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Considering the actual and predicted values, the model generated through the different inputted parameters should be diagnosed satisfactorily. It is pretty understanding that agreement between the actual and predicted values given the effectiveness and accuracy of the generated model, as shown in Fig. 2. The following polynomial regression model equations were obtained:$$begin{aligned} COD;removal , % , & = 76.63 – 0.019*A , + , 0.064*B , – 0.511*C , – 0.405*AB , – 0.153*AC , \ &quad – 0.099*BC , + , 0.263*A^{2} + , 0.479*B^{2} – 0.303*C^{2} \ end{aligned}$$
(1)
$$begin{aligned} Nitrate;Removal , % , & = 72.04 , – 1.881*A – 0.142* , B , + , 2.384*C , + , 2.623*AB , + , 8.579*AC , \ &quad – 2.626*BC , – 10.783*A^{2} + , 0.223*B^{2} + , 0.963*C^{2 } hfill \ end{aligned}$$
(2)
$$begin{aligned} & Phosphate , Removal , % , = \ & 67.179 – 1.215*A , + , 3.539*B , – 1.068*C , + , 1.610*AB , – 2.559*AC , + , 0.392*BC , + , 0.788*A^{2} – 2.943*B^{2} + , 0.564*C^{2} \ end{aligned}$$
(3)
where A is initial pH, B is current time (min), C is MLSS concentration (mg L−1) at which the study was carried out.Figure 2Normal probability versus studentized residuals and predicted versus actual plots for (i) COD removal, (ii) nitrate removal, and (iii) phosphate removal.Full size imageIt has been observed that statistics for the model having low values represent well for the system and its predictions.Statistical analysis of COD, nitrate and phosphate removalIt was seen that 3D surface plots could provide a better understanding of the interactive effects of the parameters. The 3D surface plots are illustrated in Figs. 3, 4, and 5, respectively. It was observed that the maximum removal efficiency for COD, nitrate, and phosphate is in the range of 59% to 74%.Figure 3Model generated surface plot of % COD removal (i) pH versus current time (ii) pH vs. MLSS (iii) MLSS vs. current time.Full size imageFigure 4Model generated surface plot of %nitrate removal (i) pH versus current time (ii) pH vs. MLSS (iii) MLSS vs. current time.Full size imageFigure 5Model generated surface plot of %phosphate removal (i) pH versus current time (ii) pH versus MLSS (iii) MLSS versus current time.Full size imageTable 4 (i) shows the statistics for COD removal. Adeq Precision is desirable, which measures the signal-to-noise ratio and a ratio greater than 4. For the COD removal, Adeq Precision was 19.255, indicating an adequate signal. It was also observed that the adjusted R2 is 0.9118 (difference less than 0.2), and the predicted R2 of 0.8601 was significant, implying that the predictions are in good agreement with experimental values.Table 4 Fit statistics for (i) COD removal, (ii) Nitrate removal, (iii) Phosphate removal.Full size tableFigure 3 illustrates the effect of current flow time and pH concerning the percentage removal of COD. The model predicted values observed were seen to lie in the range of 73.1% at MLSS values of 2500 mg L−1, keeping initial COD values as 200 mg L−1. As the COD load increases, it seems to be predicted that the overloading of bacteria occurs, thereby slowing down the consumption of organics. In Fig. 4, the expected removal efficacy shows upward trends with an increase in the values of MLSS, which also coincided with previous studies. As the value of MLSS increases, the contact time of biomass in the system increases, hence producing more effective results than others.Table 4 (ii) shows the statistics for nitrate removal. The predicted R2 of 0.9164 was in reasonable agreement with the adjusted R2 of 0.9730. For the nitrate removal, Adeq Precision was 29.608, indicating an adequate signal. This model can be used to navigate the design space.Table 4 (iii) shows the statistics for phosphate removal. The predicted R2 of 0.9165 was in reasonable agreement with the adjusted R2 of 0.9720. For the phosphate removal, Adeq Precision was 34.945, indicating an adequate signal. This model can be used to navigate the design space.Figure 5 illustrates that as we reduce the cycle time from 24 to 18 h, the system efficacy, i.e., COD removal effectiveness shows a downward trend due to less contact time with biomass. Meanwhile, if we increase the cycle time, we observe higher efficacy in the system. The model generated surface plot in Fig. 5 illustrated that increasing MLSS values by 3000 mg L−1 will enhance the COD removal by 73.1%, keeping the initial pH constant. This may be due to many microbes that can break down organic matter. In aerobic reactors, pH is an essential factor in the growth of the microbial population. To create granules, the pH of the reactor has a direct impact. Studies have shown that granule formation occurs when bacteria grow at the ideal pH level, whereas mass proliferation of fungus occurs in an acidic environment.COD removal in EBR and tubesettlerThe Influence, effluent, and removal of COD in EBR & tubesettler are illustrated in Fig. 