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Disease data sourceAll analyses were conducted at the administrative level, and the exact list of known zoonotic diseases is recorded in the GIDEON database22. GIDEON is currently the most comprehensive and frequently updated infectious disease outbreak database reporting epidemics of human infectious diseases at the global scale and has been widely used in global zoonosis studies42,43 (Last access date, November 9, 2020). The administrative designations used in our analyses were based on the Global Administrative Areas (GADM) database (www.gadm.org, downloaded on November 8, 2020), which includes very detailed boundary data for global countries and major island groups.Pattern and correlates of zoonosis events worldwideNumber of zoonosis eventsGIDEON defines human infectious disease reservoirs as any animal, plant, or substrate supporting the survival and reproduction of infectious agents and promoting transmission to potential susceptible hosts. Its host category therefore includes all human-specific, zoonotic, multihost, and environmental agents. As our main aim was to test the role of established alien animal species in the emergence of zoonotic diseases, we focused on a total of 161 diseases specified in GIDEON’s host designations and definitions as nonhuman zoonotic (n = 115) and multihost (n = 46) diseases (Supplementary Data 1) and excluded diseases with human-specific hosts that do not need animals to persist or be transmitted. The infectious agents of nonhuman zoonotic diseases complete their entire lifecycle in nonhuman hosts but may have the potential to spillover and infect human populations. Infectious agents of multihost diseases can use both human and animal hosts for their development and reproduction. We measured the number of zoonosis events for each jurisdiction according to five host taxonomic groups: mammals, birds, invertebrates, reptiles and amphibians. These zoonoses were mainly caused by bacteria, viruses, parasitic animals and fungi. We excluded zoonoses from the Algae (3 diseases) due to low sample sizes in GIDEON.Correlates of the number of zoonosis eventsClimatic variablesFollowing a previous study21, we used global environmental stratification (GEnS) as a composite bioclimatic variable generated by stratifying the Earth’s surface into zones with similar climates44. The GEnS database was constructed based on a total of 125 strata across 18 global environmental zones with a spatial resolution of 30 arc seconds (equivalent to approximately 0.86 km2 at the equator). The values in GEnS range from 1 to 18 with a higher value indicating warmer and wetter conditions.Human population densityWe used human population density as one general anthropogenic factor reflecting propagule pressure and human-assisted pathogen movements1,21,45. Human population size data and the land area of each jurisdiction were collected from World Bank Open Data from 2011 to 2020 (available at https://data.worldbank.org/indicator/SP.POP.TOTL, accessed on November 18, 2020). We then calculated the human population density using the human population size divided by the land area.Native potential host richness and biodiversity lossData on the richness of native amphibians, birds, and mammals were derived from the Biodiversity Mapping website (https://biodiversitymapping.org/wordpress/index.php/home/, accessed on August 19, 2020), which were based on studies from Jenkins et al. (2013)’s and Pimm et al. (2014)46,47. The map of reptile diversity is based on an updated database of the global spatial distribution of reptiles48. All diversity maps for each taxon were generated through the calculation of grid-based richness at a spatial resolution of 10 km × 10 km in ArcGIS46. We did not include native invertebrate richness, as global maps for most invertebrate taxa are not yet available. For the loss of native biodiversity, we followed the previous study by first extracting the list of threatened species (NT, EN and VU categories evaluated by the IUCN Red List, access on May 10th, 2021)29, and then calculated the number of threatened species for each taxon distributes in each administrative unite as a proxy of biodiversity loss.Richness of established alien zoonotic host speciesWe quantified the richness of established alien animal species from the five main taxonomic groups (mammals, birds, reptiles, amphibians and invertebrates) based on 4,522 establishment events of 795 alien animals in each of 201 jurisdictions according to various databases. Data on 262 established alien reptiles and amphibians were compiled from multiple publications, including Kraus’s compendium49 and other recent updates50. Data on 337 established alien birds after removing all migratory bird species as vagrants were collected from the Global Avian Invasions Atlas (GAVIA)51, which is a comprehensive database of the global distribution of established alien birds. Data on 119 established alien mammals were obtained from the Introduced Mammals of the World database52 and the more recent update53. Data on 77 terrestrial alien invertebrates (66 insects and 11 other groups) across 7 taxa with native and invaded range information were obtained from the Global Invasive Species Database (GISD, http://www.iucngisd.org/gisd/, accessed on July 1, 2020). We calculated the richness of both zoonotic and non-zoonotic alien host species for each order. We first conducted an intensive literature review for each established alien species of each of the four taxa to determine whether they transmit pathogens to humans (Supplementary Data 2). The identification of zoonotic or non-zoonotic host may be influenced by under-sampling in the literature. We therefore incorporated the latest synthesis of human-infecting pathogens in the ‘CLOVER’ dataset to identify zoonotic and non-zoonotic animal hosts54. The CLOVER dataset compiled GMPD255, EID256, HP323 and Shaw57 databases and is currently the most comprehensive dataset on host-pathogen associations. Based on this information, we then categorized each alien species as a ‘zoonotic host’ or ‘non-zoonotic host’. The records of the established alien species were assigned to GADM jurisdictions, and we calculated the richness of the established alien zoonotic and non-zoonotic host species for each taxonomic group within each jurisdiction. In order to increase the statistical power, we conducted subsequent modeling analyses based on four mammalian orders (i.e., Carnivora, Cetartiodactyla, Lagomorpha, and Rodentia), five avian groups (i.e., waterfowl including five orders: Anseriformes, Gruiformes, Pelecaniformes, Phoenicopteriformes and Suliformes; Columbiformes, Galliformes, Passeriformes, Psittaciformes), the order Diptera of the invertebrates, and herpetofauna as a whole, which have established alien populations in at least 50 administrative units.Climate changeWe extracted historical monthly mean temperature and precipitation data recorded between 1901 and 2009 from the University of East Anglia Climate Research Unit (CRU, https://sites.uea.ac.uk/cru/, accessed on November 30, 2020)58. This database provides historical global-scale yearly climatic data with the finest resolution of 0.5° grids. We generated the temperature and precipitation values for all grids in each jurisdiction, calculated the slope of the temperature and precipitation for the time series of the years 1901 to 2009 for each grid and generated the averages based on all grids within each jurisdiction.Anthropogenic land-use changeWe downloaded global land-use data from the Anthromes v2 Dataset (Anthropogenic Biomes version 2, accessed on October 15, 2020) in ESRI GRID format59. We used the 1900 and 2000 data to calculate the temporal changes in land use. By using the reclassify and raster function in ArcGIS, we calculated the percentage of grids in which the land-use type changed to a more anthropogenically influenced type from 1900 to 2000 for each jurisdiction, including 15 scenarios: Wildlands to Seminatural, Wildlands to Rangelands, Wildlands to Croplands, Wildlands to Villages, Wildlands to Dense Settlements, Seminatural to Rangelands, Seminatural to Croplands, Seminatural to Villages, Seminatural to Dense Settlements, Rangelands to Croplands, Rangelands to Villages, Rangelands to Dense Settlements, Croplands to Villages, Croplands to Dense Settlements, and Villages to Dense Settlements.Sampling effort, reporting bias and incomplete dataA potential issue in quantifying the effects of different predictor variables on the number of zoonosis events is the need to account for the differences in survey effort, reporting bias and incomplete disease data among regions1,21,28. There is a high probability that zoonosis discovery is spatially biased by uneven levels of surveillance across countries, as the global allocation of scientific resources has been focused on rich and developed countries. We thus included the Infectious Disease Vulnerability Index (IDVI), which is a comprehensive metric reflecting the demographic, health care, public health, socioeconomic, and political factors that may have an impact on the capacity of surveillance and detection of infectious diseases in each country60. Second, we followed the methods of a previous study21 to control for reporting biases. We incorporated PubMed citations per disease for each jurisdiction using a Python-based PubCrawler21. In addition, we added the longitude and latitude of the geographic centroid of administrative units to control for spatial autocorrelation as there would be a higher probability of having similar diseases in nearby than distant administrative units61.Statistical analysisThe number of