Philippa Kaur

Among the 325 municipalities in Greece during the period 2010–2021, WNV events, defined as the occurrence of at least one laboratory-confirmed human WNV case during a specific year, were reported in 154 (47%) municipalities, while the remaining 171 did not report any WNV case. WNV events were reported for a period ranging from one to eight years: 54 (35%) municipalities reported laboratory-confirmed WNV cases in only one year, 38 (25%) in two years, 30 (19%) in three years, 12 (8%) in four years, 10 (6%) in five years, 6 (4%) in six years, 1 (1%) in seven years, and 3 (2%) in eight years. This means that in 60% of the positive areas (82 municipalities out of 154), WNV appeared at most for two years, in 27% (42 out of 154) between three and four years, and in the remaining 13% (20 out of 154) for five years or more. Considering the total number of reported laboratory-confirmed human WNV cases across the twelve years (Fig. 1), in approximately 50% of the positive municipalities (78 out of 154), at most 4 cases were reported: 1, 2, 3, and 4 WNV cases were reported in 24, 32, 11, and 11 municipalities, respectively. Overall, 39 municipalities recorded a number of WNV cases ranging from 5 to 10 (third quartile), 34 a number ranging from 11 to 46, while the remaining 3 municipalities recorded a number of WNV cases equal to 56, 71 and 94.Figure 1(a) Map of Greece with total numbers of laboratory-confirmed human WNV cases throughout the 12-year period 2010–2021, with breakdowns by municipality. White denotes municipalities where no human cases were observed. (b) Map of Greece with total numbers of modelled human WNV cases throughout the 12-year period 2010–2021, with breakdowns by municipality. White denotes municipalities where no human cases were modelled.Full size imageModel evaluation and comparison with MIMESISWe investigated the ability of the MIMESIS-2 model to correctly identify the occurrence of WNV events, both in space and time, and its capacity to quantify the annual number of human WNV cases and the timing of the first WNV event in the year. The performance of many quantities of interest, such as the severity and timing of occurrence of human WNV cases, was also compared output from the original MIMESIS model26.Occurrence of WNV eventsStarting with the spatial analysis, we considered the fit of the model to replicate the observed 385 WNV events out of 3,900 (325*12) possible events across municipalities. MIMESIS-2 was able to correctly identify 356 of them, generated only one false alarm, and correctly modelled 3,514 true negatives.The performance of MIMESIS-2 was then evaluated according to four indices: the probability of detection (POD), false alarm rate (FAR), miss rate (MIS), and critical success index (CSI), described in the Methods section. For the POD, MIS and CSI, we considered the 154 municipalities with at least one reported and laboratory-confirmed human WNV case over the 12-year period, while for the FAR, we considered the 153 municipalities where at least one human WNV case was modelled over the same period. We split the (0.0–1.0) index interval into five equally sized bins to derive for each index, the fraction of municipalities falling into each bin. Both the POD and CSI were above 0.8 for 139 municipalities out of 154, while the MIS was below 0.2 for 142 municipalities (out of 154) and the FAR was always below 0.2, with one false alarm produced in a municipality where WNV events were observed in eight out of twelve years (Table 1).Table 1 Capacity of the MIMESIS-2 model to correctly model laboratory-confirmed human WNV cases.Full size tableWe also analysed how the model performed in different years by studying the multiannual evolution of the indices. Both the aggregated POD and CSI were equal to 0.92, with annual variations ranging from 0.72 (2021) to 1 (2011 and 2014). The aggregated MIS was 0.08, ranging from 0.0 (2011 and 2014) to 0.28 (2021). The FAR was virtually 0, being always equal to 0.0, with the only exception being 2017, when it was 0.1 (Table 2).Table 2 Capacity of the MIMESIS-2 model to correctly model laboratory-confirmed human WNV cases by year and in the whole observed time period.Full size tableMagnitude and timing of WNV events: performance and comparison with MIMESISTo evaluate the ability of MIMESIS-2 to capture the magnitude and timing of WNV events, we first considered the discrepancy between the overall number of observed and modelled WNV cases during the 12-year period for each municipality. Out of the 153 municipalities where at least one case was modelled across the 12 years, 76 (50%) had at most 4 modelled cases of WNV: 1, 2, 3, and 4 WNV cases were modelled in 22, 31, 13, and 10 municipalities, respectively. In 42 municipalities, the number of modelled cases ranged from 5 to 10 (which, as for the observed WNV cases, coincided with the third quartile), and in 32 municipalities, the number ranged from 11 to 47, while the remaining 3 municipalities had 55, 70, and 99 modelled cases (Fig. 1).The MIMESIS-2 model closely replicated the total number of laboratory-confirmed WNV cases during the 12-year period. When considering only the 154 municipalities that recorded at least one WNV event during the considered period (excluding the true negatives), for 140 of them, the modelled number of cases fell within a ± 10% error range of the observed value, whereas for 149 the modelled number of cases fell within the ± 25% error margin. Only two municipalities showed a percent error above 50%. These were particular instances where only one WNV case was reported throughout the considered period, while MIMESIS-2 fitted zero human cases. For the original MIMESIS model, 63 and 84 municipalities fell within the ± 10% and ± 25% error margins, respectively, while 31 municipalities—mainly those where few cases were observed— had a relative error ≥ 100% (Fig. 2).Figure 2(a) For MIMESIS-2, modelled (IHMOD) vs. observed (IHOBS) human WNV cases in each municipality in the period 2010–2021. The inner black line represents the main diagonal where ideally the points would lie in case of perfect fit, while the dashed green, black and red lines represent, respectively, the ± 10%, ± 25% and ± 50% error margin. (b) Same quantities for MIMESIS. (c). Breakdown of the week of first WNV incidence by year. Plotted are the modelled quantities (WYMOD) for each of the 325 municipalities on the y-axis and the observed quantities (WYOBS) on the x-axis. The continuous line represents the main diagonal where ideally the points would lie in case of perfect fit, while the dashed lines represent the ± 4-week error margins.Full size imageTo further evaluate the bias of the model across all municipalities and years, we explored the difference between the yearly modelled and observed human WNV