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COVID-19 - the Swedish experiment - is it working?

Posted 1 year ago
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Jan! Good work. My own Swedish estimates are rather "black". It's going to be very bad with the Swedish "open" strategy. Based on a previous SEIR model published in Mathematica, I predict around 14000 deaths in Sweden by September... Check the file... Any comments are welcomed! Best regards Christos


Thanks Christos. It all depends on how many that have actually been infected this far (with this one could to a good estimate of the Swedish fatality rate) and how many are needed for herd immunity (with this one can estimate how many that will actually get infected eventually).

Just by looking at your graph comparing estimated with observed deaths it is quite obvious that your model is not correctly tuned. Does this mean that your total in September will be wrong? Not necessarily, but I would say it will quite likely be wrong.

You are using a very high beta resulting in 3.6 infected per infected person, while data shows that Sweden has been just above 1 for most of the time, and now has had an R value below 1 for at least a week (I don't remember exactly for how long).

Thanks Jan. I am very aware of that and have tried with much lower beta-values and a large variation of the other parameters and time as well. The above parameters were the best I could get to approximate the death numbers, so far. The death statistics are the only ones that are true, all others are not observed. To argue that the Swedish Rho is about 1 right now might be wrong too, since there are very few tests in Sweden, people are outside and nobody knows how many each (unkown) infected person infects. What we do know is that out of about 200000 tests so far, there have been slightly more than 30000 positive (i.e. a ratio of 15%). This ratio is almost equal to the Italian ratio 6 weeks ago. I therefore doubt if our Rho is so low. By the way, according to FHM, they believe that the ratio of infected in Sweden right now is about 15-17%. My dynamic graph does estimate it to about 1.8 million people (18%) when t = 82.

Well, death numbers in general are not as reliable as people think in most countries (see This combined with the fact that you point out yourself, that the number of tests varies from country to country makes it completely pointless to compare case fatality rates at this point.

Sweden has taken way more tests then is needed to get reliable data for calculating the current R (not R0, nobody knows R0). As long as you have control over your test strategy and do enough tests, then you don't need anywhere near complete testing to get a reliable number (similar to that you do not need to poll the while population in order to get a reliable answer on e.g. political opinions). But even more important than this is that you can now clearly see in the ICU numbers (steadily going down) and death rates (same there) that those claiming that R was under 1 since a few weeks back were most likely right. Reference:

Thanks Jan! I hope I am very wrong and my death estimates are too high! But I am very worried with the Swedish strategy. By the way, my initial R is about 3.84 = (0.275/0.0715) solvS[t] /. solv, if t = 0, i.e. if S[0] = 1. Today, when t = 84, the R-ratio is about 1.23 since the susceptible is about 32%, and in 4 days, it will fall to 0.99. By the end of September it will fall to less than 0.08, since the model predicts that there will be about 2% of the population as potential susceptible during the fall/winter.

There something wrong in your model. If we assume an R0 of 3.84 (which I guess you mean with initial R), then herd immunity is easy to calculate and you would reach it when 1/R0 are susceptible, i.e. 26% of the population is susceptible. To get down to only 2% susceptible you need either a much higher R0 or that you run towards the herd immunity, so the herd immunity does not have enough tome to slow down the growth. Considering that you talk about a time frame for this fall/winter then we are apparently not running towards the herd immunity.

See herd immunity here:

Ok Jan!

It is not my own model. It is posted by Arnoud Buzing, Wolfram Research, 2020-03-22 , "The SIR Model for the Corona Pandemy and modified it slightly. If you check the differential equations you see the initial R is very high, when all 10 million people in Sweden are susceptible, and it falls overtime when the S[t] falls so that with the same beta & gamma parameters there are fewer non-infected people to be infected. The infection and death rate fall (accumulated deaths reach about 13600 by the end of september). I have tried with a various length of t but the best I one I found was about 220 days, i.e. by the end of September. I repeat, I hope I am wrong! By the way, the deaths today were only 19!

A model is never better than the data it is based on, the initialization, and parameter values. In this case

As far as I can see your parameter setting do not take account at all for the impact that policies had on R0. You are using an R0 of 3.65. This might be correct (no one knows). However, we know that there has been several policies introduced and that these have affected the effective "R0". We know that this effective R0 i closer to 1 than 3.65, see and

Btw, your number of 16,000 in itself is quite reasonable. Reasonable numbers is easy to calculate by just multiplying fatality rate (0.2 - 2% perhaps) with number of infected (50 - 90% perhaps) giving between 10,000 to 180,000 deaths depending in which figures apply. Of course, the fatality rate is the most important factor here (I think they believe it's around 0.2% in Stockholm to date). That's why it is so important to protect risk groups.