6a,b. Results demonstrate that the COD concentration is consistent and better COD removal efficacy rate. The average removal rate values observed in the EBR were between 74 and 79%, with the initial COD concentration kept around 360–396 mg L−1. It was also observed that tubesettler resulted in approximately 25–36% efficacy when the initial concentration was between 75 and 97 mg L−1. The results of EBR are promising and can be attributed to the fact that electrocoagulation takes place along with the oxidation and biodegradation process. It was also observed that the percentage removal of COD shows downward trends due to electrochemical oxidation and adsorption, thereby resulting in physical entrapment and electrostatic attraction30. It has also been reported in many other studies that COD removal of around 85–90% was observed using composite cathode membrane using MRB/MFC system19 for the specialized treatment of landfill leachate. It was seen with the electrooxidation process having COD removal of around 80–84% and 84–96% with submerged membrane bioreactors, using Iron electrode6. For the Coal industry, it was found to be around 85% using membrane electro bioreactors31.Figure 6(a) Influent, effluent and removal of COD in EBR (IEBR = Influent Electrobioreactor, EEBR = Effluent Electrobioreactor, STD = Standard, REBR = Removal Electrobioreactor), (b) Influent, effluent, and removal of COD in tubesettler (IT = Influent tubesettler, ET = Effluent tubesettler, STD = Standard, RT = Removal tubesettler).Full size imageIn the current study, results seemed to be lower than the values reported in the previous studies. The main reason might be the employment of a modified EBR system and the production of biomass species. When the overall COD removal with tubesettler is considered, up to 83.58% removal efficiency is observed. The overall COD removal efficiency is significant and is at par with other studies3,4,5. This signifies that EBR performed better than tubesettler in COD removal. The tubesettler’s lower removal efficiency can be attributed to lower influent concentration from already reduced wastewater from EBR.Nitrate removal in EBR and tubesettlerIt was observed in many studies that nitrifying is the leading cause of nitrification, i.e., conversion of NH3-N to nitrate NO3-N10. The indirect method of system nitrification process claudication was to be ascertained using measurements concerning ammonia values32,33. In the current study, the nitrification process was considered using the nitrate concentration measurement from the influent and effluent in both systems, i.e., EBR and tubesettler34,35,36. The nitrate concentration of influent and effluent was observed and illustrated in Fig. 7a,b. The system stabilized and produced enhanced results up to 70% of nitrate removal, and it was seen to be in the range of 40–45% for the tubesettler. It has been observed that EBR produced better results than the tubesettler. The results variation in both the systems were reasonably attributed mainly to two primary reasons (1) low influent concentration in the influent compared to the EBR system and (2) inhibition effect due to the applied DC field, which was absent in tubesettlers.Figure 7(a) Influent, effluent, and removal of nitrate in EBR (IEBR = Influent Electrobioreactor, EEBR = Effluent Electrobioreactor, STD = Standard, REBR = Removal Electrobioreactor), (b) Influent, effluent, and removal of nitrate in tubesettler (IT = Influent tubesettler, ET = Effluent tubesettler, STD = Standard, RT = Removal tubesettler).Full size imageThe removal efficiency of around 70% was achieved, lower than the values in submerged membrane bioreactors, i.e., 82%6. However, including a membrane would have enhanced the removal efficiency and considered a hybrid EBR system. The results of the current study are close enough to many other studies with a similar system and different operating parameters. Hence, a combined approach can be used for better efficacy. During the weekly analysis, the nitrate concentration during the 1st to 3rd week is lower than in the following weeks. As the concentration of nitrifying bacteria decreased, they had less to work with. Thus, the substrate concentration grew, and so did the removal rate. Nitrate concentrations rose by more than twice the previous week during Week 7. They slowed the bacterial activity, resulting in an efficiency decline to 47% from 70% during the last week’s study period and weeks 6 and 8. A similar pattern emerged for the seventh week in a row in tubesettler. On the other hand, microorganisms overcame differences in engagement because the nitrate content was low in other weeks.Phosphate removal in EBR and tubesettlerMany researchers have looked at nitrate content, but none have looked at phosphate concentration. Eutrophication in receiving water bodies, on the other hand, is predominantly caused by phosphate and nitrate. Additionally, there is a lack of information