Homogenous seed infections combined with heterogeneous county population sizes

[innovative-simulator]

Not a bug but a potential flaw in the method.

The expected time to peak cases (as well as the times to other events such as peak infections, peak deaths, reaching 1000 ICU beds etc.) tends to a linear trend with the logarithm of (population size / number of seed infections). This is true of other compartmental models. See for more details: https://rofasss.org/2020/08/14/role-population-scale/

But in UK.R all counties receive the same seed infections (2 per day for 28 days in the Base scenario - see line 376 and the paper).

So a small county (Isles of Scilly, 2200 people) will tend to peak weeks earlier than a large one (West Midlands, 2.9 million). As a result, the UK aggregate time series will have a broader, shallower peak than they would have had if all county peaks had tended to occur in sync. Given that the impact of an intervention can depend on its timing, homogenous seeding of heterogeneous counties will yield heterogeneous intervention impacts on them.

Fortunately, my initial tests so far suggest the effects on the model's results are small (relative to other things - the effects of interventions, the bug in intervention seed infections).

But it prompts the question, how to avoid a inserting this systematic bias between counties? E.g.

• Run the model for UK level (level 0), rather than running at county level (3) and aggregating. (Problem then: The universal mixing assumption looks really absurd: people in far north of Scotland having contacts with those in the far southwest of Cornwall etc.)
• Run each county with a seed infection schedule re-scaled to match the county population size. (Problem then: If the county receives too few seeds, it might not have an epidemic in all 200 runs. If you give Isle of Scilly sufficient seeds to avoid this, the re-scaled number of seed infections for West Midlands is big at 1300 times bigger.)
• Use a social/spatial networks model instead. (Problem: If you didn't have one for the UK back in February, then you couldn't use it.)

No clear solution - just be aware of the issue.