your assertion around population density, as the Republic of Ireland has (post lockdown) a rate of 88.5 per 100k, whereas Northern Ireland has a rate of 2788 per 100k.
Source 1: https://www.ecdc.europa.eu/en/cases-2019-ncov-eueea Northern ireland: https://www.health-ni.gov.uk/covid-19-statistics
So, in this particular case, it seems unlikely that population density is driving the differences.
I do agree that raw country comparisons can often mislead, but i stand by my original points.
The figure you've quoted is close to the total for all of Northern Ireland (2,505) for the last 7 days.
I think the general point is still valid though, as there's a substantial difference between the two regions.
Northern Ireland also has loads of inter UK travel every day, I know people who were at some points commuting from London to N.Ireland.
I didn't want to get into a whole explanation for someone, just to make a point about density not being the primary driver in this case (although it definitely has an impact).
So it's not people per area. Perhaps a better measure is "mean distance" between people? That means Australia is pretty dense because most people live in dense areas. Urbanization is obviously a much better metric than raw density.
But this also misses another important factor: Australi, and Sweden (which are sparse but urbanized so low pop/sq.qm but low mean distance), unlike the UK is pretty "disconnected". There are clusters with high density, but they are separated by areas of low density.
It's likely better in an epidemic to have 3 cities with 1 million separated from each other, than 30 cities with 100k people each, where people in each cities visit/commute to the next 5 cities. That's what some places like UK/Netherlands/Belgium have. They are extremely dense in the sense that it's always close to the next population center. There are no natural borders or empty spaces. People from city A work in town B, and some fraction of people in town B work in city C and so on. Towns A and Z are connected by just a few days worth of normal commute for thousands of people.
https://www.sheffield.ac.uk/news/nr/land-cover-atlas-uk-1.74...
I commute to the CBD every day and it's nowhere near like it was, I can get a seat on the train, even with distancing. I couldn't even get a seat during rush hour before covid.
The UK is one of the most densely populated countries in the world, 14th according wiki.
Ireland is one of the least densely populated countries in the world 112th.
I see these intercountry comparisions all the time and it makes no sense, every situation is vastly different. I'm in Australia, and know I have it good, but Australia had all the factors going for it, it's easily isolated from inter country travel and it has very sparsely populated cities. It's economy is also propped up with an abundance of natural resources unlike services based economies like the UK.