available on hospital wastewater. The influent and effluent phosphate concentrations in the Electro bioreactor and the tubesettler is shown in Fig. 8a,b. A 75% reduction in the effluent phosphate content in EBR was achieved tubesettler had a 67% effectiveness in phosphate removal but a lower efficiency in nitrate reduction. A previous similar study that used a Submerged Membrane Electro bioreactor claimed a clearance rate of 76% to 95%, which is lower than this study’s results6. Phosphate removal was reported at 50–70% using the electrocoagulation process for different Ph and current6.Figure 8(a) Influent, effluent, and removal of phosphate in EBR (IEBR = Influent Electrobioreactor, EEBR = Effluent Electrobioreactor, STD = Standard, REBR = Removal Electrobioreactor), (b) Influent, effluent, and removal of phosphate in tubesettler (IT = Influent tubesettler, ET = Effluent tubesettler, STD = Standard, RT = Removal tubesettler).Full size imageIn week 6 and week 8, the EBR’s phosphate removal efficiency fluctuated dependent on the weekly average concentration in EBR. This volatility can be linked to a shift in the composition of hospital wastewater. tubesettler had a modest variation ranging from 5 to 6%. Although phosphate concentrations rose in week two, tubesettler removal efficiency improved. As demonstrated in Fig. 8a,b, the arriving wastewater ingredient exhibited a strong affinity in terms of phosphate reduction.Excess effluent concentration and standard deviation from EBR and tubesettler are shown in Table 5. EBR performed better than tubesettler in COD reduction when nitrate and phosphate were compared. Because tubesettler solely employs a physical process to remove contaminants, this is to be anticipated. Effluent from the secondary treatment facility is sent to a tubesettler, which acts as a polishing unit. EBR eliminated COD by 91%, nitrate by 85%, and Phosphate reduction by 81% compared to tubesettler’ s total efficiency. At the same time, tubesettler reduced COD by 37%, nitrate by 51%, and phosphate by 53%. Hence, EBR primarily removed pollutants from wastewater while tubesettler acted as a polishing unit. Table 5 illustrates the effluent wastewater characteristics of EBR and tubesettler.Table 5 Effluent wastewater characteristics of EBR and tubesettler.Full size tableKinetic models post optimizationFirst-order modelA first-order linear model was analyzed on the experimental data by plotting (So − Se)/Se against hydraulic retention time (HRT), providing K1 and R2. For COD, R2 values were 0.761 with a constant value of 1.213, as shown in Table 6. Henceforth based on the results, the obtained model did not seem to fit well for either of the cases.Table 6 Analyzed kinetic models.Full size tableGrau second-order modelA Grau second-order model was analyzed on the experimental data by plotting HRT/((So − Se)/So) versus HRT. The COD constant obtained was Ks = 10–5, as shown in Table 6. The R2 value of 0.99 suggests a good correlation coefficient. Therefore, the obtained results fit well for AOX and COD.Modified Stover–Kincannon modelSubstrate utilization rate expressed as organic loading in this model is widely used in biological reactor kinetic modelling of wastewater. The developed model can evaluate the performance of the biological system and estimate its efficiency based on the input parameters. The kinetic constant KB and Umax for COD were 0.35 and 1.73 g L−1 d−1, respectively. The R2 was 0.98 for the substrate removal, as presented in Table 6.Monod modelCOD utilization rate was obtained by plotting VX/Q (So − Se) against 1/Se. The value of 1/K (0.421) was obtained from the intercept, while the Ks/K value (1.235) was the slope of the line. COD removal half-saturation values were 0.045 and 0.056 g L−1. These values infer a high affinity of bacteria for the substrate. The R2 value of 0.95 depicted an excellent correlation coefficient in the case of COD. The Monod model fits well for COD, resulting in R2 = 0.98, as shown in Table 6. More

Lattice data geoprocessing and temporal extentWe latticed the data49 using a worldwide grid composed of 18,874 hexagonal 7774 km2 units, built using Discrete Global for R (https://github.com/r-barnes/dggridR)50. All the information we processed on yellow fever cases, on urban and sylvatic vectors presences, and on zoogeographic, spatial and environmental variables (see details on this information below) was aggregated at this spatial resolution. We used zonal statistics to calculate average variable values using ArcMAP 10.7.The temporal extent for our analysis was divided into three periods: the late 20th century (1970–2000), the early 21st century (2001–2017), and the period 2018–2020. Predictions estimated by the late 20th century models were validated using cases reported in the early 21st century, and predictions from the early 21st century models were validated with records from 2018‒2020. Although the limit between periods at the turn of