The top model for Finland, the community where I live, is added in this response, is now a "TRUE" model of the outbreak (in a "TRUE" model, the detected cases are the removed ones, - R curve - not the infectious ones - the I curve - ... they are no longer in the infectious chain - see the main section of this post). The rest of the models here for Finland are SIR models for the data in the spirit of the original post and most of it. As a rule of thumb, the blue I curve peaks about 13 days after daily new cases peak. The end of outbreak point is from one to four months after the peak of the I curve, depending on the parameters, which depend on the containment measures and the assumption that they stay in place during the whole outbreak.
The data for the Finnish model comes from the Finnish Department of Health and Welfare (THL in Finnish). There is a delay in the release of the data of 1-2 days. however, the recovery data comes from Johns Hopkins University or from occasional Finnish health reports. According to the medical chief of staff of the infections diseases clinic at the Helsinki and Uusimaa hospital district, it was "important to define what people mean when they talk about recovery", and that "eventually it would be important to compile statistics to better understand the disease" and "was taking the numbers with a grain of salt" noting that "the criteria underlying the data are not always clear and they are not always the same in each country". He also said that "tracking recovered patients was not a top priority". (quotes source is Yle news, the state run news agency). We have serialized the occasional recovery data according to how cases might have arisen in time to obtain a model. We then compute an estimate recovery function.The recovery period appears to be 17 days or so. We will check with future disclosures the accuracy of this function.
The first model posted is a "TRUE" SIR model of the outbreak (see opening paragraph of the post for an explanation, along with further comments in the top section). The second model has been removed; it was an SIR model (see the SIR model section for the equations) with a much more optimistic forecast than the SEIR model. The now second model posted is an SIR model with a recovery scheduled taken from an estimate function based on a few recovery data points for Finland - we believe this is the best of the standard models we have been producing that we have, and it has not been adjusted for a while. The third model is a model for Norway using the same recovery schedule as in the third model for Finland. The fourth model is a "TRUE" model of the outbreak in Sweden. I have removed the model which explores the possibility that Finland has reached a plateau, a very negative outlook (in this model, the number of people that can be exposed each day remains high and constant from a certain time on). Since there are only guidelines in place and no policy changes are expected, this model should be very stable, and I believe it is possible to make long term forecasts from it ... we will use it as a benchmark.
The models for other European countries are found in another response under this one. In this section, where there is space, I include a pdf document with the daily tallies per million inhabitants (smoothened, 4 day moving average) for several countries in Europe, USA, and South Korea. According to this parameter, almost no country in Europe is ready to move forward, contrary to what many authorities are starting to say. Countries like Denmark, Norway, Austria, and the Czech Republic have daily tallies p.m. that are nowhere nearly as low as those of South Korea, the role model country for the exit strategy. This will be updated daily.
Also, in the section of alternative SIR models, which has a model for China and a model for Itally (not updated) there is now a SIR model for Finland based on the JHU data ... it will be updated regularly; as well as another SIR model using a different estimate for the recovery schedule.
August 30, September 6, 12, 20,27: We have updated the Swedish model picture and the Finnish daily tally has been replaced by a graph showing the average daily incidence per 100000 inhabitants by week for recent weeks. Next update in about two weeks
August 22: We have updated the Swedish weekly model. We will only update the rest of the pictures occasionally. Except for Sweden, all other countries have run the course of their model. If a true second wave ensues, we will calculate new models when there is enough data.
August 16: Updated. We will not update the Norwegian model anymore because we do not have real recovery data. Instead, it will eventually be replaced by a TRUE model, even if at this stage, these countries are past the validity of any models and entering either new phases of the outbreak, whether it be a steady state or a new wave.
August 2, 9: We have updated all the pictures today. Next update in a week, during the weekend.
July 26: Updated. Our next update is in a week (the Swedish section just below this one is updated daily except on weekends, although it has been updated today). All Scandinavian countries (except Sweden) show a flattened data curve, as opposed to decreasing further as per the models, or even increasing. See the section just below for weekly totals
July 20-23: Updated, Today we have a new model for Finland, and a new weekly totals model for Sweden that corrects for the increase in cases due to testing. Next update over the weekend.
July 19: We are updating the weekly model picture for Sweden. We will update the rest of the pictures here tomorrow, except for the Finnish model. We need a window of time to recalculate the model after the time series was modified.
July 15: The entire time series for Finland has been modified due to a change in accounting methods. This requires a new model. We will calculate it as soon as we have time, towards the end of this week or next. But in any case, the outbreaks throughout Scandinavia, except Sweden, are quite very much under control, so we will shift to a weekly reporting, and weekly totals modeling. We will follow the situation in Sweden daily, except for today, in the reply to this section just below. Apologies for not reporting today.
July 5-14: updated … We are replacing the Swedish model with a model based on weekly totals. Pertinent information is in the picture label. It will be updated during weekends. We expect the numbers to come down during the holiday month when people move to summer cottages, something which might work effectively as a lockdown. We might need a new model in a month or so.
July 1-4: In the reply to this section below we are adding a picture of the weekly total number of cases for Scandinavia minus Sweden. A similar picture for the five big euro countries is found in the reply to the Euro section below. No update 4th and 5th of July, next update 6th of July.
June 22-30: Updated. This section will be updated only during weekdays as some Scandinavian countries no longer provide information during the weekends.
June 19-20: The Finnish website is back up. However, now there is no information coming out of Sweden, so we cannot update the Swedish picture nor the pictures in the reply to this post below it. Nor information for Denmark. Next update for this section, June 22, after the midsummer holiday.
