Fig 1.
TOP: By individual vehicle. BOTTOM: By public transport. Source: [1].
Fig 2.
How duration (in hours) translates into the infection probability for two different contact intensities.
The linear approximation of Eq (2) is given for either curve by a dashed line.
Table 1.
Normalized contact intensities ci′, relative to the contact intensity at home, .
Fig 3.
LEFT: State transitions [70–75]. RIGHT: Age-dependent transition probabilities from infectious to symptomatic, from symptomatic to seriously sick (= requiring hospitalisation), and from seriously sick to critical (= requiring breathing support or intensive care). Source: [15], except that the numbers in the second column are divided by 2 (discussed in Under-reporting, and its variation over time).
Fig 4.
LEFT: Case numbers. The green and red dots denote case numbers as reported by Robert Koch Institute [77]; the blue dots denote positive test fractions [78] multiplied by 200. RIGHT: Hospital numbers. Each simulation curve is averaged over 10 independent Monte Carlo runs with different random seeds; the shaded areas denote 5% and 95% percentiles of those 10 runs.
Fig 5.
Based on data taken from [77] (always on Tuesdays), but multiplied by 4 in spring, and divided by 2 in summer (see text for Discussion).
Fig 6.
Unrestricted base case, but with initial disease import from data.
LEFT: new cases; RIGHT: hospital occupancies. One finds that the initial slope dynamics is rather independent from the thetaFactor.
Fig 7.
Change in activity participation compared to the baseline for normal workdays.
All out-of-home activities are combined into one number. (*) denotes the first day of closures of schools, clubs, and bars; and (#) the first day of the so-called contact ban which came together with closures of all restaurants and non-essential stores.
Fig 8.
Simulations with reductions of activity participation as obtained from mobility data.
LEFT: new cases; RIGHT: hospital occupancies.
Fig 9.
Outdoors fraction for activities of type leisure, depending on the temperature of each day.
Fig 10.
Simulations that now also include a symmetric indoors/outdoors model, with a threshold temperature of 17.5C both in spring and in fall.
LEFT: new cases; RIGHT: hospital occupancies. A thetaFactor between 0.6 and 0.8 is most plausible, but the second wave would come too late (starting after September) and would not be steep enough (compare slope of red dots in right plot after September) (cf. in particular the hospital numbers).
Fig 11.
Simulations that now also include an asymmetric indoors/outdoors model, with a threshold temperature of 17.5C in spring, and 25C in fall.
LEFT: new cases; RIGHT: hospital occupancies. A thetaFactor between 0.6 and 0.8 is most plausible, which would well reproduce the second wave (cf. in particular the hospital numbers).
Fig 12.
LEFT: new cases; RIGHT: hospital occupancies. All simulation results are averaged over 10 runs with different Monte Carlo seeds; the shaded areas denote 5% and 95% percentiles of those 10 runs. Evidently, the relative errors become larger with smaller case numbers. The simulation model can only be fitted against the hospital numbers (right) when significant under-reporting is assumed in the early phase (left).
Fig 13.
TOP: absolute numbers. Note logarithmic scale. BOTTOM: Share of infections per activity type. The values are averaged over the same 10 runs as for the other figures, and in addition aggregated into weekly bins. One can see, for example, the return to school near the beginning of August, and the fall vacations in October.
Fig 14.
Reproduction number R(t) for the duration of the simulation.
As explained in the text, we explicitly count the reproduction number per agent, and then average them over all agents that turned contagious on a given day.
Fig 15.
Reproduction number per activity type.
Table 2.
Contributions to R by activity type and intervention according to our model.
Fig 16.
Effect of dividing a group of 10 persons into two groups of 5 persons each.
In the original situation, each of the 9 susceptible persons (white and cyan) has a probability to get infected of p0, resulting in a expected number of infected persons of 9p0. In the divided situation on the left, the expected number of infections is 4p0. On the right, it is 0. Overall, this results in an expectation value of . In consequence, when dividing classes and alternating their attendance, the number of infections is reduced from 9p0 to 2p0. For large group sizes, the reduction converges to 1/4. The same holds when each individual attendance is decided randomly with probability 1/2 at the beginning of each day.
Fig 17.
Hospitalized persons for different calibration runs compared to real data.
Θ is calibrated such that hospital numbers in the simulation match the real data (red dots) until different points in time as indicated by the legend. After this date, an out of sample prediction is carried out. Until the calibration date real weather and disease import data is used. After the calibration date average weather data from the past ten years is used and the disease import is set to 4 imported cases per day (1 agent per day) LEFT: Activity levels are frozen at the level of the last day of the period used for calibration. RIGHT: Real activity levels are used.—Results are averaged over 30 Monte Carlo seeds.
Table 3.
Calibration parameter Θ and activity participation for the different out of sample predictions shown in Fig 17.
Table 4.
Average time consumption of out-of-home activities.
Table 5.
Percent reduction of R in other studies.