zoonosis events, native potential host richness, established alien animal richness and human population density were log-transformed to improve linearity. A potential issue in our data analysis is that the numbers of zoonosis events and the numbers of native and alien animal species are strongly influenced by geographical area, as larger countries or regions may host more native or alien animal species and more disease events. We therefore calculated the density of native or alien species richness and the number of zoonosis events using the total number divided by the geographical area of each jurisdiction. Furthermore, the number of zoonosis events may also be influenced by the degree of local disease surveillance. We thus obtained the residuals from a regression correlating zoonosis event density and all disease event density, and used them as the dependent variable for further analyses (Fig. 1). As some of our variables may be expected to be nonlinear, we performed generalized additive mixed model (GAMM) analyses following Mollentze & Streicker 2020’s framework25 to quantify the relationships between different predictor variables and the number of zoonosis events. We started with a full model with zoonosis event density controlling for overall disease surveillance as the response variable and 13 smoothed fixed effects (Fig. 1 and Supplementary Data 4): GEnS, human population density, density of native species richness, biodiversity loss, density of alien zoonotic host richness, density of alien non-zoonotic host richness, climate (temperature and precipitation) change, land-use change, IDVI, PubMed citations, longitude and latitude of geographic centroid of administrative units. The reason why we included the density of alien non-zoonotic host richness as a covariate is because this variable can serve as a positive control for propagule pressure, allowing us to more explicitly test whether zoonotic alien hosts contribute to zoonoses beyond propagule pressure associated with non-zoonotic alien hosts, which cannot directly increase zoonotic diseases. These predictor variables were not highly collinear as their correlation coefficients based on Pearson rank correlation analyses were all More

The crowdsourcing campaign was organized as a competition with prizes offered to those who contributed the most, based on a combination of quality and quantity. The Geo-Wiki platform (www.geo-wiki.org), a web platform dedicated to engaging citizens in environmental monitoring, was used as the tool to perform the campaign. A customized user interface was prepared for the campaign (Fig. 2), where participants were shown a random location in the tropics (here broadly defined as the area between 30 degrees of latitude north and south of the equator, i.e., including part of the subtropics), where a blue 1 × 1 km box showed the location to be visually interpreted. The Global Forest Change (GFC) tree loss map (v1.7)10 was overlaid on the imagery to show all areas where tree loss was detected at any point between 2008 and 2019. The tree loss area was shaded in red and the map itself was aggregated to 100 m for fast rendering.Fig. 2Customized Geo-Wiki interface for the ‘Drivers of Tropical Forest Loss’ crowdsourcing campaign showing: (a) Tools available to participants such as the NDVI and Sentinel time-series profiles, visualizing the location on Google Earth and exploring the imagery time-series, reviewing the quick-start guide and exploring examples to identify specific drivers of forest loss as well as contacting IIASA staff via chat or email; (b) country and continent of the location as well as dates of the imagery shown; (c) campaign statistics; (d) available background imagery; and (e) tasks to be undertaken by the participants along with buttons to submit or skip the location.Full size imageThe year 2008 was selected as the start date because the RED states that date as the cut-off year for conversion from high-carbon areas, i.e., forest, to other land uses7. In order to capture the main drivers of forest loss, but also include potential additional drivers such as the existence of roads as precursors of deforestation, the participants were asked to complete three steps: 1) To select the predominant tree loss driver visible inside the tree loss pixels in the blue box from a list of nine specific drivers; 2) to select all other tree loss drivers visible inside the tree loss pixels in the blue box from a list of five more general drivers, and 3) to mark if roads, trails, or buildings were visible in the blue box. The list of specific and general drivers as well as their definitions is shown in Table 1. The Geo-Wiki interface allowed participants to switch between different background imagery such as ESRI, Google Maps, and Bing Maps as well as Sentinel 2 satellite imagery. The different sources of imagery