The disease was spreading too quickly in my updated model. The proportion of asymptomatics is not as high as I believed the Swedish data was suggesting. The problem was/is that the numbers of deaths for the final 14 days or so of each edition of the published data are incomplete, so are revised upwards in subsequent editions with data arriving from the regions. That meant that the rapid fall in the death rate after a peak the data seemed to show when I last wrote was just artefact of the data collection system. You can see this in the attached worksheet, in the two charts below the Sweden data in “Common and calibration data”.
I followed this for a few weeks to see how the process works and then, this week, I felt I could make a reasonable estimate the adjustments that will take place over the next few weeks to obtain a sensible set of calibration data. It is clear that my model cannot replicate the smooth and prolonged log-linear decline in the actual numbers of daily deaths in the latest data using the numbers of cases implied by the very low mortality rates I was using last time.
To match the latest data I reduced the number of cases by increasing the mortality rate. The model started to approach a calibration at a mortality rate of 0.1%. I also looked again at the actions the Swedish authorities took in March. These included limits on meeting sizes and some distancing restrictions and recommendations in mid-March tightened somewhat at the end of March. You can see from the data that, contrary to popular belief, the Swedes and their government have been very effective at limiting the rate of spread, apart from a blip in care homes for the elderly that was quickly dealt with.
I used a second distancing phase match the tightening of the distancing measures in late March, which shows in the data, and tried calibrating the model for mortality rates of 0.1%, 0.2%, 0.3%, 0.4% and 0.5%. The rates above 0.1% do a better job of modelling the log-linear decline in the numbers of deaths, but the higher mortality rates require increasingly long doubling times. I think that rates of 0.2%, 0.3% and 0.4% give the best calibration results.
I kept the second distancing rate going until daily deaths fell to zero but then I always end up with a big ‘second wave’, sometimes months later. I introduced a third distancing phase to deal with this and experimented with that for mortality rates of 0.15%, 0.2% and 0.25% (which seemed to give the best calibrations). Fine-tuning this third distancing phase eliminates a ‘second wave’ altogether and shows that the final death toll is very sensitive to its timing and intensity.
If you have the time, it is worth playing with the four variables that control the third phase (in cells AF5, AD8, AF8 and AD9), while keeping the calibration values for the first and second distancing periods unchanged, and seeing how the final death toll (in cell G51, under the chart) responds. In the model, it seems that the best policy, to minimise the overall number of deaths, would be an immediate and controlled relaxation of distancing. This leads to a temporary increase in the number of daily deaths but an earlier end to the epidemic. In Sweden the second peak is below the first one, so would not over-stretch the medical resources, but that is unlikely to be the case in countries with much larger populations.
Death is a tricky subject. The increase in life expectancy in most places since 1945 is one of the many benefits of the global civilisation that has taken root since then and is currently being tested by this epidemic (among other things). Most people now die when they are old, which necessarily also means that most people who die are old. Some day, something, little or large, will tip each of us over the edge and into oblivion. At the moment COVID-19 is one of those things and wrinklies like me naturally make up the majority of the casualties. This is no excuse for negligence or disregard for the welfare and treatment of the elderly, but it’s not a reason for a lot of hand-wringing either.
The data seems to show that most Swedes have responded very effectively. Apparently traffic reduced immediately as people took fewer journeys and various other statistics show that responsible self-restraint has worked very well. I see that that there is now some internal dissent there because their death rate is much higher than in Norway and Denmark, where stricter measures were introduced. I think that the difference comes from Sweden being much closer to an end of the epidemic than their neighbours and that the final death tolls are probably a year away. When those numbers finally emerge they will probably be explained by demographic differences and the incidence of co-morbidity factors in the general population.
I hope that the Swedish government sticks to its guns and treats its people like the responsible citizens they seem to be, as an example to almost all the other governments in the western world.
Download the updated model here.