cases both with MIMESIS-2 and the original MIMESIS (IHMOD-IHOBS) across municipalities. In MIMESIS-2, we excluded 3,514 true negative cases to avoid distorted conclusions. For the remaining 386 cases, the mean bias was -0.04 indicating a possibly unbiased model, with the standard deviation (SD) of the residuals equal to 0.66 (original MIMESIS: mean bias 0.33, SD 2.07, after removing 3,387 true negatives) (Supplementary Fig. 1).Across the 325 municipalities and the 12 years, 385 WNV events were observed, while on 3,515 occasions, no laboratory-confirmed human WNV cases were reported; on 162 occurrences, 1 case was reported, and on 67 and 39 occasions, 2 and 3 cases were reported, respectively. The maximum yearly number of human WNV cases observed in a single municipality was 38. Considering the modelled human WNV cases with MIMESIS-2, the distribution of the 356 hits ranged between 1 and 37 modelled cases, closely mimicking the distribution of the observed cases, since 1, 2 and 3 human WNV cases were modelled on 129, 72 and 37 occasions, respectively. For the 29 misses, the observed numbers of human cases were 1 (24 times), 2 (3 times), or 3 (2 times). The only false alarm was produced in the Pellas municipality, where WNV events were observed in 8 out of the 12 years.We evaluated the timing of the first occurrence of WNV in humans for any municipality and year. Ignoring the municipalities with zero cases, the observed and MIMESIS-2-modelled first WNV cases occurred between weeks 22 and 44 and weeks 24 and 36, respectively. Modelled values tended to be dispersed around the observed ones: excluding the 3514 true negatives, 290 (75.13%) of the remaining 386 cases fell into the ± 4-week error margins from the observed cases (Fig. 2). This translated into a much lower bias of the week of first appearance (WYMOD-WYOBS) with respect to MIMESIS (Supplementary Fig. 2).Case study: The Pellas municipalityIn addition to presenting the overall performance of the model throughout different years and Greek municipalities, we highlight here the capacity of the model to capture population-specific behaviour and epidemiological features, such as the force of infection, that is, the rate at which susceptible humans, birds, and mosquitoes become infected, by presenting a single municipality case study for the municipality of Pellas. The Pellas municipality had the highest number of observed WNV cases over the 12-year period with a total of 94 human WNV cases, 38 in 2010, 16 in 2018, and 13 in 2021, no cases from 2014 to 2017, and between 4 to 8 cases in the remaining years.We considered the impact arising from the changes in parameters defining the forces of infection. In addition to the introduction of bird (({psi }_{B})) and human (({psi }_{H})) host selections, changes included modifications for the mosquito-to-bird (({p}_{M})) and bird-to-mosquito (({p}_{B})) probabilities of transmission, whose values were made temperature-dependent following Vogels et al.21, and the replacement of the mosquito-to-bird (({varphi }_{B})) and mosquito-to-human (({varphi }_{H})) ratios with their dynamic counterparts, ({N}_{M}/{N}_{B}) and ({N}_{M}/{N}_{H}), respectively (Fig. 3). We used the May–October period for the 12 years that were considered, because this is the part of the year when Culex pipiens mosquitoes are reproductively active and the majority of human WNV cases are reported. In each year of the 12-year period, ({p}_{M}) started from 0.02, reached its peak—ranging from 0.16 to 0.25—in midsummer, and then decreased to the initial values (in the original model, ({p}_{M}=0.9)). Similarly, ({p}_{B}) started from 0.28, peaked in the same time interval—with maximal values ranging from 0.51 to 0.56—and then returned to the initial values (in the original model, ({p}_{B}=0.125)). Additionally, the dynamic specifications of ({varphi }_{B}) and ({varphi }_{H}) were shown to play an important role. Whereas in MIMESIS ({varphi }_{B}=30), in MIMESIS-2 the values started at approximately 8.6 and peaked in late summer when more human WNV cases are reported, reaching values of approximately 57, before decreasing to values ranging from 31.15 to 41.60 in late October. In MIMESIS, ({varphi }_{H}) was calibrated at the municipality level, and for Pellas municipality, it was 0.0001, whereas the dynamic counterpart in MIMESIS-2 showed a temporal evolution with a shape (but different scale) similar to that of ({varphi }_{B}), starting from values of approximately 1, peaking in late summer to values of approximately 7, and then decreasing to values of approximately 4 in late October.Figure 3The temporal evolution during May to October of the (a) mosquito-to-bird probability of transmission, ({p}_{M}), (b) bird-to-mosquito probability of transmission, ({p}_{B},) (c) mosquito-to-bird ratio, ({varphi }_{B},) and (d) mosquito-to-human ratio, ({varphi }_{H},) for both MIMESIS-2 across different years and MIMESIS for each of the 12 years from 2010 to 2021. The plots refer to the simulations for the municipality of Pella.Full size imageChanges in these parameters enter into the expression for the forces of infection. It is of major practical interest to investigate how the values for the forces of infection resulting from MIMESIS-2 may vary for different values of the relative abundance of the vectors with respect to the corresponding carrying capacity and the temperature in different months (Fig. 4). As expected, all forces of infection increased with both the temperature and the relative abundance of the infectious vertebrate hosts. It is worth noting the importance of day length, as this affects the fraction of nondiapausing mosquitoes, ({delta }_{M}), and causes the forces of infection, all other things being equal, to be potentially higher in June and July than in the other months. However, in these two months, the modelled forces of infection tend to be smaller than those in August due to the lower abundance of infectious hosts.Figure 4Contour plots of the forces of infection for May to September for different values of the relative abundance of infected hosts/vectors with respect to the carrying capacity and the temperature. All the other quantities were fixed to the amounts obtained in the simulations for Pellas municipality for 2021 at the end of the corresponding month. (a) Bird-to-mosquito force of infection (({lambda }_{BM})) as a function of the relative abundance of infected birds (({I}_{B})) with respect to the bird carrying capacity (({K}_{B})) and temperature. (b) Mosquito-to-bird force of infection (({lambda }_{MB})) as a function of the relative abundance of infected mosquitoes (({I}_{M})) with respect to the mosquito carrying capacity (({K}_{M})) and temperature. (c) Mosquito-to-human force of infection (({lambda }_{MH})) as a function of the