[07/01/20 Update: The model is tracking well within the model bounds showing Sweden’s soft mitigation mode is working. This model continues to be an excellent example for the rest of the world. IHME and others now predict future trends for Sweden in a manner consistent with our model.]
Sweden has taken a different approach to managing the crisis. They have kept primary schools open and do not have hard stay-at-home orders in place. They do have a variety of measures that limit international travel, restrict large groups, manage density in restaurants and bars, encourage distance learning in secondary and advanced education, and are also encouraging people to work remotely. A good summary can be found on Wikipedia. All this adds up to significant social distancing. These measures allow for reasonable activity, but still have a similar effect to a hard lock-down.
An article published on 04/19/20 by Bloomberg‘s Niclas Rolander details why the author feels the approach is effective. His observations are consistent with the assumptions in this model. The data below are from the Sweden FOHM.
Sweden: Infectious Contact Reduction
We examine four case scenarios using the Monte Carlo method; see figure SW1.
Case 1 (red curve) represents a highly effective mitigation program that reduces potentially infectious contacts by 90%. This case predicts approximately 1,820 deaths. See below for more details.
Case 2 (orange curve) represents a moderately effective mitigation program that reduces potentially infectious contacts by 80%. This case is likely a more realistic model of the current Swedish social distancing policy. This case predicts approximately 3,200 deaths. This case would be considered a likely scenario. See below for more details.
Case 3 has no mitigation program and reduction in contacts. This is a hypothetical case to determine the worst case outcome. This case predicts approximately 20,000 deaths. This outcome is very similar to the IHME model which predicts 18,000 deaths by August. See below for more details.
Case 4 (green curve) represents a moderately effective mitigation program that reduces potentially infectious contacts by 75%. This case predicts approximately 6,100 deaths. This case would be considered a likely scenario. See below for more details.
Current Data and IHME Projections
The death curves below for Sweden are from Wikipedia. They show a reduction in deaths over multiple days. The Institute for Health Metrics and Evaluation (IHME) is a global health research institute at the University of Washington. Researchers there have developed a prediction model that has been the basis for many of the policy decisions made in the United States. The IHME model is consistent with the Monte Carlo model with NO mitigation at all, but not a reasonable fit to existing trends in Sweden. This will be shown below as we apply the model to the cases described above.
The IHME model has been shifting.
IHME Projected Deaths, Sweden
Monte Carlo Model Sweden Case Study Input Parameters
The outcome table used is similar to the other case studies with 50% asymptomatic cases.
The population was simulated with a base of 2 million scaled up by 5x to 10 million, the population of Sweden.
A seed of infections was introduced consistent with a mid-February spread from European travelers, primarily from northern Italy.
CASE 1: 90% Contact Reduction
In this first case, we assume that even though primary schools are open, the cumulative effect of social distancing policies results in a 90% reduction in contacts relative to the time before the infection. The social distancing measures are held in place for the duration of the run. This case predicts that there will be less than 1500 deaths going into May. This case likely overstates the effectiveness of Sweden’s social distancing measures. If this is case is accurate, they will not have additional growth; the infection will be largely mitigated by the end of April and R0 will be well below 1.
Ten simulation runs were completed. The following graph shows the distribution of deaths per day for each of the ten runs and the mean which is shown in red. Generally the curve is of the same shape and peaks around April 8. There is some variation in the timeline, but the distribution is tight.
A single run with infections, deaths and recoveries:
This is a representative sample of cumulative values from one of the simulation runs. In this case the overall infection rate is fairly low. This may not be consistent with actual sample testing in dense metropolitan areas but may be true for the country as a whole.
The dynamic infection growth metric R0 is tracked above. Once mitigation measures are put in place it quickly drops below 0.5 and the infection’s spread dissipates.
CASE 2: 80% Contact Reduction
In this case we look at the effect of moderate social distancing. This would be what one would assume Sweden currently has in place (compared to other countries with more stringent restrictions). The transmission factor is decreased to 20% of the baseline.
The net effect of this more relaxed social distancing is a similar peak death rate, but a longer residual tail resulting in more overall deaths. In this simulation, the peak death rate continues for approximately one week beyond the more stringent social distancing model of Case 1.
The cumulative deaths peak above 3000, a significant increase over the more restrictive approach but still significantly less than the IHME predictions. More than 10% of the population is infected.
Looking at the R0 over time, the overall trend is a decrease but it takes longer to quell the infection.
Case 3: 0% Contact Reduction
In this case there are no mitigation effects at all. We know that this is not realistic but this is a useful look to see what might have been if soft measures were not taken early.
The death rate in this case is almost an order of magnitude higher than previous mitigation cases and does not correlate at all with the actual death curves.
The cumulative deaths peak at close to 20,000. This is relatively close to the IHME prediction, but seems unrealistic. Also note that for this baseline more than 50% of the population is infected. Once 50% of the population is infected R0 is pushed below 1 and the infection no longer propagates.
Looking at R0, we can see that it is fairly level during the infection growth, in the range of 3 to 3.5. This is to be expected. Once about a quarter of the population is infected it falls sharply.
CASE 4: 75% Contact Reduction
In this case we look at the effect of moderate social distancing. This is a slightly more conservative estimate of the measures in Sweden compared to other countries with more stringent restrictions. In this case we push the transmission factor down to 25% of the baseline, so we expect slightly more deaths than Case 2 with 80% reduction.
The net effect of this more relaxed social distancing is a similar peak death rate as Case 2 but a longer residual tail resulting in more overall deaths. In this simulation the peak death rate continues for a couple of weeks in April and then declines through May and into June.
The cumulative deaths peak above 3000, a significant increase over the more restrictive approach but still far under the IHME predictions. More than 10% of the population is infected.
Looking at the R0 over time, the overall trend is a decrease but it takes longer to quell the infection as R0 is pushed just below 1.
This analysis indicates that Sweden has been fairly successful with soft mitigation policies. The net result is probably not very different than other countries under lock-down. Sweden may be an excellent model of a reasonable balance of public health, economic health and personal liberty.