allowed the participants to see the location at different resolutions and in different periods of time. It also provided participants with information about the current country and the continent as well as the dates of the background imagery. Furthermore, it provided the participants with links for displaying NDVI and Sentinel time series, and to see the location and explore the historical imagery using the Google Earth platform. All these tools were meant to help with easier identification of the forest loss drivers by allowing participants to look at the locations during different times and at different spatial resolutions.Table 1 List and description of the available list of tree loss drivers that participants could select for steps 1 and 2 of the campaign.Full size tableAt the beginning of the campaign, each participant was shown a quick start guide of the interface and the tasks requested. As shown in Fig. 2, this quick start guide could be accessed again at any point during the campaign. Figure 2 also shows that the interface had buttons for four further functions. The first was to see the gallery of examples with access to pre-loaded video-tutorials and examples of images describing each driver of forest loss and how to do visual interpretation and selection of each of these (available at https://application.geo-wiki.org/Application/modules/drivers_forest_change/drivers_forest_change_gallery.html). An illustration of the gallery of examples shown to participants is shown in Figure S1. The second function was to ask experts for help, which automatically sent IIASA experts an email regarding a specific location. The third was to join the expert chat, which led participants to a dedicated chat interface on the Discord messaging platform. Here participants could pose questions and interact with staff and other participants directly. Finally, there was a button to see the leader board as well as the aims, rules and prizes of the campaign (available at https://application.geo-wiki.org/Application/modules/drivers_forest_change/drivers_forest_change.html). When the participants started the campaign, they were shown 10 initial practice locations, where they could try out the user interface (UI) with control points, which showed the participants how to identify the different drivers of forest loss. This set of videos, the images and the training points, together with the gallery of images, were developed to train the participants before and during the campaign.Campaign set-up and data qualityAs the aim of the campaign was to determine the drivers of tree loss across the tropics, the sample locations were selected from the GFC tree loss layer10 for the tropics (between 30 degrees north and south of the equator). No stratification was used since a completely random sample across the tropics was deemed to be the fairest representation of tree loss and their corresponding drivers. The previous map of deforestation drivers6 used a 5 K sample of 10 × 10 km grid cells to produce a global map. Here the sample size was largely driven by the estimated capacity of the crowd. Hence, we aimed to validate ca. 150k 1 × 1 km locations across the tropics, which is a considerably larger sample size than that of Curtis et al.6. In order to reduce noise, the GFC tree loss layer10 was first aggregated to a 100 m resolution from the original 30 m, and 150 K centroids were then randomly selected. From these, a sub sample of 5000 random locations were selected for visual interpretation by six IIASA experts (with backgrounds in remote sensing, agronomy, forestry and geography). Due to time constraints, only 2001 locations were evaluated by at least three different experts. In these locations, agreement was discussed and once a consensus was reached, these locations became the final control or expert data set. The control locations were then used to produce quality scores for each participant as the campaign progressed in order to rank them and determine the final prize winners. The list of prizes offered to the top 30 participants is shown in Table S1 in the Supplementary Information (SI), and a list and rank of motivations mentioned by the participants is shown on Figure S2 in the SI.The control locations were randomly shown to the participants at a ratio of approximately 2 control locations to every 20 non-control locations visited. If the participants correctly selected the predominant tree loss driver (in step 1), they were awarded 20 points; if they selected the wrong answer, they lost 15 points. If participants confused pasture and commercial agriculture or wildfire with other natural disturbances, they lost only 10 points instead of 15. Furthermore, they could win 8 additional points by selecting the correct secondary drivers in step 2. If a mixture of correct and incorrect answers were provided in step 2, the participants gained 2 points for every correct choice and lost 2 points for every incorrect one, with a minimum gain/loss of 0 points. Finally, participants could earn 2 additional points by correctly reporting the existence of roads, trails or buildings in step 3. The scoring system was based on previous Geo-Wiki campaign experiences and aimed to promote focus on the primary driver selection. The points were used to produce a leader board with the total number of points by participant. Additionally, a relative quality score (RQS) was derived from the score received by the users and the potential score that could have been obtained if all control points were correctly interpreted. This is shown in Eq. 1.