the century is arbitrary, it reflects: 1) Distributional changes in the ranges of the Ae. aegypti and Ae. albopictus vectors51; 2) after 1999, the yellow fever genotype I has spread outside the endemic regions, and the genotype I modern-lineage has caused all major yellow fever outbreaks detected in non-endemic regions of South America since 200013; 3) the maximum potential of globalization was realised at the beginning of the 21st century with the opening of international borders, the widespread access to the Internet and to cell phones, and the generalization of online travel booking and of low-cost flights34. The end of the second period, 2017, was chosen in order to include three years with occurrence of yellow fever cases in south-western Brazil (and two since its occurrence in Angola and the DRC), while retaining three later years for predictive testing purposes (details on this testing are given below).Yellow fever datasetsWe used georeferenced cases of yellow fever in humans for a period of 51 years (from 1970 to 2020). This study period starts immediately after the suspension of the use of DDT due to to the appearance of resistance of Ae. aegypti in the late 1960s in several countries, after 50 years of eradication efforts10. We took from Shearer et al.6 the distribution of yellow fever cases for the period 1970–2016. We extracted additional cases for the period 1970–2020 from various sources (Supplementary data 1), including ProMED-mail: Program of International society for infectious diseases; World Health Organization (WHO): Yellow fever outbreak weekly situation reports, Rapport de situation fievre jaune en RD Congo and Weekly epidemiological record; Health Ministry of different countries: Epidemiological Bulletins of yellow fever in Brazil, Peru, Colombia, and Paraguay; Pan American Health Organization (PAHO): Epidemiological Update Yellow Fever; European Centre for Disease Prevention and Control (ECDC): Communicable disease threats report and Rapid risk assessment report; Nigeria Centre for Disease Control (NCDC): Situation report, yellow fever outbreak in Nigeria and Global Infectious Disease and Epidemiology Online Network (GIDEON). The reported cases were complemented with publications available since 2016 with geo-referenced information on case location (Supplementary data 1). In addition, information was also sought on cases reported in French and Portuguese from local news reports in Africa.We only represented in the hexagonal lattice the reported cases of yellow fever that had a precise location or that were referred to administrative unit was smaller than or of similar size to the hexagons. This dataset was transformed into a binary variable per study period representing the presence (n = 218 hexagons in the late 20th century; 493 hexagons in the early 21st century, see Supplementary data 2) or absence (n = 18,656 hexagons in the late 20th century; 18,381 hexagons in the early 21st century), hereafter the distribution of reported cases of yellow fever.Vector datasetThe georeferenced presences of vectors involved in the urban cycle of yellow fever (i.e., the mosquitoes Ae. aegypti and Ae. albopictus) were taken from “The global compendium of the Ae. aegypti and Ae. Albopictus occurrence”26 for the period 1970–2014. We complemented these records with georeferenced data scientifically validated for the period 2014–2017, taken from VectorBase (https://www.vectorbase.org/) and Mosquito Alert (http://www.mosquitoalert.com/). We included both species because, although Ae. Aegypti is the main vector of yellow fever, Ae. albopictus can also transmit the yellow fever virus to humans4,52.In addition, we included georeferenced occurrence data of sylvatic vectors (Haemagogus janthinomys, H. leucocelaenus and Sabethes chloropterus in South America; Ae. africanus and Ae. vittatus in Africa), which were obtained from Vectormap (vectormap.si.edu) and Gbif (https://gbif.org).We represented in the hexagonal lattice the reported occurrence of mosquitoes that had a precise location or were located in administrative smaller than or of similar size to the hexagons. With this information, we built binary variables representing the presence or absence of each mosquito species in each hexagon. For species involved in the urban cycle, we built two binary variables per species: one for the late 20th century, and another for the early 21st century. For species involved in the sylvatic cycle, we merged the data of late 20th century and early 21st century in order to build a binary variable per species, due the scarcity of data and under the assumption that their distributions have been stable during the four last decades53,54,55.Zoogeographic, spatial and environmental variablesWe built zoogeographic variables based on chorotypes, or types of distribution ranges, of all non-human primate species, as all are potentially vulnerable to yellow fever56. A chorotype is a distribution pattern