relative abundance of infected mosquitoes (({I}_{M})) with respect to the mosquito carrying capacity (({K}_{M})) and temperature. The ranges for ({I}_{B}/{K}_{B}) and ({I}_{M}/{K}_{M}) were fixed, increasing the maximum modelled value by 20% for the considered period, while the range for the temperature was chosen considering that in the period of interest, the average daily temperature ranged from 16.6 to 27.1 degrees Celsius. Black crosses represent the modelled values for 2021.Full size imageThe bird-to-mosquito force of infection, ({uplambda }_{BM}), took values on the order of 10–4, with possible peaks of approximately 7 × 10–4 in the case of high temperature and high prevalence of birds in June and July, which were nevertheless not reached due to a low abundance of infected birds in that period. Considering the months of July and August 2021 for illustrative purposes, the resulting modelled values were 1.20 × 10–4 and 2.19 × 10–4, respectively, with the increase in August explained by a higher abundance of infected birds in that period. It is worth noting that if the infection across birds had a lead period of two weeks, the resulting ({uplambda }_{BM}) in July would become 3.91 × 10–4 (+ 226%), while an increase in the average temperature in August by 1 °C would result in ({uplambda }_{BM})= 2.36 × 10–4 (+ 8%). The mosquito-to-bird, ({uplambda }_{MB}), and mosquito-to-human, ({uplambda }_{MH}), forces of infection showed similar qualitative behaviours, albeit at different scales, and in this case, they were higher in August due to a higher prevalence of infected Culex mosquitoes in that month. More specifically, ({uplambda }_{MB}) equalled 1.06 × 10–3 and 1.22 × 10–3 at the end of July and August, respectively, and an expected two weeks for the infection of mosquitoes would result in ({uplambda }_{MB})=4.15 × 10–3 (+ 292%) at the end of July, while an increase in the average temperature in August by 1 °C would result in ({uplambda }_{MB})= 1.31 × 10–3 (+ 7%) at the end of August. Finally, ({uplambda }_{MH})=2.86 × 10–6 at the end of July, while ({uplambda }_{MH})=3.26 × 10–6 at the end of August, with the anticipation of the infection among mosquitoes by two weeks resulting in ({uplambda }_{MH})=1.12 × 10–5 (+ 290%) and an increase in the average August temperature by 1 °C leading to ({uplambda }_{MH})=3.51 × 10–6 (+ 8%). It is worth recalling that since we calibrated the model on the number of reported laboratory-confirmed human WNV cases, ({uplambda }_{MH}) represents the rate at which susceptible humans contract infection and become symptomatic leading to a recorded human WNV case.We explored changes in the populations of infectious hosts and the total population number for both mosquitoes and birds over 2010–2021 for the period spanning from May to October (Figs. 5 and 6). The population of infected mosquitoes (({I}_{M})) was initialised by calibration (see the Methods section). Each year, after a short period in which the population of infected mosquitoes slightly decreased due to a very small number of infectious birds (({I}_{B})) that prevented the infection from spreading, it started growing substantially during summer, reaching its peak in late summer, coinciding with the period when most human cases were recorded. The observed increase in ({I}_{M}) was combined with the growth ({I}_{B}) at approximately the same time (with a slightly anticipated peak), which had an amplification effect on the spread of the infection. Both ({I}_{M}) and ({I}_{B}) showed significant yearly variation, with higher modelled numbers in years where more human WNV cases were reported. The modelled total population of mosquitoes (({N}_{M})) did not show significant interannual variability, always peaking in late summer. Finally, the overall population of birds (({N}_{B})) did not show any variability in the first part of the year, when an increase due to immigration and offspring generation was observed, whereas it had a moderate interannual variability in the second half of the year. These differences may be due to heterogeneous numbers of observed infected, dead and immune birds.Figure 5The temporal evolution during May to October of (a) the number of infected mosquitoes modelled by MIMESIS-2 (({I}_{M})), (b) the total number of mosquitoes modelled by MIMESIS-2 (({N}_{M}))(,) (c) the number of infected birds modelled by MIMESIS-2 (({I}_{B}))(,) and (d) the total number of birds modelled by MIMESIS-2 (({N}_{B})) for each of the 12 years from 2010 to 2021. The plots refer to the simulations for the municipality of Pella.Full size imageFigure 6The temporal evolution during May to October of (a) the ratio between the number of WNV-infected mosquitoes modelled by MIMESIS-2 (({I}_{M,MIM-2})) and the ratio modelled by MIMESIS (({I}_{M,MIM})), (b) the ratio between the total number of mosquitoes modelled by MIMESIS-2 (({N}_{M,MIM-2})) and the ratio modelled by MIMESIS (({N}_{M,MIM}))(,) (c) the ratio between the number of infected birds modelled by MIMESIS-2 (({I}_{B,MIM-2})) and the ratio modelled by MIMESIS (({I}_{B,MIM}))(,) and (d) the ratio between the total number of birds modelled by MIMESIS-2 (({N}_{B,MIM-2})) and the ratio modelled by MIMESIS (({N}_{B,MIM})) for each of the years from 2010 to 2021. The plots refer to the simulations for the municipality of Pella.Full size imageComparison of these population dynamics with those of MIMESIS revealed interesting patterns (Fig. 6). Considering the relative number of mosquitoes in MIMESIS-2 with respect to MIMESIS, the populations in MIMESIS tended to grow faster due to a higher mosquito carrying capacity (({K}_{M})) in the original model (({K}_{M}) ≈ 8.3 × 105 in MIMESIS versus ({K}_{M}) ≈ 2.4 × 105 in MIMESIS-2), resulting in a decrease in the ratio between the amounts modelled by MIMESIS-2 and the ones modelled by MIMESIS. Significant interannual variability could be seen in the first part of the year for infectious mosquitoes, where different initial calibration values played an important role. For the populations of birds, until midsummer, the overall number modelled by MIMESIS-2 tended to be approximately 1/4 that of MIMESIS, while as of July, different patterns were observed due to the higher mortality of birds in the original MIMESIS model. In years with higher virus spread, higher mortality was reflected in a sharper decrease in bird populations; therefore, the ratio between the population modelled by MIMESIS-2 and that modelled by MIMESIS increased up to approximately 0.6 (2010). More