Anyways, the number in itself is not that strange, but the parameter settings you have in your model simply don't add up with the current development, so the trajectory will most likely not be as in your simulation while the end result might be the same.

Great work (+1). Economically it seems that so far the Swedish experiment has not brought tremendous advantages: [Pandemic, Shutdown and Consumer Spending: Lessons from Scandinavian Policy Responses to COVID-19][1]?


Interesting, tough not very surprising. I would assume that both countries have a big part of their consumer consumption online, which is probably not that dependent on the lock down. Of course, things like restaurants, are mainly an onsite transaction (even though a lot has moved to take away), but most other businesses are no longer really in need of any physical interaction.

The question I think, is not the momentary difference, but the difference over time. Assume that Sweden goes through the Pandemic in half the time then Denmark, then the total impact on consumer consumption will probably be substantial. However, we do not know that yet. What happens if it is the other way around (yes, not that likely, but still with limited data there is still a small possibility for this)?

A probably more important factor is unemployment rates. Unfortunately, I don't think it is possible to find rates for April yet, and there will also be a lag due to employment regulations (in both countries).

As a side note, they point out that they have only looked at card payments, and mention that as a limitation for the study. For Sweden, and probably Denmark, I would guess that this a minor problem as cash is hardly used (at least in Sweden). When we don't use card we pay with the phone. I would guess that I have spent less than 50€ in cash during the last couple of years in Sweden.

Another thing that I missed mentioning, and that is really important too is which type of government support businesses and consumers have been provided, and how that affects e.g. the national dept. There's a lot of things to consider...

Thanks for the work. I see a lot of "excess of deaths" this year. And a lot of them in countries with lockdown protocols, Something that almost no one is talking about is the fact that, if we keep away from sun, we are goona have a lack of vitamin D, that is fundamental for the inmmune system. Also we are isoleting our body, this is another way to depress our inmmune system, it is call "hygienist hypothesis".

Another issue is that, people arround the globe, where quarantine have been apllied, is under a cronic stress; they are loosing their jobs, therir companies etc. This condition, stress, is a strong apigenerator, it means that modifies the DNA expression pattern, it have been assoieted with the development diseasess like cancer, coronary diseasess, mental diseasess etc.

The idea of use a medieval strategy, in order to avoid the health collapse, is probably going to be the cause of more diseasess and death in the near future. Unfortunately we can not make a model with those conssiderations.

Nice post! I like the way you very "conversationally" retrieve data and visualize them!

The time series plot very clearly shows the increased number of deaths in April 2020, but that observation does not come across in the subsequent bar charts. Making a 2D bar chart with an additional breakdown by month shows that April 2020 really stands out:

chartData = 
  TakeList[#, {31, 29, 31, 30}] & /@ dailyDeaths[[All, 1 ;; 121]] // 
   Map[DeleteMissing /* Total, #, {2}] &;
 ChartLabels -> {{2015, 2016, 2017, 2018, 2019, 2020, "Average"}, 
   None}, ImageSize -> Large, BarSpacing -> {0.25, 2}, 
 PlotLabel -> "Sweden monthly deaths", 
 ChartLegends -> {"Jan", "Feb", "Mar", "Apr"}]

enter image description here

The effect is not lost looking at the population-adjusted deaths:

chartData = 
  TakeList[#, {31, 29, 31, 30}] & /@ dailyDeaths[[All, 1 ;; 121]] // 
   Map[DeleteMissing /* Total, #, {2}] &;
chartData = MapThread[Divide, {chartData, pop}];
BarChart[1000 chartData, 
 ChartLabels -> {{2015, 2016, 2017, 2018, 2019, 2020, "Average"}, 
   None}, ImageSize -> Large, BarSpacing -> {0.25, 2}, 
 PlotLabel -> "Sweden monthly deaths (per 1,000)", 
 ChartLegends -> {"Jan", "Feb", "Mar", "Apr"}]

enter image description here

It's probably going to take years to sort out all the effects of this pandemic. The problem will be hampered by siloed data, which will compounded by too much political influence on the collection and reporting of those data.

Thanks Rob, I completely agree with you.I'm skeptical to anyone that draws too big and definite conclusions at this very early stage. Data will be added bit by bit, and as we learn to understand it and understand how reliable it is, we can start making more precise conclusions.

So far, the Swedish open society experiment has not been very successful compared to the majority of European countries that have applied much restrictive lockdown policies. For instance, if the Swedish Song Contest for Eurovision that took place on March 19 in front of 30000 people at Friends Arena in Stockholm was without public, precisely as in Denmark, it could have reduced the number of infections and deaths.


Is there any data showing that the event at Friends arena helped spreading Corona, or is that just a guess?

Your notebook shows that short term lock-down saves lives. I don't think no one is disputing that (not me at least, and no one that I have heard has done that). The question is how will it look on the long run, and especially when you count in other factors such as the effect that economic losses will lead to decreased well-being, kids will have lost valuable education, students completing school might end up in short or long term unemployment instead of getting their first job, and so on. The solution is much more complex than just counting the number of dead each country has to date.

Jan, By the day the Euro- Song contest took place in Stockholm, there were at least 1500 infected in Sweden (tested positive) and 12 people were already dead. No other measures had been taken until March 19 and Stockholm was (and still is) the main source of epidemy in Sweden. Anders Tegnell did not think it was necessary to use its power to close the doors to Friends Arena. When he limited the number of people in gatherings to 500 a few days later, he found it sufficient and "restrictive" enough. When he was questioned by the SVT if 500 is not a very high number compared to 10 that was the average number in Europe, he answered that it does not make a big difference... Personally, I was in accordance with the Health authorities to keep the schoolls open, and against the total lockdown. We see if the Swedish strategy was right.

By the way, many countries in Europe do not want tourists from Sweden this year. If Anders Tegnell and the government were consistent with their recommendations to not travel abroad (not even within the country for more than 2 hours), they should be happy if the Norwegians, Danes, Greeks and Cypriots do not like the Swedes this summer...

Of course countries that have very different levels of infection at a given moment might not want people to travel between them. Clusters were you are allowed to travel e.g. between Sweden, UK, France, and Italy, or e.g. Denmark, Norway, Cyprus, and Germany respectively are not unreasonable. The big problem is if there are intersecting clusters, then the clusters become pretty pointless.

The first relevant antibody tests for Sweden came just a couple of days ago. As expected the largest proportion of positive antibody tests are found in Stockholm. A total of 7.3 percent of the blood samples from people in Stockholm were positive. For the southern region of Skåne (that borders to Denmark), the proportion of positive samples was 4.2 percent and for Västra Götaland, where the second largest city, Gothenburg is located, the figure was 3.7 percent.

The analyzes also show that there is a big difference between age groups. Antibodies were most common in people aged 20-64, a total of 6.7 percent of the samples in the group were positive. In the 65-70 age group, the proportion of infected persons was less, 2.7 percent. This indicates that protection of elderly has worked to some extent at least.

The tests were taken end of April, so more people will have antibodies by now. It is my understanding that it can take a few weeks after an infection before you have built antibodies. If that is the case, it means that means that even more people have been sick at this point. Does someone know? @Robert Nachbar perhaps?

As a comparison Denmark's first tests show that only 1% of the Danes have antibodies yet. Just as in the Swedish case, it is based on quite few samples (but more than Sweden) that are not completely randomized either, so the data might not be that reliable yet. In both cases the studies continues of course.

A thing I should have included is the Black Lives Matters manifestations in Stokholm and other parts of Sweden (as well as the world of course). With large crowds gathering one might expect an increase in cases after a week or two. Whether it's enough to have a substantial effect depends on many things, such as if people with symptoms avoided the crowds or not, the quantity of people participating, and if those that participated were good at isolating themselves after the events or not. Something, to look at in the next follow-up.

Jan, The death statistics (per capita) in Sweden are getting a little bit better, since we have not deteriorated our position and remain in 5th place in Europe. On the other hand, we are much worse in infected per capita, (third place), behind Belgium and Spain, but in front of the UK and Italy. ( Anders Tegnell's explanation "we find more since we test more", is not exactly true, because we have increasing returns to testing, both compared to our own testing previously and in comparaison with other countries. Last week, we were on top in Europe, with at least 1,000 new positive cases per day out of approximately 6,500 daily tests. Yesterday in Italy they tested 56,527 people and found only 338 positive cases ( The italian ratios over the last 3-4 weeks are among the lowest in Europe, while the Swedish ratios are the highest. Hopefully, the new cases they find everyday are not as dangerous as previously...

Jan. check the following official site where you can find the number of tests and tests/capita etc. Many European countries publish it every day, others (like Sweden) once per week. At the same site you find the number of infected and Infected/capita. Then, you can simply find infected/tests. Sweden has a low rate (tests/capita) and a high rate (infected/capita), therefore a rather high ratio infected/tests, while Italy much lower.