June 18: The Finnish health authorities website is being serviced. There will probably be no update until next week. We will calculate an alternative model based on the daily announced totals, which is not the true time series. But it probably has a better averaging behavior. It is worth doing the experiment. It will be ready tomorrow or the day after. In the meantime, we replace the picture of the SIR model with the daily totals series plus the forecasted model we had before. We leave the TRUE model picture up.
June 5-17: Updating. The number of cases in Sweden seems to be growing again. Apparently the increase in cases is due to increased testing. In a reply to this section just below we have posted the model forecast for Sweden updated today. In the same reply we include a model based forecast of fatalities (the actual model curve is in the response to the European section below these sections). When there is enough data we will compute a new model, as well as for Denmark.
June 4: Updating
June 3: There is a huge uptick in the number of cases for Sweden today. Apparently this is due to results previous unpublished results from one lab, and the correction term is known; we have applied it
May 28-June 2: Updating. There is a new SIR model for Finland, and a new "TRUE" fit as well. The "TRUE" model yields quite a different forecast than the previous one. At the very bottom of the entire post there is a section with the forecasts. You can compare both forecasts in the picture corresponding to Finland.
May 27: We now have a tighter end of outbreak forecast for Norway in a new model. On Wednesdays I check the accuracy of the models, in particular, of the Swedish "TRUE" model, which is remarkably stable (on Wednesdays the weekly oscillation comes closest to its resting average). The forecast for today was 35077 cases, the actual number was 35088. Considering that the model was fitted on May 4, this is great accuracy.
May 25-26: Updating. Norway reached its technical end of outbreak (by one measure) on May 24.
May 23-24: A semiautomatic, almost optimal fit for the Finland model has been obtained. A better fit will be provided eventually (they take time to compute). We will fit a new "TRUE" model for Finland in a week as it seems necessary. On May 23 Norway published an estimate of recoveries and our estimated recovery function is within .5%. So this means that our model for Norway is very close to what is happening, as it shows in the picture. There are new recovery estimates for Finland which required an adjustment of the Finnish model. The model has been fitted now semiautomatically, not quite optimally though. With an increasing number of published recovery estimates our estimate function becomes more accurate. According to the Finnish health authority, a case is considered recovered if 21 days have gone by and the individual is not in the hospital or under treatment. The Swedish and Danish models are now updated (May 24).
May 19-22: updating. In the "TRUE" models for Finland and Denmark a deviation from the forecast trend can be observed. It would seem that in these two countries, the outbreak has been brought under control. However, in Sweden, where there is no active effort to slow the progress of the disease and there are no expected policy changes, the model is right on track with the data. Our model for Norway also indicates that the outbreak is under control and Norway is on target to reaching the end of outbreak threshold (about ten daily new cases on average).
May 18: there is no data for Finland May 17 yet, the time series is updated today though
May 12-17: Updating. I am adding a "TRUE" model for Denmark (semioptimized - the quality of the initial segment of the data is not good) and moving the daily tally pdf document to the section where the original notebook is posted.
May 10-12: Updating. Besides these optimally fitted "TRUE" models we have obtained from them a forecast of daily new cases. There is a section at the end of the post with those pictures and that information. Since these models seem to be very accurate, one can obtain these long term forecast, and fixing them at a date before restrictions are lifted, it allows one to see the daily new cases numbers deviate (or hopefully not) from the forecast trend. The daily cases pdf document now has 14 day moving averages, a much better rendition.
May 8-9: updating. The May 9 "TRUE" model for Finland is now optimally fitted almost fully automatically. It is a much better fit than previously and it pushes the forecast in the picture further out by a month (and that is assuming there the situation in the country stays more or less the same with regards to social distancing). The "TRUE" models will start to be produced in a fully automated way (I will later post a notebook with the code that does the optimization; it is written withing the simplicity of built in Mathematica functionality, which means it is somewhat slow and NMinimize needs help). The Swedish model however will be alternate with the automatically fitted one until 15 June since it is being used as a benchmark for this kind of model. Once in a while we will post the model generated on May 4 to compare with the automatically fitted one.
May 6-7: updating. The Swedish model should be very stable due to the conditions under which the outbreak is evolving in Sweden (guidelines instead of formal lockdown and no policy changes expected). We can attempt to make long term forecasts from this model. It shows, among other things, how prevalent the infection will be during this outbreak. We will use it as a benchmark. These "TRUE" models seem remarkably stable and reliable once there is enough data to fit.
May 5: We now have different models, including "TRUE" models of the outbreak for Finland and Sweden. See comments above, and comments in the opening paragraph of the post and in that secition.
April 30-May 4: updating
April 28-29: updating. We have switched the third model with our alternative recovery estimate model, which squares with the recovery estimates published by THL yesterday. This model has been right all along, so we plant to keep it now. The picture will be updated at around 2 PM EEST.
April 27: in today's update, the pdf is now the plain daily tally, and the moving average is now over 7 days ... what you get out of it is more illustrative of what is going on.
April 22-26: of all the models posted, it is starting to feel like the third one is the more accurate one, it hasn't been adjusted now in several days. I will have to wait until I have new recovery data to decide if it really is. I have removed the steady state illustration and included a model for Norway using the same recovery schedule as Finland.
April 19-21: updated. A new SIR model based on a different recovery schedule taylored for Finland is included in the SIR models section.
April 18: updated. A new SIR model based on the JHU data is included in the section of SIR models
April 17: updated. A new estimate of recoveries was published today and we have adjusted our models to reflect this estimate, in particular, the first two.
April 15-16: updated. A fourth model that explores reaching and staying in a plateau is shown. Today a recovery figure was published that certifies that our r
Attachments:
