jaap wrote: ↑Thu Apr 02, 2020 11:47 am
greyspoke wrote: ↑Thu Apr 02, 2020 11:15 am
I was thinking about this. Caused by some people on the twitters going on about how the graphs by country are not informative as countries are different sizes, when that particular comparison by country graph was published. I can see the logic for a single centre of growth. But when a country has several centres (several major cities), some of which may have got their first cases independently (ie not spread from the first city to get it), will this not complicate matters?
The growth rate will be the same in both places regardless of the absolute number, so it does not matter. Every day the total gets multiplied by the same factor R in each city, and since city1*R + city2*R = (city1+city2)*R you can just lump everything together.
Only if there is reason to believe there are different growth rates, e.g. if one region is locked down and the other is not, would you need to model it separately.
Well yes, but that was not exactly my point. It was the values of city1 etc. which were the issue. Or, to put it another way, how would the figures look if you decided to split a large country up into several smaller ones for the purposes of the graph. The thing I didn't join up to this until just now was the starting points chosen for the x-axis on that graph, the time when
k (three or five I think, can't find it now) cases were discovered
in that country. That time will be earlier when you are looking at the single big country model (say, the UK) than when you are looking at the small countries (say England, Scotland, Wales and NI) separately. Or to put it another way, SUM[city0... cityn]=
k.
So looking at the UK, England saw
k cases a few days before any were seen in the others, so the England graph will be lower (for times after cases started cropping up elsewhere in the UK) but start in the same place, the graphs for Wales etc. will contain much lower numbers but with a few days shift to the left. Hmmmm.