shared by a group of species57. For obtaining these zoogeographic variables, we proceeded in 4 steps: (1) Distribution maps of non-human primates were obtained from the IUCN for South-America and Africa; (2) the species ranges were classified hierarchically using the classification algorithm UPGMA according to the Baroni-Urbani & Buser´s similarity index58; (3) we evaluated the statistical significance of all clusters obtained as a result of the classification using RMacoqui 1.0 software (http://rmacoqui.r-forge.r-project.org/)59; (4) in each hexagon, the number of species belonging to each chorotype was quantified. We generated a zoogeographic model based on the non-human primates chorotypes by running a forward-backward stepwise logistic regression using presence/absence of yellow fever cases and the number of species of each chorotype as dependent and predictor variables, respectively. This procedure was made for two periods: late 20th century and early 21st century. Henceforth, only the selected chorotype variables were considered in the baseline disease favourability models explained below.We built a yellow fever spatial variable for each continent (South-America and Africa), which were calculated through the trend surface approach, by performing a backward-stepwise logistic regression of the distribution of yellow fever cases on a ensemble of variables defined for polynomial combinations of longitude (X) and latitude (Y) up to the third degree: X, Y, XY, X2, Y2, X2Y, XY2, X3, and Y3. We transformed probability values derived from logistic regression into spatial favourability values by applying the Favourability Function60,61, using the following equation:$$F=frac{P}{1-P}Big/left(frac{{n}_{1}}{{n}_{0}}+frac{P}{1-P}right)$$
(1)
where P is the spatial probability of occurrence of at least a case of yellow fever at each hexagon, and n1 and n0 are the numbers of hexagons with presence and absence of yellow fever cases, respectively. We built a different spatial variable for each continent and time period.We used environmental variables related to the following factors: climate, human activity, topography, hydrography, biome, ecosystem type, and forest loss. For details about the source and description of the environmental variables selected, see Supplementary Table 3.Pathogeographical approach to transmission risk modellingOur objectives were to construct a global yellow fever transmission risk map, and to identify areas where primates contribute to increased risk, using the methodology previously used to analyse the worldwide dynamic biogeography of zoonotic and anthroponotic dengue34 (see flowchart in Fig. 1 and Supplementary Methods). We produced a transmission model focused on the late 20th century and another for the early 21st century.The risk of transmission was assessed by combining a first model describing areas favourable to the presence of yellow fever, i.e., the “baseline disease model”; and another model describing areas favourable to the presence of mosquitoes known to act as vectors, i.e., the “vector model”. For this combination, we used the fuzzy intersection62, i.e., the risk of transmission at each hexagon was valued at the minimum between favourability in the baseline disease model and favourability in the vector model.In this way, we considered that the vectors are a limiting factor, and that the risk of transmission derives from the degree to which the environmental conditions are simultaneously favourable for the presence of vectors and for disease cases to occur63. In order to analyze the spatio-temporal dynamic of yellow fever, we made comparable models for the late 20th century and the early 21st century, using predictor variables that are available for both periods. Later, we made a 21st-century enhanced model that optimized the predictive capacity of availabe information in the search for current risk areas. For this purpose, we included, in the variable set, predictors that are only accessible for the 21st century (e.g., high-resolution population density, livestock, irrigation, infrastructures, intact forest, and GlobCover land cover classes; see Supplementary Table 3).Baseline disease modelsThe baseline disease model in the late 20th century was expressed in terms of favourability values, using the Eq. (1) (see above). This time, P was calculated through a multivariable forward-backward stepwise logistic regression of the 20th-century yellow fever presences/absences on a set of zoogeographic, environmental and spatial variables. This was made in two blocks: 1) a stepwise selection of environmental and spatial variables; 2) a later stepwise addition of chorotypes whose presence contribute to improve significantly the likelihood of the model based only on the first block. Variables for each block were preselected using RAO´s score tests (which estimated the significance of its association to the distribution of yellow fever cases), and Benjamini and Hochberg´s (1995) false discovery rate (FDR) to control for Type I errors, which could pass due to the number of variables analysed. We also avoided excesive multicollinearity by preventing that variables with Spearman correlation values >0.8 were included in the same model. In case this happened, only the variable with the most significant RAO´s score-test value was retained, and the multivariable model was re-run. The parameters in the models were estimated using a gradient ascent machine learning algorithm, and the significance of these paremeters was assessed using the test of Wald. The goodness of fit of the models was established using the test of Hosmer and Lemeshow, which checks the significance of the difference between expected and observed values, so that non significant differences mean that the fit is good. We used IBM-SPSS Statistics 24 software package to perform the models and all the associated tests.We subsequently updated the baseline disease model to explain the distribution of yellow fever cases in the early 21st century. Compared to the procedure described for the 20th-century model, we included a new block before the two ones mentioned above. Thus, the methodological sequence was as follows: (1) forcing the input, as a predictor variable, of the logit of the late 20th century baseline disease model (the logit being the linear combination of variables in the 20th-century model); (2) making a later stepwise selection of spatial and environmental variables; and (3) a stepwise addition of chorotypes that contribute to improving the model’s likelihood. In this way, we took into account that the current spread of yellow fever is influenced by the inertia of previous situations. This is equivalent to assuming that there is temporal autocorrelation (i.e., disease cases in the early 21st century are more probable to occur in areas where they already occurred in the late 20th century). In the 21st-century model, the variables entering in blocks (2) and (3) represent the drivers potentially favouring the spread34. The preselection of variables for blocks (2) and (3) and the control for excessive multicollinearity between environmental variables were made as explained for the late 20th-century model.Vector modelsWe produced a favourabuility model for each vector species for the late 20th century and for the early 21st century separately. We built multivariable favourability models for urban vectors using the distribution of each urban mosquito species in the late 20th century and the spatial and environmental variables for the late 20th century, following the same procedure used for block (1) in the 20th-century baseline disease model. We also updated each urban vector model for the early 21st century as in the baseline disease model, using the procedure described for blocks (1) and (2).A single model, referred to both the late 20th and the early 21st centuries, was made for sylvatic vectors, for the reasons explained above. Finally, we built up the vector models for the late 20th century and for the early 21st century by joining all individual vector models of each period using the fuzzy union64 (i.e., considering for each hexagon the maximum value shown by any of the species models). This criterion was taken into account because, if the pathogen were present, the occurrence of a single vector species would involve potential for yellow fever transmission.Model fit assessment and validation of its predictive capacityFavourability models were assessed according to their classification and discrimination capacities respect to the training data set (i.e., to the observations used for model training). The classification capacity was based on two classification thresholds: F = 0.5, which represents the neutral favourability, and F = 0.2, below which the risk of transmission was considered to be low61. Six classification assessment indices were used65: (1) sensitivity (i.e., proportion of presences correctly classified in favourable hexagons), (2) specificity (i.e., proportion of absences correctly classified in unfavourable hexagons), (3) CCR (i.e., proportion of presences and absences correctly classified in favourable hexagons respectively), (4) TSS (that is sensitivity + specifity – 1), (5) underprediction rate (i.e., proportion of favourable areas that are recorded to have presences), and (6) overprediction rate (i.e., proportion of favourable areas that are not recorded to have presences). The discrimination capacity was assessed using the area under the receiver operating characteristic (ROC) curve (AUC)66.The validation of the predictive capacity of the late 20th century disease and transmission-risk models was done by evaluating, with the same indices used above, classification and discrimination capacities with respect to the cases of the period 2001‒2020. The predictive capacity of the models for the early 21st century was validated with respect to the yellow fever cases