Yes, "Black Lives Matter" demonstrations can have a positive impact on infected numbers, but such demonstrations have taken place everywhere in Europe recently and not only in Stockholm. Yesterday, they tested 46,882 people in Italy and found 210 positive cases (the accumulated values are 237,500 out of 4.7 million tests). The number of positive cases in Sweden yesterday was 940, and given the fact that they do not test more than 8,000 per day, that is a rather big ratio. You say that " I really hope that we have more infected per capita than most other countries" and I respect your honest statement (altough I prefer as few as possible). Perhaps Anders Tegnell's goal was also to get higher infected/capita in Sweden and in that case he has succeeded ... But, since deaths are strongly positive related to infected cases, he (and everyone who has been rensponsible for health care) has failed. Shouldn't had been better to have had 2,500 (deaths) / 25,000 (infected), instead of the currect ratio 4,891 (deaths) / 53,323 (infected), even if the first ratio is higher?

First of all I'm not mentioning Black Lives Matters in order to compare with other countries, I'm just interested to see if an effect can be seen in the Swedish numbers or not.

As I believe I have clearly stated, I don't think data is good enough to do relevant comparisons between at the moment. Once we have more reliable on actual number of infected/immune and reliable data on excess deaths then I will for sure compare. Until then I see it as a rather pointless thing to do as data quality is simply too bad (and I don't know enough about the flaws in order to be able to use the data in a meaningful way).

As for the site on number of tests I have the same problem: without knowing the test strategy it is hard to make any real comparison. One country might be focusing on testing risk groups more than others, another perhaps tests medical staff more, and a third just test whoever wants to get tested, etc. Without knowing this I think it's way too easy to draw incorrect conclusions, so I rather avoid using that, until I have better information/knowledge.

(Btw, I'm not at all as strong of a believer in the value of massive testing as many others seem to be. I am yet to see anyone explain why mass testing would limit the pandemic. I'm not saying it isn't a good tool for it, just that I still haven't seen anyone actually being able to show that it is.)

As far as I know there is no reliable and comparable information on infected per capita. Where did you find that?

All data that I see is number of known cases, and as test strategies vary so much they are not really comparable.

That said I really hope that we have more infected per capita than most other countries. If we don't then for sure our strategy has failed. For instance, the comparison that could be made with Denmark after both countries published their first antibody studies, suggested that Sweden has had a lower death rate per infected. However, I prefer not to draw any conclusions from that yet. I just don't think the data on that is anywhere as reliable as it should do do this.

Ok, Jan! It is meaningless to use Wolfram to debatte about Sweden. Here is my last comment.

If the current statistics are not that favourable for Sweden, one can be happy with the Swedish strategy because (i) the statistics can't be compared and (ii) it is too early to rely on these (misleading) statistics.

Regarding argument (ii), it is frequently used in Sweden to calm the people now and as we say in football, "spark the boll at the public". Arguing like that one "hopes" that other countries, like Denmark, Norway, Finland, Greece, Poland etc will be soon hit by much higher death and infected ratios, while the Swedish ratios will suddenly improve significantly and, by Christmas or Easter next year we will be better off...

Regarding argument (i), that will remain for ever in Sweden, because it would be almost impossible for other countries to adjust their sampling and measurements of "deaths" and "infected" to the Swedish one. I find it rather strange when Sweden, a country that has promised so many tests before and never managed to do that, shifts its position and argues that testing is not that important now (which is true, since the more we test the more infected we get and many of them continued to work with old people without knowing that they were infected...). Perhaps the Italian sampling (almost 8% of its population) is biased while the Swedish (about 3.5%) is statistically correct. But the possible bias in sampling is impossible to explain the much higher infected/tested ratios in Sweden. By the way, right now we got the daily statistics, worse than yesterday, 102 deaths and 1239 infected....

I'm not arguing that other countries will soon hit larger numbers (or that they ever will), I'm just saying that I don't know and hence I don't think I can do a relevant comparison on that. If others feel they can, they are free to do that of course.

I have added a new section to the post, with a short updated from the last few months, including some comparison between genders, age groups, and regions.

Jan, great work. It looks like Sweden did it right, minus some excess nursing home deaths that might have been avoidable.

Thanks Nicholas. I think it's still too early to say if we did it right or not, but it is for sure not obvious that we did it wrong at least. In a sense nobody will have made it right (there will always be one sort of mistake or the other). In another sense two countries with completely different strategies might end up having done most things right, considering there situation.