$${rm{RQS}}=(({{rm{NCP}}}^{ast }15+{rm{SumScore}})/{rm{NCP}})/45$$
(1)
where RQS ranges between 0 and 1, NCP is the number of control points visited and SumScore is the number of points obtained.The RQS was crucial in understanding how each participant performed in terms of the quality of their visual interpretations, as this was independent of the number of locations interpreted. Once the campaign ended, an average RQS was used as a minimum criterion for participants to receive a prize, independent of where they were located on the leader board. Additionally, all users who submitted a substantial number of interpretations, i.e., more than 1000 with the minimum required RQS, were invited to become co-authors of the current manuscript, independent of whether they received a monetary prize or not. All these co-authors additionally contributed to the editing and revision of this manuscript. Furthermore, future users of the data set could use the RQS as a key data quality indicator.After the campaign, the data post-processing included eliminating interpretations made by users who broke any of the competition rules. Additionally, during the campaign, some users communicated with IIASA staff using the “Ask Experts” button and pointed out that some control points were mistaken. Consequently, the corresponding points lost were added to the final score of those participants where the correction was made. A total of 18742 validations from 1 participant were removed before the end of the campaign and the user was disqualified since their account was deemed to be shared across several people and computers, which was not allowed. Validations from another user (38,502 out of 40,828) were also removed due to inconsistencies but the user remained in the competition. Before the prizes were awarded to the top 30 users, a questionnaire was administered to all users to gather information about participant characteristics and gauge their motivations. Participation was mandatory for the top 30 users. A summary of the participant backgrounds is provided in Figure S3 in the SI. More

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Tagging deployments and study subjectsTable 1 contains an overview of the fields in the metadata file (JWS_metadata.xlsx) providing extensive background details on each of the 79 tag deployments and 63 study subjects. The data in this file give essential contextual information needed to understand the methodological, environmental, and demographic factors surrounding the deployments, which are critical for further examination and hypothesis testing of the sensor data. These metadata fall into several specific categories, but are not limited to, (i) information on the deployed electronic devices (platform, model, Platform Transmitter Terminal identifications), (ii) sharks (unique identifying numbers, sex, length), (iii) capture event (date, location, duration, methodology, interaction type), and (iv) the reporting period (duration, linear surface travel distance).Table 1 Metadata descriptions of the sharks, tagging operations, and deployments for all tags included in the database.Full size tableFigure 1 illustrates a typical C. carcharias tagging operation. This involves a contracted commercial fishing vessel with purpose-built gears to capture sharks (Fig. 1a) and a research crew to handle animals, monitor health (Fig. 1b) and attach electronic tags (Fig. 1c). More details on the tagging program and its methodologies are provided elsewhere14,19,20. Figure. 2 provides summaries of the deployment schedule, geographic locations, devices, and capture operations. Of note, 39.7% (25/64) of all tagging operations involved collaborations with commercial fishery operators (Fig. 2f–h), whose engagement was temporarily impacted (Fig. 2a) during the scientific review process when the population was under consideration for US Endangered Species Act listing. Figure 3 displays the demographic focus on small juvenile C. carcharias, with modest deployment durations and travel distances.Fig. 1Depiction of a typical research operation for capturing and tagging juvenile White Sharks in the Southern California Bight. (a) Aquarium research vessel (RV Lucile) with crew approaching a contracted purse seine vessel containing a captured juvenile white shark. (b) Research crew on the RV Lucile leading the shark into a sling, where it is subsequently transferred to the vessel’s deck for tagging. (c) Successfully applied PAT and acoustic tags each positioned lateral of the dorsal fin, anchored via leaders, and affixed with titanium darts (yellow arrows). All images taken by Steve McNicholas (Great White Shark 3D) for the Monterey Bay Aquarium and used with permission.Full size imageFig. 