reported in the period 2018‒2020.Relative importance of the zoogeographical factorWe estimated the pure contribution of non-human primates to the baseline disease model, i.e., how much of the variation in favourability for yellow fever cases was explained exclusively by the zoogeographical factor, by performing a variation partitioning analysis67. This implied the use of the zoogeographic model and a spatio-environmental model constructed with the environmental and spatial variables that entered the baseline disease model. This approach also allowed us to calculate how much is the variation of the baseline disease model attributable simultaneously to the zoogeographical and other factors. We built maps identifying the zones where the non-human primates could increase yellow fever cases in humans, that is, where the presence of primates could favour the occurrence of yellow fever regardless of correlations with other factors. To map these areas we identified the hexagons that fulfilled these conditions: 1) favourability values for the baseline disease model were ≥ 0.2; and 2) the difference between the favourability values provided by the baseline disease model and the spatio-environmental model was positive and ≥ 0.01.Reporting summaryFurther information on research design is available in the Nature Research Reporting Summary linked to this article. More

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Experimental dataThe dataset used in this study is the global long-term air quality indicator data of 5577 regions from 2010 to 2014 extracted by Betancourt et al.14 based on the TOAR database (https://gitlab.jsc.fz-juelich.de/esde/machine-learning/aq-bench/-/blob/master/resources/AQbench_dataset.csv)29. As shown in Fig. 3, the monitoring sites include 15 regions, including EUR (Europe), NAM (North America), and EAS (East Asia), and are mainly distributed in NAM (North America), EUR (Europe) and EAS (East Asia). The dataset mainly includes the geographical location information of the monitoring site, such as longitude and latitude, the area to which it belongs, altitude, etc., and the site environment information, such as population density, night light intensity, and vegetation coverage. Since it is difficult to directly quantify factors such as the degree of industrial activity and the degree of human activity, environmental information such as the average light intensity at night and population density are used as proxy variables for the above factors. The ozone indicator records the hourly ozone concentration from air quality observation points in various regions and aggregates the collected ozone time series in units of one year into one indicator. Using a longer aggregation period can be used to average short-term weather fluctuations. The experimental data have a total of 35 input variables, including 4 categorical attributes and 31 continuous attributes. The predictor variable is the average ozone concentration in each region from 2010 to 2014. The specific variable names and descriptions14 are shown in the supplementary materials. A total of 4/5 of the total samples were used as the training set, and 1/5 were used as the test set.Figure 3Global distribution of monitoring sites.Full size imageResults of BO-XGBoost-RFEAccording to the XGBoost-RFE algorithm for feature selection, XGBoost-RFE combined with the cross-validation method is used to calculate the selected feature set in each RFE stage for fivefold cross-validation, and the mean absolute error (MAE) is used as the evaluation criterion to finally determine the number of features with the lowest mean absolute error (MAE). At the same time, the Bayesian optimization algorithm is used to adjust the hyper-parameters of XGBoost-RFE, and then the feature subset with the lowest cross-validation mean absolute error (MAE) is obtained. The main parameters of the XGBoost model in this article include the learning_rate, n_estimators, max_depth, gamma, reg_alpha, reg_lambda, colsample_bytree, and subsample. All parameters used in the model are shown in the supplementary material. Within the given parameter range, the Bayesian optimization algorithm is used, the mean absolute error (MAE) of the XGBoost-RFE fivefold cross-validation is used as the objective function, and the number of iterations is controlled to be 100. We obtained the hyperparameter combination corresponding to the lowest MAE and the corresponding optimal feature subset. The iterative process of Bayesian optimization is shown in Fig. 4.Figure 4Iterative process of Bayesian optimization.Full size imageThe parameter range and optimized value of XGBoost-RFE are shown in Table 1. The XGBoost-RFE feature selection results under the above optimized hyperparameters are shown in Fig. 5. The number of features in the feature subset with the lowest mean absolute error is 22, and the MAE is 2.410.Table 1 Main hyper-parameter range and optimized value.Full size tableFigure 5XGBoost-RFE feature selection results: Cross-validation MAE under optimal hyperparameter combination.Full size imageAdditionally, the XGBoost-RFE feature selection model without Bayesian optimization is compared with the algorithm in this study. The default parameters of the underlying model XGBoost are set to learning_rate as 0.3, max_depth as 6, gamma as 0, colsample_bytree as 1, subsample as 1, reg_alpha as 1, and reg_lambda as 0. The comparison results are shown in Table 2. The results show that the XGBoost-RFE cross-validation MAE without parameter tuning is larger than that of the algorithm in this study, and the dimension of the feature subset obtained is also higher than that of the algorithm in this study.Table 2 Comparison of MAE and feature num before and after BO.Full size tablePrediction resultsTo test the prediction accuracy of the prediction model with the optimal subset obtained by BO-XGBoost-RFE, three indexes, MAE, RMSE and R2, are used to evaluate the prediction results, and the expressions are as follows:$$begin{array}{*{20}c} {MAE = frac{1}{n}mathop sum limits_{i = 1}^{n} left| {left( {y_{i} – widehat{{y_{i} }}} right)} right|} \ end{array}$$
(8)
$$begin{array}{*{20}c} {RMSE = sqrt {frac{1}{n}mathop sum limits_{i = 1}^{n} left( {y_{i} – widehat{{y_{i} }}} right)^{2} } } \ end{array}$$
(9)
$$begin{array}{*{20}c} {R^{2} = 1 – frac{{mathop sum nolimits_{i = 1}^{n} left( {widehat{{y_{i} }} – y_{i} } right)^{2} }}{{mathop sum nolimits_{i = 1}^{n} left( {y_{i} – overline{{y_{i} }} } right)^{2} }}} \ end{array}$$
(10)
n indicates the number of samples, yi is the true value, (widehat{{y_{i} }}) is the predicted value and (overline{{y_{i} }}) indicates the mean value of the predicted value.The XGBoost-RFE feature selection algorithm based on Bayesian optimization in this study is compared with feature selection using full features and features selected by the Pearson correlation coefficient, which measures the correlation between two variables. In this study, the correlation with predictor variables was selected to be less than 0.1, and the variables with correlations greater than 0.9 were deleted to avoid multicollinearity.XGBoost, random forest, support vector regression machine, and KNN algorithms were used to predict ozone concentration with full features, features selected by Pearson’s correlation coefficient, and features based on BO-XGBoost-RFE. According to the evaluation indicators described above, the comparison of the prediction performance results of the three algorithms before and after dimensionality reduction can be obtained. The MAE, RMSE and R2 results of each prediction model are shown in Table 3.Table 3 MAE, RMSE and R2 of each prediction model.Full size tableAmong the four prediction models, random forest has the lowest MAE and RMSE and the highest R2 based on three different dimensions of data and therefore has the best prediction performance. The prediction accuracy of all four prediction models based on Pearson correlation is lower than that based on BO-XGBoost-RFE, indicating that only selecting features by correlation cannot accurately extract important variables. Although the RMSE of the support vector regression model based on BO-XGBoost-RFE is slightly lower than the RMSE based on full features, the prediction accuracy of XGBoost, RF, KNN after feature selection of BO-XGBoost-RFE is higher than that based on full features and Pearson correlation. Among the four prediction models, random forest has obtained the highest prediction accuracy. The MAE based on BO-XGBoost-RFE is 5.0% and 1.4% lower than that based on the Pearson correlation coefficient and the full-feature-based model, and the RMSE is reduced by 5.1%, 1.8%, R2 improved by 4.3%, 1.4%. Additionally, the XGBoost model achieved the greatest improvement in accuracy. The MAE was reduced by 5.9% and 1.7%, the RMSE was reduced by 5.2% and 1.7%, and the R2 was improved by 4.9% and 1.4% compared with the Pearson correlation coefficient-based and full-feature-based models, respectively. This indicates that feature selection based on BO-XGBoost-RFE effectively extracts important features, improves prediction accuracy based on multiple prediction models, and has better dimensionality reduction performance.Figure 6 shows the importance of each feature obtained by using the random forest prediction model, reflecting the degree of influence of each variable on the prediction results of the global multi-year average near-ground ozone concentration. The most important variables that affect the prediction results according to the ranking of feature importance are altitude, relative altitude, and latitude, followed by night light intensity within a radius of 5 km, population density and nitrogen dioxide concentration, while the proxy variables for vegetation cover have a relatively weak effect on the prediction of ozone concentration.Figure 6Feature importance in random forest.Full size image More