(If my simulations from early April are right Sweden will have a small increase in October when the seasonal effect is over, but if we relax just a tidy bit too much then we might very well have a second wave coming. The simulations should be taken with a pinch of salt though, as there are a lt of unknowns and simplifications in them)

Jan, indeed, the social optimization involved in this has many factors more than counting the dead per million, although that is by far the most important. The countervailing concerns are that the measures that a society implements must allow the surviving population to sacrifice not too great an amount of physical and non physical values. For example, a complete early lockdown that would have produced a smaller number of deaths could have significant mental health and youth development issues, severe economic consequences, as well as being antithetical to concepts of western liberalism. A country like Greece, for example, which can partially rely on its European Union allies for some assistance, can decide to take the economic risk because it has less to lose. Pillars of an alliance, like Germany, and countries less closely associated with an alliance, like Sweden, cannot afford to sacrifice as much economically to combat a pandemic that has this low a death rate. The pain of the survivors counts, despite that we cannot easily either measure it or weigh it against the number of deaths. But most visibly, as more countries reach worse numbers in deaths per million residents than Sweden, Sweden's response gets validated. That list presently includes Italy, Spain, Belgium, Great Brittain, and the US, with France not being that much better. We can reasonably say that of the leading Western democracies very few have done a significantly better job. Germany stands out as a success that is very much worth understanding, since it does not seem to have sacrificed much either economically or in terms of freedom of movement.

The big risk for Sweden was the emergence of a cure in April or May 2020. Then all the countries that did the early complete lockdown would avoid any additional deaths. The only treatment close to a cure that I have heard about is the Eli Lilly sequenced antibody, which, from its early trials, seems about twice as effective as plasma therapy without reaching anything close to 95% avoidance of hospitalizations. We should hope that its effectiveness is confirmed, and it comes to the market quickly and a yet better treatment develops.

I think the above mostly addresses Chritos's concerns too but let's try to build a complete optimization model, which takes into account the economic harm as well as non-economic harm people suffer from lockdowns. Preventing 100 deaths per million at the cost of 600 depression cases per million may not be the preferred path but let's try to estimate those figures.

Agreed, one thing I would like to add though is that there is likely a short term and a long term economical impact from Corona itself and the restrictions. Things like closing restaurants will have an immediate impact of course, just as sick leave will. Naturally, if you had a lot of people being sick, then that will have a negative effect on economy. To me, this effect is likely to be a short term effect. This part of the economic downfall should be relatively easy to come back from, while e.g. consequences of missed school or unemployment will have a more lasting impact.

Niko, The overall efficiency should be measured by its "output" performance in terms of "infected per tests", or "infected per capita", or "deaths per capita" from the start, up to now. Sweden has done it much worse than the other nordic countries and even compared to many countries in Europe (including our own country, Greece). The Swedes are rather happy and proud these days because having around 250 infected daily is "success", while similar numbers in Greece (with almost same population) is "terrible". If Sweden is going to be a success story with so far almost 90,000 infected, compared to roughly 15,000 in Greece, the greek cases must be three times higher per day over many months to come... We will see. To argue that "these people would die because they were sick and/or old", is a bad excuse for the failure. Every country can argue like that! Euthanasia is not allowed in Sweden and the authorities should do their best to save lives, period!

In addition, if one takes into consideration the very low density of population per square km in Sweden, compared to almost all countries in Europe, "social distance" should have worked much better here, but it did not! Stockholm with less than 1.5 million has much less intensity than Athens, Paris, London, Brussels, Milano etc...

Posted 11 months ago

The fact that the graph points move on their own. While we just entered the number on each day. This coding is absolutely amazing.

How is going at the current date? Did you calculate some updated results?

Gianluigi, I haven't done anything new. The main reason is that the Swedish authorities stopped publishing daily COVID19 statistics long time ago. They just update it twice or sometimes three times per week. Such discrete observations can't be integrated with the daily statistics I had it before. The other reason is that the vaccination, as well as other recommendations that were introduced, have improved the overall picture. Sweden over the last months has improved its position compared to other countries and will open up everything in October. Since you seem to be Italian, a country that I followed and compared with, you know of course that even Italy has improved its position. On the other hand, Greece, my own country, is much worse than it was a year ago. The simple reason is the strong "anti-vacc" movement in the country, even by medical workers...

Yes, here in Italy the situation is almost fine. As a neighbour country (Italy, Spain and Greece share a similar climate, culture and economical situation), I'm really sorry for Greece. The Greek economic crisis, in my opinion wasn't managed in a correct way from europe, and now, this piece of news on the anti vacc movement and the situation in Greece... :(

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