2Metadata summaries of the field program that deployed biologging tags on juvenile white sharks in the southern California Current. (a) Deployment schedule for 72 electronic tags released on 64 White Sharks from 2001–2020 (b) Tagging activity peaked in the late summer months when the population is most locally abundant. Field operations decreased from 2011–2013 when the population was being considered for listing under the U.S. Endangered Species Act (ESA). (c) Deployments focused on opportunities in the Southern California Bight coastline and included deployments in the nursery area of Bahía Sebastian Vizcaíno, Mexico and releases after exhibition at the Monterey Bay Aquarium. (d) Researchers released a variety of pop-up archival transmitting (PAT, 58 sharks), acoustic (21 sharks), and smart position and temperature (SPOT, 20 sharks) tags. This manuscript only reports the geolocation, temperature and depth data from the PAT and SPOT platforms. (e) Half (35 of 64, 54.7%) of all sharks received multiple tags, primarily to compare their relative performance. (f) Most tags (38 of 64, 60.3%) were deployed during focused scientific research operations. (g) The remainder were joint operations resulting from opportunistic bycatch in commercial fisheries using various gears and (h) Targeting various species. “Jab” gear refers to research operations that uses pole extensions to apply tags to sharks without capturing and handling.Full size imageFig. 3Demographic and deployment summaries from the juvenile white shark tagging program. (a) Total body length (TL) histogram indicates that most individuals tagged were either neonates ( More

Ebola datasetThe 2018–2020 DRC EVD outbreak lasted over 24 months and spread over 3 distinct spatial and temporal waves. Between the emergency declaration of the EVD outbreak in northern DRC on August 1, 2018 and the outbreak’s official end on June 25, 2020, the DRC Ministry of Health has reported a total of 3481 cases (including confirmed and probable), 1162 recoveries, and 2299 deaths16 in the provinces of Northern Kivu, Southern Kivu, and Ituri. The dataset considered here is a large subset of the entire EVD database compiled by the University of Kinshasa School of Public Health, which comprises 3117 total case records (confirmed and probable) recorded between May 3, 2018, and September 12, 2019. The data included partially de-identified but still detailed patient information, such as each person’s location, date of symptom onset and hospitalization, as well as discharge due to recovery or death. These individual records came from the Ebola treatment centers in 24 different health zones, spread out among the three DRC provinces of Northern Kivu, Southern Kivu, and Ituri.Of the 24 health zones, 77.1% of all cases were from only 6: Beni, Butembo, Katwa, Kalunguta, Mabalako, and Mandima. Only 9.7% of cases were under the age of 18. There is also a slightly larger proportion of females contracting the disease, comprising 57.0% of the cases. Approximately 5% of the cases were health care workers. About one-third of the EVD fatalities were not identified until patient’s death and thus not effectively isolated from the time of infection. Although over 170,000 contacts of confirmed and probable Ebola cases had been monitored across all affected health zones for 21 days after their last known exposure by the end of the epidemic, some of the contact tracing was incomplete due to insecurity that prevented public health response teams from entering some communities. The overall case density map is presented in panel (A) of Fig. 1 with the animated version of the map presented in the online appendix in Fig. A.1. Notice that the high-density areas, particularly Butembo, Katwa, and Beni, are all spatially small health zones corresponding to cities or towns with larger populations.Figure 1DRC Ebola dataset. (A) The spatial distribution of 3481 EVD cases across the northern DRC health zones during Ebola 2018–2020 outbreak. (B) The flowchart of personal records available up to September 12, 2019 available for the current analysis. The total number of available individual disease records was 3080. Map created using open software R17 with geospatial data obtained from18.Full size imageFigure 2Daily incidence and removal rates. Daily incidence (grey bars) and removal counts (red dots) during DRC Ebola 2018–2020 outbreak between August 15, 2018 and September 12, 2020 along with their respective trendlines (loess smoothers). The blue trendline above the plot represents daily effective reproduction number (mathcal{R}_t) defined as the ratio of daily number of new infections to new removals. The vertical lines indicate cut-off dates for data collection in each wave as listed in Table 1.Full size imageTable 1 Observed cases by EVD wave.Full size tableCase alerts and definitionsSince early August, 2018, the DRC Ministry of Health has been collaborating with several international partners to support and enhance EVD response activities through its emergency operations center in Goma. To the extent possible given regional security considerations19, the response teams were deployed to interview patients and their suspected contacts using a standardized case investigation form classifying cases as suspected, probable, or confirmed. A suspected case (whether surviving or not) was defined as one with the acute onset of fever (over 100(^{circ })F) and at least three Ebola-compatible clinical signs or symptoms (headache, vomiting, anorexia, diarrhea, lethargy, stomach pain, muscle or joint aches, difficulty swallowing or breathing, hiccups, unexplained bleeding, or any sudden, unexplained death) in a North Kivu, South Kivu, or Ituri resident or any person who had traveled to these provinces during this period and reported the signs or symptoms defined above. A patient who met the suspected case definition and died but from whom no specimens were available was considered a probable case. A confirmed Ebola case was defined as a suspected case with at least one positive test for Ebola virus using reverse transcription polymerase chain reaction (RT-PCR)20 testing. Patients with suspected Ebola were isolated and transported to an Ebola treatment center for confirmatory testing and treatment2.Onset and removalIn our analysis of the DRC dataset, we focused on dates of symptom onset and removal, with removal defined as either a death/recovery at home or transfer to an Ebola treatment center (ETC). It was assumed that, once in the treatment center, the probability of further infection spread by an isolated individual was very small due to the strict safety protocols—and later due also to vaccination of healthcare personnel and family members who were in contact with the suspected Ebola case. As summarized in panel (B) of Fig. 1, we were able to access 3117 out of 3481 individual records of confirmed and probable Ebola cases. Of these 3117 records, 37 were missing both the onset and recovery dates and were removed from further analysis. In about 30% of the remaining records, either their dates of onset or removal were missing. A detailed flow diagram summarizing the amount of missing data and data processing leading to the final dataset is presented in panel (B) of Fig. 1. The distribution of the original and the partially imputed records across the three waves of infection is provided for further reference in Table 1.Spatial and temporal patternsThroughout the pandemic, the incidence rates exhibited strong spatial and temporal patterns that can be summarized as three distinct waves of infections with approximate boundaries marked by vertical lines in Fig. 1. The distribution of weekly reported cases across the most affected health zones listed in Table 1 is provided in the bar plot and in the corresponding animation in the appendix (see Figure A.1). As seen from the bar chart and the animated plot, the epidemic was initially driven largely by infections in the health zones of Beni, Mandima and Mabalako. After several months, the incidence of new cases in these zones subsided, but the epidemic moved south to the health zones of Katwa and Butembo, where the majority of new infections was registered between weeks 22 to 45 of the epidemic (see Panel (A) in Figure A.1 in the online Appendix). In the final spatial shift, around week 49, the epidemic returned to the health zones of Beni, Mandima, and Mabalako, where it was mostly extinguished around week 60 (September 2019). Isolated Ebola incidences occurred sporadically across northern DRC until end of the outbreak was officially declared in June 2020.The empirical patterns of incidence and removal for EVD cases are summarized in Fig. 2 with the bar and the dot plots representing the daily numbers of new infections and removals, respectively. As seen from the plot, these daily counts closely follow a three-wave temporal pattern in Table 1. This is further evident from the black and red trendlines representing the loess smoothers (see21). The daily ratio of new cases and removals may be interpreted as a crude estimate of the effective reproduction number (mathcal{R}_t) defined more formally in (2) in Model for Data Analysis below. In particular, the blue trendline for (mathcal{R}_t) indicates that towards the end of the observed time period, the number of removals outpaced the number of new infections ((mathcal{R}_t 0) and (r_t = 0) where (beta > 0) is the rate of infection, (gamma > 0) is the rate of recovery and (rho > 0) is the initial amount of infection. In particular, the model implies the existence of the basic reproduction number (mathcal{R}_0) (R-naught), which determines the average speed of disease spread11 and is given by the formula$$mathcal{R}_0=beta /gamma .