Fig 1.
28-day forecast of the daily incidence for four countries, using the data up to May 5, 2022.
The current original raw incidence curve which suffers from periodic weekly effects. In the current incidence trend computed by EpiInvert [6], in
the forecast of the incidence trend curve by EpiLearn, in
the ground truth given by the incidence trend curve obtained 50 days later and in
the forecast of the raw incidence using Eq (8). The
shaded area represents a 95% empirical confidence interval of the incidence trend forecast. The discontinuity at the past-future junction in Germany is due to a sharp drop of the incidence after the last observed day. When recalculating the incidence trend curve, the values of the past days are also changed by smoothing, thus creating the observed gap.
Fig 2.
Shape of the functions e−0.0475x which determines the weight assigned to each day in the past in the distance estimation (6) for the proposed forecast method.
Fig 3.
Illustration of the variability of closest curves.
For France, the USA, Germany and the United Kingdom: in black, the normalized curve of the last 28 values of the incidence trend curve up to May 5, 2022, in
the normalized forecasting curve
obtained by EpiLearn. Are also displayed in a
scale the five curves ik in the database with the lowest distance
to the incidence trend curve
. The lighter the blue, the larger the distance to the input curve.
Fig 4.
Illustration of some statistics of the Ed = {ed,k} distribution defined by (10) for the entire database: the curve indicates the mean of the distribution that is greatly affected by the skewness of the distribution, which justifies using the median (the curve in
) instead of the mean. The median is indeed very close to zero, which proves the consistency of the approximation adopted in Eq (12). From the outside to the inside, the shaded areas represent the estimated (1 − αk) × 100% central prediction intervals
for αk = 0.05, 0.1, 0.2, …, 0.9.
Fig 5.
Figure showing the actual observed weekly disease incidence by country during the time span evaluated in the comparative results from the European COVID-19 Forecast Hub.
This period showed challenging behaviors in disease incidence trends.
Fig 6.
Plot of the relative absolute error (rel_ae) and the relative weighted interval score (rel_wis) presented in Table 1 using the evaluation data provided by the COVID-19 European Hub.
Table 1.
Comparative results. In bold the best result of each column for each week for the main quality measurements promoted by the European hub: rel_ae and rel_wis (for both quality criteria, the lower the better).