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We performed data acquisition, processing, analysis and visualization using Python23 version 3.8 with the packages Numpy24, Pandas25, Geopandas26, Matplotlib27, Selenium, Beautiful Soup28, SciPy14 and scikit-learn29. The functions used for specific tasks are explicitly mentioned to allow validation and replication studies.Data acquisition and processingHuman PUUV-incidenceHantavirus disease has been notifiable in Germany since 2001. The Robert Koch Institute collects anonymized data from the local and state public health departments and offers via the SurvStat application2 a freely available, limited version of its database for research and informative purposes. We retrieved the reported laboratory-confirmed human PUUV-infections (({text{n}}=text{11,228}) from 2006 to 2021, status: 2022-02-07). From the attributes available for each case, we retrieved the finest temporal and spatial resolution, i.e., the week and the year of notification, together with the district (named “County” in the English version of the SurvStat interface).To avoid bias through underreporting, our dataset was limited to PUUV-infections since 2006. The years 2006–2021 contain 91.9% of the total cases from 2001 to 2021. Human PUUV-incidence was calculated as the number of infections per 100,000 people, by using population data from Eurostat30. For each year, we used the population reported for the January 1 of that year. The population for 2020 was also used for 2021.In the analysis, we only included districts where the total infections were (ge {20}) and the maximum annual incidence was (ge {2}) in the period 2006–2021. The spatial information about the infections provided by the SurvStat application refers to the district where the infection was reported. Therefore, in most of the cases, the reported district corresponds to the residence of the infected person, which may differ from the district of infection. To compensate partially for differences between the reported place of residence and the place of infection, we combined most of the urban districts with their surrounding rural district. The underlying assumption was that most infections reported in urban districts occurred in the neighboring or surrounding rural district. In addition, some urban and rural districts have the same health department. Supplementary Table 1 lists the combined districts.Weather dataFrom the German Meteorological Service31 we retrieved grids of the following monthly weather parameters over Germany from 2004 to 2021: mean daily air temperature—Tmean, minimum daily air temperature—Tmin, and maximum daily air temperature—Tmax (all temperatures are the monthly averages of the corresponding daily values, in 2 m height above ground, in °C); total precipitation in mm—Pr, total sunshine duration in hours—SD, mean monthly soil temperature in 5 cm depth under uncovered typical soil of location in °C—ST, and soil moisture under grass and sandy loam in percent plant useable water—SM. The dataset version for Tmean, Tmin, Tmax, Pr, and SD was v1.0; for ST and SM the dataset version was 0. × . The spatial resolution was 1 × 1 km2.The data acquisition was performed with the Selenium package. The processing was based on the geopandas package26 using a geospatial vector layer for the district boundaries of Germany32. Each grid was processed to obtain the average value of the parameter over each district. We first used the function within to define a mask based on the grid centers contained in the district; we then applied this mask to the grid. In this method, called “central point rasterizing”33, each rectangle of the grid was assigned to a single district, the one that contained its center. The typical processing error was estimated to be about 1%, which agrees with the rasterizing error reported by Bregt et al.33; we consider that most likely this error is significantly less than the uncertainties of the grids themselves, caused by calculation, interpolation, and erroneous or missing observations.Data structureOur analysis was performed at the district level based on the annual infections, acquired by aggregating the weekly cases. From each monthly weather parameter, we created 24 records, for all months of the two previous years. Each observation in our dataset characterized one district in one year. Its target was acquired by transforming the annual incidence, as described in the following section. Each observation comprised all 168 available predictors from the weather parameters (7 parameters × 24 months), thereafter called “variables”. The notation for the naming of the variables follows the format Vx__, where “Vx” can be V1 or V2 that corresponds to one or two years before, respectively;  is the abbreviation of the weather parameter (see previous subsection: “Weather data”); and  is the numerical value of the month, i.e., from 1 to 12.The observations for combined districts retained the label of the rural district. For their infections and populations, we aggregated the individual values, and recalculated the incidence. For their weather variables, we assigned the mean values weighted by the area of each district.Target transformationTo consider the effects that drive the occurrence of high district-relative incidence, we discretized the incidence at the district level. The incidence scaled at its maximum value for each district showed extreme values for minima and maxima. About 49% of all observations were in the range [0, 0.1) and 8% in the range [0.9, 1] (Fig. 5). Therefore, we specifically selected to discretize the scaled incidence with two bins, i.e., to binarize it.Figure 5Histograms 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).Full size imageWe first applied a log-transformation to the incidence values34, described in Eq. (6).$${text{Log – incidence}} = log_{10} left( {{text{incidence}} + 1} right)$$
(6)
The addition of a positive constant ensured a noninfinite value for zero incidence, with 1 selected so that the log-incidence is nonnegative, and a zero incidence was transformed into a zero log-incidence. This transformation aimed to increase the influence of nonzero incidence values; values that are not pronounced, but still hint at a nonzero infection risk. Its effect is demonstrated in the right plot of Fig. 5, where the positive skewness of the original data is reduced, i.e., low incidence values are spread to higher values, resulting to more uniform bin heights in the range [0.05, 0.95] after the transformation. Formally, in this case the log-transformation achieves a more uniform distribution for the non-extreme incidence values.For the binarization, we performed unsupervised clustering of the log-transformed incidence, separately for each district, applying the function KBinsDiscretizer of the scikit-learn package29. Our selected strategy was the k-means clustering with two bins, because it does not require a pre-defined threshold, and it can operate with the same fixed number of bins for every district, by automatically adjusting the cluster centroids accordingly.Classification methodWe concentrated only on those variable combinations that led to a linear decision boundary for the classification of our selected target. We selected support vector machines (SVM)35 with a linear kernel, because they combine high performance with low model complexity, in that they return the decision boundary as a linear equation of the variables. In addition, SVM is geometrically motivated36 and expected to be less prone to outliers and overfitting than other machine-learning classification algorithms, such as the logistic regression. For the complete modelling process, the regularization parameter C was set to 1, that is the default value in the applied SVC method of the scikit-learn package29, and the weights for both risk classes were also set to 1.Feature selectionOur aim was to use the smallest possible number of weather parameters as variables for a classification model with sufficient performance. To identify the optimal variable combination, we first applied an SVM with a linear kernel for all 2-variable combinations of the monthly weather variables from V2 and V1, i.e., 168 variables (7 weather parameters × 2 years × 12 months). Only for this step, the variables were scaled to their minimum and maximum values, which significantly reduced the processing time. For all the following steps, the scaler was omitted, because the unscaled support vectors were required for the final model. From the total 14,028 models for each unique pair ((frac{168!}{2!cdot left(168-2right)!})), we kept the 100 models with the best F1-score, i.e., of the harmonic mean of sensitivity and precision, and counted the occurrences of each year-month combination in the variables. The best F1-score was 0.752 for the pair (V1_Tmean_9 and V2_Tmax_4); and the best sensitivity was 83% for the pair (V2_Tmax_9 and V1_ST_9).The year-month combinations with more than 10% occurrences were: V1_9 (September of the previous year, with 49% occurrences), V2_9 (September of two years before, with 12%) and V2_4 (April of two years before, with 10%). To avoid sets with highly correlated variables, we formed 3-variable combinations, with exactly one variable from each year-month combination (threefold Cartesian product). From the total 343 models (73 combinations, i.e., 7 weather parameters for 3 year-month combinations), we selected the model with the best sensitivity and at least 70% precision, i.e., the variable set (V2_ST_4, V2_SD_9, and V1_ST_9). We consider that the criteria for this selection are not particularly crucial; and we expect comparable performance for most variable sets with a high F1-score, because the variables for each dimension of the Cartesian product were highly correlated. The eight variable sets with at least 70% precision and at least 80% sensitivity are shown in Supplementary Table 2.The SVM classifier has two hyperparameters: the regularization parameter C and the class weights. By decreasing C, the decision boundary becomes softer and more misclassifications are allowed. On the other hand, increasing the high-risk class weight, the misclassifications of high-risk observations are penalized higher, which is expected to increase the sensitivity and decrease the precision. The simultaneous adjustment of both hyperparameters ensures that the resulting model has the optimal performance with respect to the preferred metric. However, in order to avoid overfitting, we considered redundant a further model optimization with these two hyperparameters. For completeness, we examined SVM models for different values of the hyperparameters and found that the global maximum for the F1-score is in the region of 0.001 for C and 1.5 for the high-risk class weight. Our selected values C = 1 and high-risk class weight equal to 1 give the second best F1-score, which is a local maximum with comparable performance, mostly insensitive to the selection of C from the range [0.2, 5.5].The addition of a fourth variable from V1_6 (June of the previous year) resulted in a model with higher sensitivity but lower precision and specificity (for V1_Pr_6). The highest F1-score was achieved for the quadruple (V2_ST_4, V2_SD_9, V1_ST_9, V1_Pr_6). 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Owing to drastic changes in the environment caused by human interference, wild mammals that are reservoirs of Leishmania have invaded residential areas where species of sand flies with eclectic feeding habits are found, and established a transmission cycle that eventually reaches humans23,24,25. In the study area, it was observed that the largest frequency of specimens over the years was captured in the residential environment, which are represented by residential and peridomicile areas. The lowest frequency was captured in the borders of the forest.The municipality of Paraty, located on the southern coast in the state of Rio de Janeiro, where the study was conducted, has many preserved areas of the Atlantic Forest and its climate is wet with no dry season13, which was confirmed during the three years of the present study, where the relative air humidity stayed high every month. The highest average rainfalls occur in summer and fall (autumn). The average temperature during the hottest months of the year was between approximately 25 °C and 26 °C, with a maximum of 31 °C, and in the coldest months, the temperature averaged between 20 and 21 °C, with a minimum of 16 °C, exhibiting an ideal environment for the activity of sand flies throughout the year.Barretto26 noted that atmospheric conditions, such as relative humidity, rainfall, and temperature directly influence the activity of these sand fly species. Migonemyia migonei and Ny. whitmani had lower activity at temperatures below 15 °C, Pi. fischeri below 10 °C, and Ny. intermedia at temperatures below 9.5 °C. The author also reported that heavy rains prevent sand flies from leaving their shelters; however, this can increase their density within residences, especially for species located next to residential areas. Light rain will not impede their activity, but in these conditions, they are not as frequently observed as they usually are. However, during rain periods, especially in the hot and humid summer period, the density of sand flies increases considerably.In the present study, four key vector species of Leishmania braziliensis Vianna, 1911, the etiologic agent of tegumentary leishmaniasis, were captured throughout the year. The most frequent was Ny. intermedia, followed by Pi. fischeri, Mg. migonei, and Ny. whitmani. Carvalho et al.27, in the State of Pernambuco, northeast region of Brazil, reported having found Mg. migonei infected with Leishmania infantum Nicolle, 1908, the etiologic agent of visceral leishmaniasis.According to Forattini28, there are sand fly species that are essentially resistant to climate changes throughout the seasons. Several are found, albeit in lower densities, during the cooler, dry months, while others disappear during this period. However, other factors also influence the incidence of sand flies in the same location, even under the same temperature and humidity conditions. Thus, to study the seasonality of sand fly species, it is important to perform systematized captures, for a period exceeding two years, to minimize the effects of these additional factors, for example, atypical years with a longer period of drought or humidity, more or less high temperatures, months with higher than expected rainfall or control measures applied by the municipality.In studies carried out in the Northeast region of Brazil, in a study carried out in the municipality of Codó, in the State of Maranhão, an inversely proportional correlation of the captured sandflies was observed in relation to relative air humidity, a direct correlation in relation to temperature and precipitation, a correlation directly proportional29. In the municipality of Sobral, State of Ceará, in the first year of the study, observed a negative correlation with temperature and a high positive correlation with humidity and precipitation, however, in the following year, there was no correlation between the density of captured sandflies and climatic variables30. The same occurred in this study, in the municipality of Paraty, in relation to relative air humidity and precipitation, but in relation to temperature, a strong positive correlation was obtained.In the studied area Ny. intermedia occurred in greater numbers in every month of the year, except in June and July, when it was less frequent than Pi. fischeri. The same pattern was observed for these two species, i.e., a gradual increase in abundance beginning in August, peak abundance in summer (January), followed by a decrease until winter (July). Brito et al.31, when researching the northern coast of the state of São Paulo, municipality of São Sebastião, noted the opposite, that Ny. intermedia had the highest abundance peaks during the driest and coldest period of the year, i.e., from May to August. However, the authors also emphasized the presence of this species throughout the year, mainly in the residential environment, and they stressed the importance of seasonal analyses for periods longer than a year.In the São Francisco River region, in the state of Minas Gerais, on the banks of the Rio Velhas, Saraiva et al.32, in a study over a two-year period, observed a different pattern. In the first year of study, after the rainy season from February to May, with high humidity and high temperature, Ny. intermedia was captured in greater numbers than during other months of the year. In the second year, peaks occurred in October, March, and June, with the highest peak in March, when there was elevated rainfall, high humidity, and high temperatures.In the state of Rio de Janeiro, in Serra dos Órgãos National Park, Aguiar and Soucasaux33 analyzed the monthly frequency in human bait and observed that Ny. fischeri was captured in every month except November. In the hot and humid period, from December to February, there was a gradual increase in the average abundances of this species, and then a slight decrease began in March and continued into April. During the cold and dry period of May and June, abundances started to increase, then decreased in July, and peaked in August. During August, Pi. fischeri was the dominant species of wildlife, and in September, abundances began to decline again.Mayo et al.34, studying the southeastern region of the state of São Paulo, observed that there was a seasonal trend in the abundance for species Mg. migonei, Ny. whitmani, Ny. intermedia, and Pi. fischeri, with abundance peaks recorded during the cooler, drier season (April to September) and low abundances during the warmer, wetter season (October to March). The authors revealed that the occurrence of intense fires in the study area in October, which caused severe environmental change, possibly interfered with the population dynamics of the species. In the present study, the opposite