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Recently, in the UK's daily government briefing they started showing the graphs that compare national death rates, adjusted by the population size of each country.

  1. I understand the various reasons why comparisons between countries are difficult and might not make sense right now.
  2. I understand that a country's population places an upper bound on the number of people who can become infected.
  3. I can see why population density might affect the rate of infection.

But, why would the rate of infection be different because of the population size? Surely, when a virus reaches the shores of a new country, it doesn't think to itself "hey, there are a lot of people here, I'd better spread faster"...?

I hate to sound like a conspiracy theorist, but right now we in the UK might be the worst-hit in Europe, and I wonder if showing these graphs adjusted by population size might be a political attempt to make us look "not quite so bad".

But, I am very ignorant of biology and epidemiology, so maybe there is a sensible reason for adjusting these graphs by population size. Can somebody explain it to me?

Update: I have noticed that over the last few days, the UK government briefing has stopped including the charts that are adjusted by population size.

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  • $\begingroup$ Perhaps the rates are similar, but a high rate of testing is revealing more cases. $\endgroup$ – Polypipe Wrangler May 9 at 21:55
  • $\begingroup$ What really matters is the per-capita infection rate. 2800 total cases in New York City (or London) would be almost negligible. 2800 cases on the Navajo Reservation (or say in the Hebrides) would affect a large part of the population: abc4.com/coronavirus/… $\endgroup$ – jamesqf May 10 at 4:07
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It depends on what you want the graph to show you (and not just whether it makes the epidemic look more or less scary). For example, if viewers are interested in the overall impact of the epidemic, they might want to know about per capita deaths rather than total deaths (here I will only use "rate" to mean "number per unit time" rather than "number per individuals").

You're right that (1) we don't expect the epidemic growth rate (measured by cases or hospitalizations or deaths) to depend on population size (initially - once enough people have been infected to significantly deplete the pool of susceptibles, the population size does matter) and (2) naively plotting per capita deaths of regions with widely differing population sizes can be misleading.

A good solution, used by the widely redistributed Financial Times COVID-19 plots, is to plot the time axis as the number of days since 0.1 average deaths (per million) first recorded (obviously you can pick a different per capita threshold); this sets the scale appropriately for regions of different sizes.

For example this chart:

enter image description here

It looks from The Guardian's story that the government's plots are adjusted to "number of days since 50 deaths". It would seem better to use a threshold based on a per capita threshold (larger countries will hit the 50-death threshold sooner) ...

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  • $\begingroup$ Thanks! I was also using "rate" to mean "number per unit time", so your answer makes sense to me. $\endgroup$ – Martin May 10 at 9:06

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