Here are the models for Spain, Germany (SEIR or SIR), France, and now Austria. The recovery data from the UK does not seem to be forthcoming. This makes it difficult to produce an SEIR model. Thus, I am replacing the UK model with a model in which there is an estimated resistant curve based on available data from European countries of comparable size and CFR and a time delay. I will explain this if there is interest. The UK model is now regularly updated according to this recovery schedule. Similarly, there is, in the JHU data, a huge leap in the French number of cases on 4.4, and although I was gather other figures for 4.5, I was unable to do so for 4.6. Official data can be found in the French government's site. However I have reverted to using the JHU data as of April 14.
The model for Austria now uses further modification of the SIR model equations. It allows to model growth in susceptibility at any moment of time after the initial conditions. Here, we apply the growth term (a term in the equation for s') at approximately the time when some restrictions were lifted on April 13. You can see the s curve grow from there on a bit, making the downward slope of i increasingly gentler ... the initial susceptibility is roughly the number of cases we have now.
September 5: Updating for this section is paused for now. In the reply underneath it, there is summary information pertaining to the situation in the large five Eurozone countries, up to date.
August 9, 16: We will pause the updates of models for the UK given that we have no real recovery data. We will, when we have time, replace the model by a TRUE model. We will also pause the updates for Spain and France. The outbreak has run its course past the point for which the model serves a purpose. We will try to produce new models now that there seems to be a new outbreak starting in those countries. We will, temporarily, continue to update the German and the Austrian model for one more week. The outbreaks there have also run past the point which the model serves a purpose, and it might be that new outbreaks are developing there yet, although this is not quite clear. IN THE REPLY TO THIS SECTION BELOW WE GIVE SUMMARY INFORMATION PERTAINING TO THE FIVE LARGE EUROPE COUNTRIES.
July 26, August 2: Updated. By now the models have served their purpose, and we only show here how there is new growth in all these countries. We will decide soon whether to continue to update this section, since it is past the modeling effort. The disease is now on a course of its own, perhaps a second wave, perhaps a steady state. It is possible to model all these conditions, but the models have to be revised frequently and according to what the data shows, and that is work beyond the scope of these pages. If there is an update, that will be in a week.
July 18: There is now new growth in all these countries
July 12: Updated. As the numbers in the UK come down, we see new growth in Germany, Austria, and France.
June 28-29, July 1-6: Updated with July 5 data. In the reply below we have the weekly totals since May 2, excluding the current week. Some countries which had their outbreak under control are experiencing new growth. NEXT UPDATE NOT UNTIL JULY 19 OR 20.
June 22: This section will now be updated in the early part of the day, with the results for the day before, once a week, until August 17. We will try to update it more often than once a week, but do not promise to do so. Next scheduled update, June 29. You can see that the countries in this section are now down to a trickle of cases that will take a long time to bring down. Having lifted restrictions, and without perfect contact tracing, it is almost impossible to eliminate the infection or bring it down much more. But we hope that it is done. The best model is that of Austria which accounts for the effect of lifted restrictions, and ever increasing number of susceptible people, however tiny. We might revert the UK to a TRUE model, which gives a very accurate picture of how the outbreak is really evolving towards the end (and given that there is no real recovery data), but we will keep the Austrian model as it is and the German model as it is.
June 19: Next update, June 22. After June 22, updates to this section will be weekly. The fatalities per million graph just in the reply to this section below will be updated daily.
June 4-18: updating. Label of French model corrected. Starting June 22, this model will be updated only occasionally until Aug. 17th, when we will resume normal activities. The fatalities per million in the reply to this section just below will still be updated every day if possible. As a reminder, the daily tallies pdf document for these and other euro countries if together with the notebook in a reply to Kaurov, above the Finnish section. After June 22, it won't be updated again until August 17.
June 3: Updating. The French data last night had a huge correction. We are keeping a consistent series instead of reflecting the corrections from now on, as it is almost the end of the exercise. So we just took a data point unchanged from the previous date. The French data has suffered huge corrections often. It makes for poor modeling. It would help if the whole time series were retroactively corrected, like it is in Finland. But this does not seem to happen. In any case, the model will continue to be good in that the forecast is dependable. We will make a daily cases forecast for Spain and France now that we have "TRUE" models for these countries and put them in another section soon.
May 29-June 2: Today we are replacing the model for France with a "TRUE" model. The data for France has suffered many corrections. It started as case data for hospitals, later was expanded to include nursing homes as well. To make things more complicated, the recovery data pertains, it seems, only to hospitals. So it is not really possible to model the outbreak as we had hoped. The "TRUE" model here is difficult to fit because of the many corrections that have been made to the time series. So we have fitted the curve to the last portion of the data, which are the most consistent (but even yesterday there was a major correction to the data ... in any case).