trend of seasonality was shown for the four key species, Ny. intermedia, Pi. fischeri, Mg. migonei, and Ny. whitmani, then what was observed by the above authors, the highest abundances occurred during the hottest period, increasing gradually until a maximum peak in January, and lowest abundances were seen during the coldest period, in July for the first three species, and in June for Ny. whitmani.In the neighboring municipality of this study in Angra dos Reis, in the Ilha Grande, Carvalho et al.35 reinforced the epidemiological importance of Ny. intermedia in the State of Rio de Janeiro and highlighted the role of Mg. migonei in the transmission of cutaneous leishmaniasis with its high rate of infection natural by Leishmania. Still in the same region, along the southern coast of the State of Rio de Janeiro, Aguiar et al.8 conducted systematic catches for two years, with the aim being to analyze the monthly frequency of sand flies in residential and forest environments. The authors discovered results like what occurred in this study in Paraty, that the four most important species caught, Ny. intermedia, Pi. fischeri, Mg. migonei, and Ny. whitmani, had higher average numbers during the hot and humid period of the year, i.e., between October and January, with a maximum peak in December for Ny. intermedia and Pi. fischeri, and January for Mg. migonei. The prevalence of Ny. intermedia was evident in every month, both inside the residence and around the residential area. In the colder and drier season, from May to August, there was a balance with Pi. fischeri, but from August, inside the residence, and from September, around the residence, the frequency increased until it reached its peak in December. There was a gradual increase in the frequency of this species in the warmer and wetter period (between October and January), with average temperatures ranging from 26 to 29 °C and relative air humidity between 84 and 87%.Condino et al.36, when studying the southwestern region of the state of São Paulo, observed that Ny. intermedia and Ny. whitmani had the highest frequencies during the months of May, September, and December with temperatures ranging from 21 to 25.7 °C and rainfall between 66.7 and 195.1 mm. In June, the lowest frequency of sand flies was observed, which then increased until a maximum peak in September. Temperature data and rainfall index were not correlated with the density of specimens, especially as the study was carried out over only one year. In this study, the opposite was observed for Ny. intermedia and Ny. whitmani in the month of May, one of the months with the lowest density.In the city of Petrópolis, state of Rio de Janeiro, Souza et al.24 observed a prevalence of Ny. intermedia and Ny. whitmani, with the latter species prevailing around the residence. Migonemyia migonei and Pi. fischeri were also present but to a lesser extent. In the forest, Ny. whitmani was more abundant, followed by Pi. fischeri, while Ny. intermedia was found at lower abundances. However, Ny. intermedia and Pi. fischeri were present during every month of the year. The authors also found a significant correlation between the number of sand flies and environmental changes such as temperature, relative humidity, and rainfall. The same was observed, in this study, in the forest with Ny. intermedia, however, in this environment the number of Pi. fischeri specimens was higher than that of Ny. whitmani.In the north of Espírito Santo, Virgens et al.37 observed that Ny. intermedia was present in almost every month of the study period, with peaks in the warmer and wetter months. The authors highlighted that the low numbers of this species were recorded during and after high rainfall periods, suggesting that heavy rain is unfavorable for the development of immature forms, as breeding sites in altered habitats suffered a greater impact because of extreme weather conditions.In a study carried out by Guimarães et al.38 to observe the competence of Mg. Migonei to Leishmania infantum, concluded that this species is highly susceptible to the development of this parasite and that in addition to its anthropophilia and abundance in areas with an active focus of visceral leishmaniasis, it can act as a vector of this disease in Latin America.In the studied area, Ny. intermedia, one of the main vectors of the etiological agent of tegumentary leishmaniasis in the region2, was present in significant numbers in the home environment throughout all months of the year. The species Pi. fischeri was present over the months in expressive numbers in all types and locations of capture, that is, both in the environment altered by human activity and in the natural environment where leishmaniasis occurs in its natural enzootic cycle. Migonemyia migonei, present throughout the year in the peridomestic environment, showed its association with the dog, where it was prevalent throughout the year in the kennel, being an important vector of the etiological agent of tegumentary leishmaniasis, as well as being suspected in areas of visceral leishmaniasis transmission, where the main vector of this disease is not found. And Ny. whitmani present in the peridomicile, mainly in the hottest months of the year, in addition to the forest and forest margins, it was observed that in this study region the species is emerging through a selective process of adaptation in environments that were negatively affected by the increase of human activity. Thus, despite observing a period of greater frequency of sand flies in the hottest months of the year, a period with high rainfall, the high relative humidity is observed throughout the year, as well as the presence of species of epidemiological importance Ny. intermedia, Pi. fischeri, Mg. migonei and Ny. whitmani, who are involved in the propagation of the etiological agent of tegumentary leishmaniasis to humans and animals, causing greater contact between the region’s inhabitants with these dipterans and thus, a greater risk of contracting the disease. More