Study settingUganda covers 241,037 km2 (4° N, 2° S, 29° E, 35° E) and averages 1100 m above sea level25. Uganda has a total population of 34.6 million people, with 7.4 and 27.2 million living in urban and rural areas, respectively26. It borders Lake Victoria and has an equatorial climate. The study area is mainly plateau, with a few mountains. About 20 percent of Uganda’s area is covered by swamps and water bodies, including the four Great Lakes of East Africa (Lake Edward, Lake Victoria, Lake Albert, and Lake Kyoga). The country has ten national parks housing a high diversity of wildlife and endangered species26. By 2009, agriculture ranked as the second leading contributor to the country’s Gross Domestic Product27.Surveillance data of Bacillus anthracis infectionSurveillance data of livestock and human cases from 2018 were provided by the Ministry of Health (MOH) in Uganda through the Field Epidemiology and Laboratory Training Program and the Uganda Ministry of Agriculture, Animal Industry and Fisheries (MAAIF). Geographical coordinates of anthrax cases among wildlife (from 2004 to 2010) in Queen Elizabeth National Park were obtained from a recently published study4. These cases were mapped to show the distribution of anthrax across Uganda (Fig. 1). It is only recently that Uganda has mandated systematic anthrax surveillance across the country following the outbreak that started in 2018. GPS coordinates gathered by field personnel during outbreak responses were used to map outbreak locations. The human anthrax cases were defined based on the CDC’s clinical criteria (signs and symptoms), presumptive laboratory diagnosis (Gram staining), and confirmatory laboratory diagnosis (bacterial culture, immunohistochemistry, ELISA, and PCR)28. The animal anthrax cases were also defined based on the clinical presentation, presumptive laboratory diagnosis, and confirmatory laboratory diagnosis. All cases were classified as either ‘probable’ or ‘confirmed,’ with probable defined as cases that met both the clinical and presumptive laboratory diagnostic criteria and confirmed defined as cases that met the clinical and confirmatory laboratory diagnostic criteria. A total of 497 livestock (n = 171), humans (n = 32), and wildlife cases (n = 294), both confirmed (n = 32) and probable (n = 465), occurring from 2004 to 2018 were compiled. All methods were performed in accordance with the relevant guidelines and regulations.Figure 1Distribution of anthrax presence and pseudo-absence locations across Uganda. The navy-blue circles show wildlife cases (n = 294) used for model training, the blue triangles show livestock cases (n = 171), and the red diamonds represent human cases (n = 32). The blue polygons show the locations of the 50 km, 75 km, and 100 km buffers which were constructed around the wildlife cases with a distance of 10 km between the buffers and the presence locations. The pink dots show the pseudo-absence points selected within the 50 km buffer, the orange dots show the pseudo-absence points selected within the 75 km buffer, and the white dots show the pseudo-absence points selected within the 100 km buffer. Prediction maps were developed using the Quantum Geographic Information System software (QGIS). URL: https://qgis.osgeo.org (2020).Full size imageEnvironmental variable processingCorrelative studies of environmental risk factors for anthrax outbreaks suggest that temperature6,29,30,31,32,33,34,35,36,37, precipitation6,29,30,31,32,33,34,35,36,37,38,39, elevation6,29,31,32,34,35,37,38,39, soil (type, calcium concentration, pH, carbon content, and moisture)6,30,31,33,34,36,37,39,40,41,42,43, vegetation6,29,31,34,36,37,38,39,40,42,43, and hydrology37,44 are some of the major drivers of B. anthracis suitability. A total of 26 environmental predictors (Fig. 2) were selected for this study based on these known variables. These comprised 19 bioclimatic variables (the mean for the years 1970–2000) collected from the WorldClim database version 2 (https://www.worldclim.org/data/worldclim21.html) at a resolution of 30 s (~ 1 km2)45. Four soil variables, including exchangeable calcium at a depth of 0–20 cm, soil water availability, soil pH (10×) in H2O at a depth of 0 cm, and soil organic carbon at a depth of 0–5 cm, were retrieved from the International Soil Reference and Information Centre (ISRIC) data hub at a resolution of 250 m (https://data.isric.org/geonetwork/srv/eng/catalog.search#/home). Distance to permanent water bodies was derived from a global hydrology map provided by ArcGIS online version 10.6.146. Elevation data of 1 km2 in resolution was obtained from the Global Multi-resolution Terrain Elevation Data (GMTED2010) dataset available from the United States Geological Service. Finally, the monthly Enhanced Vegetation Index (EVI) data for the years 2004, 2005, and 2010 (36 tiles in total) were obtained from The Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) Vegetation Indices (MYD13A3 v.6) at a spatial resolution of 1 km (https://lpdaac.usgs.gov/products/myd13a3v006/). The single variable, mean EVI, was calculated in QGIS by averaging all 36 tiles. The EVI minimizes variations in the canopy background and maintains precision over conditions with dense vegetation.Figure 2Results of correlation between covariates using Pearson’s correlation test. Correlation between covariates was shown by red numbers (negative correlation) and blue numbers (positive correlation). BIO1 = Annual Mean Temperature, BIO2 = Mean Diurnal Range, BIO3 = Isothermality, BIO4 = Temperature Seasonality, BIO5 = Max Temperature of Warmest Month, BIO6 = Min Temperature of Coldest Month, BIO7 = Temperature Annual Range, BIO8 = Mean Temperature of Wettest Quarter, BIO9 = Mean Temperature of Driest Quarter, BIO10 = Mean Temperature of Warmest Quarter, BIO11 = Mean Temperature of Coldest Quarter, BIO12 = Annual Precipitation, BIO13 = Precipitation of Wettest Month, BIO14 = Precipitation of Driest Month, BIO15 = Precipitation Seasonality, BIO16 = Precipitation of Wettest Quarter, BIO17 = Precipitation of Driest Quarter, BIO18 = Precipitation of Warmest Quarter, BIO19 = Precipitation of Coldest Quarter.Full size imageAll environmental variables were resampled using the R package ‘Resample’47 to a resolution of 1 km and clipped to the extent of Uganda. Since data sampling for wildlife data (used in model training) was not done systematically across the study area, target backgrounds buffers (polygon buffers created at certain radii from the training points and used for the random selection of pseudo-absences) were created for model calibration to reduce sampling bias. As there was no information on the sampling radius, a sensitivity analysis was conducted by creating target backgrounds using circular buffers of radius 50 km, 75 km, and 100 km around the presence points used for model training, leaving 10 km between the presence points and the various buffers (Fig. 1). Quantum Global Information System (QGIS) version 3.16 (https://qgis.org) software was then used to add 294 random pseudo-absence points within each buffer polygon giving a ratio of 1:1 for the training presences to pseudo-absences. A recent study explored how four approaches of pseudo-absence creation affect the performance of models across different species and three model types by building both terrestrial and marine models using boosted regression trees, generalised additive mixed models, and generalised linear mixed models48. They then tested four methods for generating pseudoabsences across all the different model types: (1) correlated random walks (RW); (2) reverse correlated RW; (3) sampling pseudoabsences within a buffer area surrounding the presence points; (4) background sampling48. The findings of the study suggested that the separation or distance in the environmental space between the presence locations and the pseudoabsences was the most significant driver of the model predictive ability and explanatory power, and thus finding was consistent across the three model types (boosted regression trees, generalised additive mixed models, and generalised linear mixed models) and both the terrestrial and marine habitats48.The values of the environmental variables were then extracted for each presence and pseudo-absence location using the raster package in R. With these, we did an initial data exploration to check for outliers within the covariates, collinearity, and to explore the relationships between the covariates and the response variables (presence or absence of anthrax). Cleveland dot plots were used to check for possible outliers. Following the outlier checks, variance inflation factors (VIF), pairwise plots, and Pearson correlation coefficients with correction for multiple comparisons were used to measure the statistically significant correlation between the covariates (Fig. 2). For variables that were highly correlated (correlation greater than 0.6) or those with high variance inflation (VIF  > 3), only one was used in the modelling process. Five variables were selected following this analysis: Temperature seasonality (BIO4), elevation, distance to water, soil calcium, and soil water (Table 1).Table 1 Summary of the environmental variables used.Full size tableModelling anthrax suitability across UgandaQGIS v.3.16 (https://qgis.org) and the R statistical package version 4.1.049 were used to conduct data visualization, cleaning, and model analysis (R code used available in a Github repository: https://github.com/valentinandolo/Uganda-Spatial_Model/tree/master). The wildlife cases (n = 294) were used for model training and testing. The remaining human (n = 32) and livestock (n = 171) cases were used for model evaluation. Since the wildlife case locations were recorded from 2004 to 2010, while the livestock and human cases were recorded in 2018, the latter locations were both spatially and temporally distinct from the wildlife cases, making an excellent basis for block cross-validation of the final model performance50. Random partitioning of the data into training and testing sets can inflate the performance of a model and underestimate the error in the spatial prediction evaluation50. Block cross-validation uses spatial blocks that separate the testing and training datasets; thus, the method has been suggested to be a good technique for error estimation and a robust approach for measuring a model’s predictive performance50.The INLA package in R was applied to model the suitability of B. anthracis across Uganda. INLA calculates the spatial interaction effects using a Stochastic Partial Differential Equation (SPDE) method, which estimates a continuous Gaussian Markov Random Field (GMRF) where the correlation between two locations in space is specified by the Matérn correlation which is explained in more detail elsewhere51. The initial step in fitting an SPDE model is the creation of a Constrained Refined Delaunay Triangulation or a mesh to illustrate the spatial process51. R-INLA uses a function called ‘inla.mesh.2d()’ that applies a variety of arguments to build the mesh, these include: loc, loc.domain, boundary, max.edge, and cutoff51. The loc argument contains the point locations which provide information about the area of study and are used to create the triangulation nodes. Alternatively, a polygon of the study area can be used to identify the extent of the domain via loc.domain. We applied the point locations using the loc argument. We then specified the boundary of the mesh as a convex hull. We used the max.edge argument to specify the maximum edge length for the inner mesh domain/triangles and the outer triangles. We did this by first studying the distribution of distances between the point locations for the training presences and pseudo-absences. Most points were within a distance of about 90–100 km away from each other, thus, a possible guess for the range at which spatial autocorrelation persists was 100 km. We used a distance of 20 km as a range guess to create a finer mesh which has been shown to produce more precise models. We specified the maximum edge length for the inner triangles as 20 km divided by 5 (4 km) and the maximum edge length for the outer triangles as 20 km. Finally, the cutoff argument sets the minimum distance allowed between point locations. We divided the maximum edge length for the inner triangles by 5 (4 km divided by 5 = 0.8 km), meaning that points that were closer in distance than 0.8 km were replaced by one vertex to avoid the occurrence of small triangles.The spatial effect, which is a numeric vector, then links each observation within the data to a spatial location, thus, accounting for region-specific variation that cannot be accounted for by the covariates. Following the recommendation by Lindgren and Rue52, multivariate Gaussian distributions with means of zero and a spatially defined covariance matrix were used to model the spatial effect. Several versions of Bayesian hierarchical additive models were created by estimating a Bernoulli generalized additive model (GAM) with and without spatially correlated random effects. The Bernoulli GAM is defined as shown in Eqs. (1) and (2)$${C}_{i} sim Bernoulli left({p}_{i}right),$$
(1)
$$logit left({p}_{i}right)= alpha +sum_{j=1}^{m}{beta }_{j}left({X}_{j,i}right)+ sum_{k=1}^{l}{f}_{k}left({X}_{k,i}right)+ {mu }_{i},$$
(2)
where ({C}_{i}) denotes the observed value, such that: B. anthracis presence or absence at a given location i (i = 1, …, n; n = 588) is given as ({C}_{i}), where ({C}_{i}) =1 if B. anthracis was present, and ({C}_{i})=0 if absent. Logit is the link function for binomial family, ({p}_{i}) is the expected value of the response variable (the probability of B. anthracis suitability) at location i, α is the intercept, ({X}_{j,i}) and ({X}_{k,i}) are the j th and the k th covariates at a location i, ({beta }_{j}) are the beta coefficients, ({f}_{k}) are the smooth functions (cubic regression splines) for k th covariates, and ({mu }_{i}) is the spatial random effect at the location i53. The number of variables in linear term (m) and the non-liner term (l) are different because the variables employed in each term are different. We estimated both linear and non-linear effects for the covariates. Our overall database had 294 B. anthracis pseudo-absences generated randomly across the target background buffers to match the number of species presences recorded. Because we had no prior information, a Gaussian prior distribution with a mean of zero (default no effect prior unless data is informative) was applied for all the model parameters. The posterior mean, standard deviation, and 95% credible intervals were estimated for all the parameters.Model selectionSeveral different candidate models were examined. First, a baseline model was built using only the intercept. A second baseline model was then built, which included the intercept and spatial random effects only. Covariates were added to the second baseline model (intercept plus spatial effects model) without any smoothing function (i.e., only linear effects). The contribution of the spatial random effect was then re-examined by taking it out from the model. Smoothing functions were then added to all covariates, and the same procedure was repeated. Model selection was done using this forward stepwise approach. The final model was run using the three different target background buffers to identify the buffer distance with the lowest Deviance Information Criterion (DIC). The various options were assessed using the DIC54, Watanabe-Akaike information criterion (WAIC), and the Conditional Predictive Ordinate (CPO). The DIC and WAIC were chosen because they are commonly used to assess model performance by measuring the compromise between the goodness of fit and complexity. For CPO, the logarithmic score (− mean(log (CPO)) (LCPO) was calculated and used55. CPO can also be used to conduct internal cross-validation of models using a leave-one-out approach to evaluate the predictive performance of the model. Lower LCPO, DIC, and WAIC estimates suggest superior model performance. Thus, the favoured model had the lowest values across the 3 metrics.Model validation and evaluationModel validation for the favoured model was conducted using an independent evaluation dataset comprising of livestock and human outbreaks occurring at different spatial locations and 8 years after the training data. The omission rate, which indicates the proportion of positive test locations that end up in pixels predicted to be unsuitable for B. anthracis56, was used to validate the model. A low omission rate indicates good model performance. The threshold for suitability was the probability threshold that maximized the sensitivity and specificity of the model. The sensitivity was then derived by calculating the proportion of positive test locations that end up in pixels predicted to be suitable for B. anthracis56. A high sensitivity indicates good model performance.Model predictionThe favoured model selected using the criteria described above was used to generate countrywide prediction maps showing the posterior mean values, standard deviation, and the 95% credible intervals of the probability of B. anthracis suitability. The raster package in R was used to make the prediction maps. Bayesian kriging was done by treating all model parameters as random variables to include uncertainty in the prediction57. This kriging is built into the INLA framework via the SPDE, which allows a Delaunay triangulation to be constructed around the presence and absence locations within the sampling frame52. INLA then conducts model inference and prediction at the same time by considering the prediction points as locations missing the response variable (set to NA)51. Following successful model prediction, additional linear interpolation functions then generate the output for the whole study area scaled from 0 to 1.Ethical approvalEthical approval for this study was provided by the Human Biology Research Ethics Committee, University of Cambridge, UK (Ref: HBREC.2019.02) the School of Veterinary Medicine and Animal Resources Institutional Animal Care and Use Committee, Makerere University, Uganda (Ref: SVAREC/21/2019); and the Uganda National Council for Science and Technology. Informed consent was obtained from all subjects and/or their legal guardian(s). All methods were performed in accordance with the relevant guidelines and regulations. More

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Sample collectionA survey was conducted among the residents of nine counties in Kenya (Mombasa, Kisumu, Machakos, Nairobi, Makueni, Bomet, Kericho, Kiambu, and Narok) and GPS location coordinates were recorded and later used to build the predictive model (“Infestation dynamics of bedbugs in residential communities” section). These counties represent diversity in cultural practices, livelihood strategies (such as fishing, tourism, farming), and infrastructure development. Also, they comprise different altitudes above sea level, temperatures, and differing in average annual rainfall.Samples identification using morphological identification keysIn each county where the survey was conducted, bedbug samples was taken and preserved in ethanol 70% for morphological identification. Cimex belonging to Cimicidae family is the common genus adapted to human environment and reported throughout the world and comprising species such as Cimex lectularius and C. hemipterus that are hematophagous mainly feeding on human blood5. The key morphological features used in identifying bedbugs include: (1) the head has a labrum that appears as a free sclerite at the extreme anterior margin, ecdysial lines form a broad V, eyes project from the sides composed of several facets and the antennae are 4-segmented, (2) thorax is subdivided into prothorax, mesothorax and metathorax, (3) legs have all other normal parts except pulvilli and arolia, tarsus is 3-segmented with 2 simple claws, (4) the abdomen has 11 more-or-less segmented recognizable segments, 7 pairs of spiracles borne on the second to eighth segments, hosts the genital structures, paramere in males and mesospermalege in females45. Bedbug specimen morphological features were examined using Leica EZ24 HD dissecting microscope (Leica Microsystems, UK) and photos documented using the associated software.Survey for household’s knowledge and perceptions on bedbugsThis study was a community-based cross-sectional survey conducted from November–December 2020 with respect of the rules/guidlines introduced by the Ministry of Health to contain the COVID-19 pandemic in Kenya (wearing mask, social distance, washing hand, etc.). It was based on a stratified, systematic random sampling where 100 respondents were selected from each county.A total number of 900 respondents were randomly selected and the household head or the representative showing willingness and consent was interviewed face-to-face. The interview was conducted using a semi-structured questionnaire prepared in the English language (Appendix A). The questionnaire was translated into the local native language (Kiswahili) to avoid biasness and improve the understanding between the enumerator and the respondent. Prior to the commencement of the survey and authentic data collection, a pre-testing exercise was performed by training enumerators on a similar socio-demographic pattern. This was useful for improving the quality of data, ensuring validity, familiarizing the enumerators with the questionnaire, and data handling.The information collected using the semi-structured questionnaire included residents’ socio-economic profiles, knowledge, and perceptions on the pest, bedbug incidence, and management practices. The socio-economic profile factors addressed in the survey comprised gender, age, education, access to basic social amenities, and household size. The study also prioritized the financial consequences, the severity of the bites, perceptions of respondents on the pest, and management practices for its control.Survey data were checked for errors, completeness, summarized, and entered in Microsoft-Excel. It was then cleaned and transferred to Statistical Package for Social Science (SPSS) version 25 software (IBM Corp., Armonk, NY) for purposes of descriptive statistics (means and percentages).In contrast, in instances where more than one reason was given for a single question, percentages were calculated based on each group of similar responses. Chi-square was performed to determine the differences regarding socio-demographic characteristics, knowledge, and perceptions on bedbugs and control practices. Additionally, data were disaggregated by gender and age categories to understand the existing differences among the various respondent categories. Besides, F-test statistics was performed on the ages of respondents to determine the mean, standard deviation and statistical significance. The level of significance was considered when the p-value was below 5%.Infestation dynamics model of bedbugModel simulation assumptionsHouses infestation dynamics was studied following Susceptible-Infested-Treatment (SIT) model46. Therefore, houses in the community are classified into three groups: susceptible, infested or treated. Within a house, bedbug population dynamics was ignored, while it was considered from one house to another where infested houses have some potential to spread the infestation to other houses in the community. A population of bedbugs in an infested house has some probability per unit of time of becoming extinct either naturally or after treatment. In the infestation dynamics, the rate of house infestation depends on the number of infested houses, the movement of people from one house to another and the proportion of treated houses in the community. We assume that infested houses (I) spread the infestation at the rate β and only a fraction S/N of the houses is susceptible (S) to infestation. Infested houses become extinct at a certain rate known as rate γ. Infested houses are treated at the rate τ and the protection conferred is lost at the rate α. Ordinary differential equation developed to study SIT model were used in this study46. All the models used have the generic formulations displayed below:$$frac{dS}{dt}=frac{beta }{N}SI+gamma I+alpha T$$
(1)
$$frac{dI}{dt}=frac{beta }{N}SI-(gamma +tau )I$$
(2)
$$frac{dT}{dt}=tau I-alpha T$$
(3)
where β  > 0, τ  > 0, α ≥ 0 and γ  > 0. The total population size is N = S(t) + I(t) + t(t). The initial conditions satisfy at S(0)  > 0, I(0)  > 0, T(0) ≥ 0 and S(0) + I(0) = N, where N is the constant total population size, dN/dt = 0.Infestation dynamics models implementationThe method used to implement the infestation dynamics model of the pest is based on the system thinking approach with its archetypes [Causal Loop Diagram (CLD), Reinforcing (R) and Balancing (B)] by a mental and holistic conceptual framework. This is important for mapping how the variables, issues, and processes influence each other in the complex interactions of bedbugs within and between houses and their impacts. Despite these archetypes being qualitative, they are necessary for elucidating and disclosing the basic feedback configurations that occur in houses and their environs when infested with pests like bedbugs. A dynamic model was generated by converting the causal loop diagram (CLD) obtained using stocks, flows, auxiliary links, and clouds. Consequently, these in turn were translated into coupled differential equations for simulations.The SIT model was translated into causal loop diagram where arrows show the cause-effect relations where positive sign indicates direct proportionality of cause and effect while negative sign shows inverse proportionality relations, and two different scenarios have been assessed: (1) homogeneous houses where there is a single community of houses of the same quality, and (2) heterogeneous houses where there is a community of good and bad houses. Ancient houses presenting slits/fissures with less cleanliness and filled with old or secondhand furniture at low grade are considered bad houses as they may sustain high level of bedbug infestation; and new houses don’t provide well enough conditions for bedbug population to survive, and they are called in the model good houses47. Bad houses are considered to act as sources while good houses act as sinks, but all together are randomly distributed where each house has the same probability to contact good or bad houses.In the scenarios of homogeneous houses, the causal loop diagram (Fig. 7) has two feedback loops: (a) one positive, as the number of infested houses increases, the probability to get susceptible houses infested also increases resulting in infested houses increase; (b) one negative, as the infested houses increases, the treated houses increase resulting in susceptible houses decrease. The causal loop diagram is displayed in Fig. 7A while Fig. 7B showed the stocked and flows diagram and axillary variables obtained from causal loop diagram.Figure 7Susceptible-Infested-Treatment (SIT) model translated into causal loop diagram (A) and stock and flow diagram (B) for homogeneous houses and causal loop diagram (C) and stock and flow diagram (D) for heterogeneous houses in the community.Full size imageSusceptible, infested, and treated houses are stocks in the system, representing the number of houses susceptible, infested, and treated, respectively at a given point of time. The rates represent in and out-flows of the diagram. Auxiliary and constants that drive the behavior of the system were connected using information arrows within them and flows and stocks to represent the relations among variables in terms of equations.In the scenarios of heterogeneous houses, the causal loop diagram (Fig. 7C) comes with the two previous feedback loops but for each category of house. In addition, there is a fifth feedback loop that connect bad house to good house and vice versa.Therefore, as the infested bad houses increase, the probability to infest good houses increases. The more they are exposed the more they get infested. In turn, as the infested good houses increase, the chance to infest susceptible bad houses increases and the more they are exposed, the more they get infested, resulting in the increase of infested bad houses. The stocks and flows diagram of each of the two categories of houses occurred with interconnexion relationships between the two categories (Fig. 7D).Models’ simulationsThe survey data (“Bedbug Genus identification” section) on prevalence, knowledge, perceptions and self-reported; in addition, the respondents’ reported control mechanisms and their average time of effectiveness (Appendix B, Table S1) were used for model simulations. The different control methods reported were reclassified in three control approaches: chemical control, other control methods (including exposure to direct sunlight, use of hot water, painting, application of diesel, paraffin and wood ash, use of Aloe Vera extract and Herbs), and combination of chemical and other control methods. All the models commodities and units were checked before performing the simulations. Simulation and implementation of the models were done using Vensim PLP 8.1 platform (Ventana systems, Harvard, USA). It consists of a graphical environment that usually permits drawing of Causal Loop Diagram (CLD), stocks, flow diagrams and to carry out simulations. After we simulated the infestation dynamics under the two scenarios, we explored the effect of the different control methods.Spatial distribution analysis of bedbugs using MaxEnt modelEnvironmental data for MaxEntThe environmental variables used as the other maxent input were obtained by deriving bioclimatic, land cover, and elevation data. Bioclimatic variables and elevation (Digital Elevation Model; DEM) data were obtained from the Global Climate Data official website, Worldclim (http://www.worldclim.org/bioclim.htm)48 including 19 bioclimatic variables (Appendix B, Table S2). The land cover data were downloaded from the Global Land Cover Facility (GLCF).In order to reduce collinearity between predictors, a collinearity test was performed on all the variables by filtering them according to the following steps36: firstly, the MaxEnt model was run using the distribution data of bedbugs and 19 bioclimatic variables to obtain the percent contribution of each variable to the preliminary prediction results. Secondly, following the generation of the percentage contribution of all the variables, we then imported all distribution points in Arc-GIS and extracted the attribute values of the 19 variables. Furthermore, the “virtual species” package49 in R-software (R Foundation for Statistical Computing, Vienna, Australia) was used to explore the extracted variables’ clusters spatial correlation using Pearson’s correlation coefficient and the cluster tree (Fig. 8). Thus, the final number of predictor variables after screening was 5 establishing the potential geographical distribution of bedbug, which includes Temperature Seasonality (bio4), Precipitation of Driest Month (bio14), Temperature Annual Range (bio7), Precipitation of Driest Quarter (bio17) and Precipitation of Warmest Quarter (bio18) (Appendix B, Table S2). The land cover was considered because studies have shown its importance on insect spatial distribution50,51,52 and it was setled as a categorical variable53. Elevation was selected as variable because it greatly influences species’ occurrence and dispersal by affecting the temperature, precipitation, vegetation, and sun characteristics (direction, intensity, etc.) on the earth’s surface54,55,56. The study variables had different resolutions and were therefore, resampled to 1 km. The variables were clipped to Kenya and Africa boundaries and converted to ASCII (Stands for “American Standard Code for Information Interchange”) format using the ‘raster’ package49 in R statistical software (R Foundation for Statistical Computing, Vienna, Australia).Figure 8Key model predictor variables.Full size imageDistribution modelling in Kenya and AfricaIn our study, we used the maximum entropy distribution modelling method. This is because it has been recommended to have the ability to perform best and remain effective despite the use of small sample size relative to the other modelling methods57.Our selected bioclimatic variables (5) and occurrence/prevalence data for bedbugs were then imported into MaxEnt model and the options of ‘Create response curves’ and ‘Do jackknife’ were selected to measure variable importance’ options. The model output file was selected as ‘Logistic’, the commonly used approach is the random portioning of distribution datasets into ‘training’, and ‘test’ sets57,58. MaxEnt model was run with a total number of 5000 iterations and five replicates for better convergence of the model and rescaled within the range of 0–1000 suitability scores using ‘raster’ package49 in R statistical software (R Foundation for Statistical Computing, Vienna, Australia).The modelling performance/MaxEnt accuracy was evaluated by choosing the area under the receiver operating characteristics (ROC) curve (AUC) as the estimation index. This was important for the calibration and validation of the robustness of MaxEnt model evaluation. Furthermore, the area under the ROC curve (AUC) was necessary as an additional precision analysis59. The range of AUC values greater than 0.7 was considered a fair model performance, while those greater than 0.9 indicated that the model was considered an excellent model performance. Therefore, by considering the AUC values, the excellently performing model was selected to analyze the suitability of bedbugs in Kenya and Africa59,60,61,62.The ASCII format output was then imported into QGIS 3.10.2 (using the QGIS 3.10.2 software, https://qgis.org/downloads/), following its conversion into a raster format file using R software. This was useful for the classification and visualization of the distribution area63,64. The potential suitable distribution of bedbugs was extracted using the Kenyan and African maps. At the same time, Jenks’ natural breaks were also used to reclassify and classify the suitability into five categories, namely: unsuitable (P  More

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