May 27-28: Updating. We have replaced the Spanish model with a "TRUE" model due to partial lack of recovery data or a good estimate for that data. Although we had not shown it before, it was fitted on May 4 and it seems very stable. Over the weekend we will try to replace some of the other models with better models using recovery estimates or "TRUE" models where this is not possible. A quick and dirty notebook that shows how susceptibility can be made to grow will be posted in the notebook section just above (in a reply to Kaurov).
May 20-26: Lately there are delays in the reporting of data for this section (as well as inconsistencies, such as fewer cumulative fatalities from one day to the next). This section will be updated with a delay of one day, except for Austria. The UK JHU time series is now inconsistent. It appears that Spain has stopped reporting recoveries. I will leave this last picture unmodified until I have time to compute an estimate based on the historical rate or replace it with a "TRUE" model.
May 8-19: Updating. Probably soon I will stop updating this section on a daily basis, to update perhaps on a biweekly basis. Another section with "TRUE" models for the countries in this section will be started, hopefully soon. Not only are the "TRUE" models standard practice in epidemiology, I can also parametrize them optimally almost automatically. They give very good forecasts once there is enough data as long as there are no changing circumstances (policy changes). The UK model has been replaced by a SIR model, and the Spain model has been adjusted. A notebook with code to produce the "TRUE" models almost automatically will be provided.
May 6-7: updating.
April 29-May 5: updating.
April 28: updating. I found a source with daily increments for the Spanish data. Let's hope they are consistent. The French data appears still inconsistent. I will try to recreate a consistent series from the French government website when time permits.
April 27: updating. I will not update Spain after today until I get hold of the data from local authorities if I can. The JHU data is inconsistent both in number of cases and in recoveries. It seems the historical series is being updated retrospectively, but according to the Spanish authorities, it is not yet ready. The temporary lump sums provided temporarily make for very poor data. When it becomes ready, I will continue to update this model. If I can obtain reliable information from press reports, I will update my data thus by hand.
April 26: updating. Today, April 26, the recovery data from Spain is highly anomalous, for the second time (in the past, counting method changed). Unless this datum is corrected, from now on I will use an estimate based on a recovery rate function that can be computed from the data up to yesterday. of adjust subsequent data with a constant after today's estimate. Using this function, we obtain today's picture. The French JHU data is still anomalous, so I will continue to use my hand curated series.
April 25: updating. I have corrected the end of outbreak for the Austria model to late summer at the earliest, if nothing changes too much ... as further restrictions are lifted, this is likely to change again. The JHU data series for France has apparently been corrected. I will try making a model with that data tomorrow. In the meantime, what I have been using is working fine.
April 24: updating. IT seems the model for Spain might need a new steeper rise ... The JHU data for France is inconsistent, and the government data is partial or I cannot curate it all ... I am curating data by hand now based on various reports, but I might have to give up on this model unless there is a consistent data source which I can easily get a hold of.
April 23: The date is now correct in the Spain model. It appears, unfortunately, that my forecast regarding the effect of going back to work to soon was correct weeks ago.
April 22: The numbers in Spain seem to be on the rise, some ten days after part of the country went back to work. In a little while we will update our forecast for Spain in the main section, which allows for growth in the number of susceptible individuals. We include the same model here ... it is based on a modified set of equations which I might post later. We hope that this will not bear out, but for now, it seems as if it might. The model is a modified SEIR model which I will post in the aftermath of all this. I also replaced my German data with the JHU curated series, resulting in a new model
April 21: Updating. The model for Austria now uses a more elaborate model based on the SIR model which allows s(t) to grow. I might post a notebook in the aftermath, without a discussion. Notice that susceptibility grows after April 13, when restrictions were ifted.
April 19: I have put the German SEIR model again.
April 18: updating, the Spanish recovery data not forthcoming ... as I said yesterday, this model will need to be revised as the data is made available. For the moment, I am using extrapolated recovery data.
April 17: updating. Spain changed its counting methods today. As was in the case of China, I will temporarily correct the data, until there is enough data to see what the trend is and revert back to the data that will be provided from now on. Surely, it will necessitate a revision of the model. Apologies for this. Also, the entire JHU data series (number of cases) has been altered. The end result of this is that I do not have good data to provide a model. I have posted what I was able to come up with based on previous estimates. It will be necessary to have at least two more weeks of data before anything reasonable can be done about this, OR, the data series needs to be corrected as it probably still needs to be.
April 15: updating I am replacing the German model with an SIR model for which I get a much better fit (it is easier to fit these models). The model gives an estimate of R0. For the equations of the SIR model used see the response towards the bottom of the post.
April 11-14: updating. (French data ok after checking, yesterday I used the government website, I use their number of cases reported there, and their TOTAL number of deceased: gouvernement.fr/info-coronavirus/carte-et-donnees). Today, April 14, I have reverted to use the JHU data.
April 10: I updated the model f
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