The Sweden herd immunity experiment and population density.

[Pobeka]

Last edited Sun Sep 20, 2020, 08:23 PM - Edit history (3)

On edit -- I discovered Sweden has municipalities, with populations and areas conveniently available on wikipedia. The average municipality area was about half the area of the averate county in the USA, so I ran 10,000 trials of the Sweden data, with random groupings of 2, then looked at the average results of all those trials. The results came pretty close to my first analysis.
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The population density of Sweden vs the USA has been bugging me for a while. Specifically I've wondered how what percent of the population resides in low densities vs high densities, and how does that compare between the two countries? Low population densities of course mean less contacts and spread of COVID19.

I finally got data for the USA an Sweden yesterday, and ran up some summaries. Sweden has 21 counties, 290 municipatlities to get areas and populations. The USA dataset has 3137 counties. I made density classes (population/square km) that were somewhat reasonable for the comparisons. In the numbers below, a %X number means X percent of the total population. Here's some summary stats:
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Sweden has 17% of the population at a density > 300, vs 40% for the USA (Stockholm is 364.9)
Sweden has 17% of the population at a density > 600, vs 25% for the USA
Sweden has 9% of the population at a density > 800, vs 18% for the USA

You can see at high population densities the USA is significantly greater than Sweden. How about the lower densities?

27% of Sweden < 25/km**2 vs 12% USA
49% of Sweden < 50/km**2 vs 22% USA
63% of Sweden < 75/km**2 vs 28% USA
74% of Sweden < 150/km**2 vs 43% USA

Wow! Sweden has about double the percentage of their population living at densities under 75 per square km relative to the USA.
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Some thoughts:

- It is not reasonable to compare Sweden to the USA because of the dramatic differences in population density
- Sweden, like all the EU, is starting to see an uptick in the number of cases in the past few days
- It would be interesting to see how Stockholm's case numbers compare to the rest of Sweden.
- There are of course other cultural differences at play. Customs regarding social interaction, education level, etc.

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Here are the outputs from my summarization. You can see the exact classes I defined, the % of the population living in that class, and cumulative %'s ascending and descending by classes. Note -- given the datasets, the total population may be slightly different than other estimates you'll see. There were also 6 or 7 counties without land areas, so I could not use them.

(Pardon the formatting, I used '_''s to space the columns.)

Population_of_SWEDEN_is_10327589,_with_290_municipalities,_area_of_407339.230001371,_mean_analysis_area=2809_sq_km
Population_of_USA_is_328142882,_with_3137_counties,_area_of_9770231.06834291,_mean_analysis_area=3115_sq_km

____________pop/(km**2)_%inclass_%above______%below
SWEDEN________0_-_25_27.01_(72.99_>_),_(27.01_<=)
SWEDEN_______25_-_50_21.86_(51.14_>_),_(48.86_<=)
SWEDEN_______50_-_75_14.18_(36.96_>_),_(63.04_<=)
SWEDEN______75_-_100_10.63_(26.34_>_),_(73.66_<=)
SWEDEN_____100_-_150__4.89_(21.44_>_),_(78.56_<=)
SWEDEN_____150_-_200__2.94_(18.51_>_),_(81.49_<=)
SWEDEN_____200_-_300__1.93_(16.58_>_),_(83.42_<=)
SWEDEN_____300_-_400__0.00_(16.58_>_),_(83.42_<=)
SWEDEN_____400_-_600__0.00_(16.58_>_),_(83.42_<=)
SWEDEN_____600_-_800__6.65_(_9.93_>_),_(90.07_<=)
SWEDEN____800_-_1000__0.00_(_9.93_>_),_(90.07_<=)
SWEDEN__1000_-_20000__9.93_(-0.00_>_),_(100.00_<=)


___USA________0_-_25_12.06_(87.94_>_),_(12.06_<=)
___USA_______25_-_50_10.01_(77.93_>_),_(22.07_<=)
___USA_______50_-_75__5.99_(71.94_>_),_(28.06_<=)
___USA______75_-_100__4.76_(67.18_>_),_(32.82_<=)
___USA_____100_-_150__9.61_(57.56_>_),_(42.44_<=)
___USA_____150_-_200__7.45_(50.12_>_),_(49.88_<=)
___USA_____200_-_300__9.37_(40.74_>_),_(59.26_<=)
___USA_____300_-_400__6.45_(34.29_>_),_(65.71_<=)
___USA_____400_-_600__9.62_(24.67_>_),_(75.33_<=)
___USA_____600_-_800__6.35_(18.32_>_),_(81.68_<=)
___USA____800_-_1000__5.97_(12.35_>_),_(87.65_<=)
___USA__1000_-_20000_12.35_(-0.00_>_),_(100.00_<=)



Data sources:

USA land areas by county:
https://www2.census.gov/library/publications/2011/compendia/usa-counties/excel/LND01.xls
(using column LND010200D for area in square miles)

USA population by county:
https://www2.census.gov/programs-surveys/popest/datasets/2010-2019/counties/totals/co-est2019-alldata.csv
(using column POPESTIMATE2019 for population)

Sweden Land area and population:
https://en.wikipedia.org/wiki/List_of_municipalities_of_Sweden
http://www.statistikdatabasen.scb.se/pxweb/en/ssd/START__BE__BE0101__BE0101C/BefArealTathetKon/

[mitch96]

1. Pardon but what does this mean? Herd immunity works in Sweden or no?? I'm really lousy

and picturing how this works. Is this a comparo of US vs Sweden effect of herd immunity?
m

[Pobeka]

2. I'm considering the possibility of confounding.

The Sweden experiment was supposedly about herd immunity (BTW for which there was no evidence long term immunity could be achieved in an individual)

What do you have to show the experiment worked? -- basicially number of cases. And now we have a voice in the Trump admin pushing herd immunity, and he'll be holding up Sweden as an example (as many do).

But, if case number are your metric for comparison, you have to have similar populations. What I am getting at is Sweden's population is so much lower in density, that they would naturally have lower case numbers simply because of the lower population density, not necessarily because there was some short or long term immunity achieved by those who became infected.

Does that make sense?

[mitch96]

7. Yes, now I see it.. Question.. would compareing percentages level out the field?

Yes we have a larger population density and if 25% of a country got the virus and 25% of a smaller country got the virus would mean they effectively have the same contamination rate?
LIke I said I'm no good with mathematical word problems so I look at the last time we used herd immunity in a pandemic... The 1918 flu pandemic... There was no vaccine and they did what we are doing now... I have to find out how long that lasted.. I know a lot of people died around the world. We have better communications now so we can get the word out on what works and what does not. Now getting people to do it is another whole ball of wax...
m

[Pobeka]

8. You are asking the million dollar question, as they used to say...

--- All things being equal ---, yes, comparing %'s would be a fair comparison. Usually you'll see numbers like cases/10,000 or cases/million capita.

But, all things aren't equal.

An important criteria is how hard are they testing?

If country A is testing everyone, then they will detect all "detectable" cases, even those with mild symptoms that need no hospitalization.
If country B is only testing people with severe symptoms, then they will miss the mild symptom cases.

So in that example, it may look like country B has a lower infection count than country A, but it's an artifact of testing protocol.

And the tests and test labs themselves may be different between country A and country B, somewhat altering results.
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I tended to look at deaths/million capita early on in the pandemic as a more robust measure for comparing populations. But in the USA, at least, some states like Florida have been reported to actively alter even death data.

Another aspect of deaths is as time goes by, less percentage of people are dying as doctors understand better how to treat people that are hospitalized. I now think a better metric for comparisons my just be ICU hospitalization rates.

[sanatanadharma]

3. Compare Arkansas and Uruguay

The two political boundaries have widely different reported experiences, although density is close.
Arkansas and Uruguay reported their first Covid-19 cases two days apart.

Their population, area and density are close.
Uruguay 68,037 mi² (176.215 km²), 3.5 million population, 20 persons/sq km
Arkansas 53,179 mi², 3 million population, 22 persons/ sq km

As of the 19th September, Uruguay, bordering Brazil, has (Arkansas in brackets):
1904 reported cases (75160)
247 active cases
0 in ICU
46 deaths (1181)
1612 reported recovered

Arkansas is much worse, but to be fair, can't secure its borders as effectively as can a country.
Arkansas is (as though) surrounded by Brazil.

[Pobeka]

4. Can you guess the average population density experienced by an Arkansas resident?

(Thank you for your question by the way, it made me rethink something important)

The answer to my question in this post is 65.9

Why such a big difference?

I don't want the population of the entire area / the area in question. I want the area broken up into subunits, so the higher population and population density of cities are appropriately accounted.

I want the mean population density per person, which is the weighted mean:

Sum of (population in county * population density in county) / Sum of (population in county)

This is the problem of coarseness of scale of the comparisons. The finer the scale, the higher the average population density (weighted by population in subunits).

Arkansas has 75 counties -- used to get the 65.9 average population density per person.
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Ideally I'd like a spatial analysis --- drop 1 sq km grids over the entire area in question, get the population of each of those units, then compute the sums...

I don't have that data at the moment. Not sure it even exists, that would be some fine grained census data.

Dang.

[Silent3]

5. This is a tricky thing to calculate and extract meaningful numbers from

The simplest way to define population density is, of course, to simply divide population by area.

But that simple definition is not very useful for epidemiology, because if most people lived in densely crowded urban areas with sprawling sparseness in between, that would be a totally different situation epidemiologically than a very evenly distributed population.

The OP obviously recognizes this problem, hence the county-based approach. But I don't think that helps the analysis enough, because even within those counties there can be a lot of sparsely populated or unpopulated area mixed with urban density. After you get beyond the next closest person being, say, 1000 feet away, does it make any great difference to disease transmission if that figure goes up to 1 mile or 10 miles away?

I think you'd have to define constant unit of area, something much smaller than a typical county, and break each country up into a grid of such smaller areas and count the people in each unit area to get to where you're trying to go.

For this, however, the raw data would be much harder to come by.

And even if you did have these numbers, you'd still only get a better rough approximation of what's epidemiologically important, which is amount of time each person spends in proximity to another person, the degree of proximity, degree of confinement and air flow, and some sort of "networking" factor that accounts for exposure to familiar people vs. unfamiliar people. Those are the factors I can think of now off the top of my head.

You might get some still-useful comparisons between different countries when lacking some of that data, or having only rough guesses at some of that data, but I don't think you'll get very far without a bit more complexity than population density.

The data best source I can think of for this kind of analysis would be anonymized cell phone location data. That data could tell you a great deal about the mixing and movements and distances between people, and the timing of it all too.

[Pobeka]

6. Thank you. Yes it's daunting.

As you point out and I said similarly in post #4, it'd be great to drop a 1 sq km grid, run the stats...

Anonymized cell phone data sounds fun, but huge and not really accessible to me.

I think finding the municipality data for Sweden helped tremendously, giving a granularity of area that is on average 1/2 the area of a US county.

Still, an analysis area of ~3000 sq km, or 1600 sq miles leaves a 30 mile travel distance edge to edge if the area is a square -- quite a distance indeed, lots of room for small cities etc.

At least, though, I have it about apples for apples.

As for the rest of the epidemiological considerations, all I can assume is equivalence with this data.

Given all that, I think there's evidence here to say the typical person in Sweden experiences much lower population density than the typical person in the USA.

It would be fascinating to see the results from a smaller analysis unit, though at some point (as you know), you have to start connecting these smaller units with probability of infection vectors.

I could work the other way and group larger and larger units, and make plots of the average population density vs analysis area size, then extrapolate (oh my!!) to an analysis area size smaller than the dataset, but that'd be a lot of work with no knowledge of the reliability of the extrapolation, so I'm not inclined...

Thanks very much for your response!

[struggle4progress]

9. But people are saying herd mentality does work. Many people. Many many people.

But you have to take it with the zinc

[muriel_volestrangler]

10. There are statistics for Swedish regions here

https://www.svt.se/datajournalistik/the-spread-of-the-coronavirus/

Deaths/100,000 for Stockholm are 101, which is the highest for the country - the average is 58, 2nd highest 85, 3rd 66.

The region ('county') has a population of about 2.3 million, and the city itself 1 million.