Machine learning identifies straightforward early warning rules for human Puumala hantavirus outbreaks

Abstract

Human Puumala virus (PUUV) infections in Germany fluctuate multi-annually, following fluctuations of the bank vole population size. We applied a transformation to the annual incidence values and established a heuristic method to develop a straightforward robust model for the binary human infection risk at the district level. The classification model was powered by a machine-learning algorithm and achieved 85% sensitivity and 71% precision, despite using only three weather parameters from the previous years as inputs, namely the soil temperature in April of two years before and in September of the previous year, and the sunshine duration in September of two years before. Moreover, we introduced the PUUV Outbreak Index that quantifies the spatial synchrony of local PUUV-outbreaks, and applied it to the seven reported outbreaks in the period 2006-2021. Finally, we used the classification model to estimate the PUUV Outbreak Index, achieving 20% maximum uncertainty.

Figure 1

Selection of the districts for the analysis. The 66 selected districts across Germany are shown in red gradient depending on their total PUUV-infections in 2006–2021. The colorbar is linear in the range [0, 50] and log-scaled in [50, 650] for increased visibility. There were 26 districts from Baden-Württemberg (BW), 16 from Bavaria (BY), 8 from Hesse (HE), 3 from Lower Saxony (NI), 10 from North Rhine-Westphalia (NW), 1 from Rhineland-Palatinate (RP), and 2 from Thuringia (TH). Thick black lines separate the federal states; thick colored lines separate four clusters of the detected PUUV-molecular clades, as described in the text. Further districts are shown in gray gradient with the same colorbar scaling. The map was generated using the geopandas package v0.9.0 (https://geopandas.org) in Python v3.8.5. Further information about the raw data, the processing, and the visualization is provided in the Methods section.

Figure 2

The annual incidence values in the selected districts from 2006 to 2021. The 66 districts are ordered by the maximum annual incidence. The low-risk bin is indicated by blue triangles (on the left side of the plot). The high-risk bin is indicated by red diamonds (on the right side of the plot). The filled triangles and diamonds indicate the average value for each bin. The solid lines highlight the incidence range for each bin. The white gaps between the blue and the red lines indicate the separation between the two bins for each district. The x-axis is linear in the range [0, 1] and log-scaled in [1, 110] for increased visibility. The naming convention matches that of the German version of SurvStat@RKI 2.0. LK: rural district (from the German Landkreis) and SK: urban district (from the German Stadtkreis).

Figure 3

Views of the model. 2D scatter plots with all 1056 observations from 2006 to 2021 for the three pairs of variables in the selected 3D model. V1_ST_9 in (a) and (b): the mean soil temperature in September of the previous year, V2_SD_9 in (a) and (c): the total sunshine duration in September of two years before, and V2_ST_4 in (b) and (c): the mean soil temperature in April of two years before. Yellow (hex color code #FDE725FF) corresponds to observations with low risk, whereas indigo (hex color code #440154FF) corresponds to observations with high risk. The overlaying red x-markers indicate the values of the variables from each year averaged over whole Germany, called cluster centers. The red diamond markers indicate the average values over Germany for 2022 (filled markers) and for 2023 (unfilled markers).

Figure 4

Estimating the PUUV Outbreak Index from the classification model. The proportion of districts with high risk for each year, which was defined as the PUUV Outbreak Index, is plotted with respect to the distance from the planar boundary of the cluster centers, i.e., of the points defined by the average values of the weather parameters over Germany for that year. The red dashed lines show a piecewise constant fit to the data (pseudo-R² = 0.87, calculated according to). The red-shaded area indicates the uncertainty. The hashed area for distances in the interval $\text{[}-\text{0.37,}-\text{0.03]}$ represents the increased uncertainty about the position of the discontinuity.

Figure 5

Histograms of the annual PUUV incidence from 2006 to 2021, scaled to its maximum value for each of the selected districts. Left: Raw incidence. Right: Log-transformed incidence, according to Eq. (6).