$$If (mathcal{R}_0 > 1), the proportion of infected initially rises and then subsides, with the final proposition of surviving susceptibles given by (s_infty = 1 – tau > 0) where (tau) is know as the epidemic’s final size. In typical statistical analysis, an estimate of (mathcal{R}_0) is obtained by separately estimating the parameters (beta) and (gamma). Another important quantity related to (1) is the effective reproduction number, which is typically defined as$$begin{aligned} mathcal{R}_t= mathcal{R}_0 s_t. end{aligned}$$
(2)
Although equation (1) is typically considered in the context of an average behavior of a large population, for our purposes we interpret it as defining the individual histories of infection and recovery, according to the idea of the dynamic survival analysis (DSA) discussed recently in10 and24 and also briefly summarized in the Appendix. With the DSA approach, we interpret equation (1) as the so-called stochastic master equation25 describing the change in probability of a randomly selected individual being at time t either susceptible, infected, or removed. These respective probabilities are represented by the scaled proportions (s_t/(1+rho )), (iota _t/(1+rho )), and (r_t/(1+rho )) and evolve according to (1). As outlined in10, the DSA-based interpretation of the classical SIR equations has a number of advantages that make it particularly convenient for analyzing epidemic data consisting of individual histories of infection onsets and removals, which is exactly the type of data available in the DRC Ebola dataset. The fact that the model is individual-based implies also that we can vary the parameters (theta =(beta ,gamma ,rho )) to account for individual covariates and changes in the parameter values over time, as different waves of infection sweep through the population. Finally, for the purpose of our analysis, it is also important to note that the DSA model does not require any knowledge of the size of the susceptible population subjected to the epidemic pressure. For the DRC dataset, that assumption would be difficult to justify due to spatial and temporal heterogeneity of the epidemic and the frequent movements of local populations driven by political conflicts and insecurity. Another element complicating the determination of the size of susceptible population was the ring vaccination campaign that has been conducted since 2019 wherever possible in the northern DRC during periods of relative stability, despite local mistrust and supply issues. This campaign ultimately resulted in over 250,000 vaccinations.Note that, because (s_0 = 1), the values of (mathcal{R}_0) and (mathcal{R}_t) coincide for (t = 0). Moreover, (s_t = exp left( -mathcal{R}_0 int _0^t r_u mathrm {d}u right)) is a decreasing function of time and therefore, so is (mathcal{R}_t). However, in practice, this implication is problematic. Rewriting (mathcal{R}_t = – {dot{s}}_t/ {dot{r}}_t) suggests that a crude but sensible way to estimate (mathcal{R}_t) empirically is to take the ratio of daily number of new infections to new removals. The empirical (mathcal{R}_t) thus estimated will not be necessarily monotonically decreasing. In the light of possibly changing parameters and the effective population size, we have adopted this approach to estimating the daily effective reproduction number (mathcal{R}_t) in Fig. 2.Parameter estimationWe assume that, for each of the three waves of the epidemic, we have a separate and independent set of parameters (theta) and that, in each wave, we observe (n_T) histories (records) of infection. The i-th individual history may be represented either by the times of disease onset and removal ((t_i,T_i)) or by (t_i) or (T_i) times alone ((t_i,circ )) or ((circ ,T_i)) ((circ) denoting missing value). We assume that among the available (n_T) histories we have n complete records ((t_i,T_i)), (n_1) incomplete ones ((t_i,circ )) and (n_2) incomplete ones ((circ ,T_i )). The wave-specific DSA likelihood function for n complete data records is (see Appendix)$$begin{aligned} begin{aligned} {mathcal {L}}_C(theta vert t_1ldots ,t_n,T_1,ldots ,T_n,T)=(s_T-1)^{-n}prod _{i=1}^n {dot{s}}_{t_i}gamma ^{w_i}e^{-gamma (T_i wedge T -t_i)} end{aligned} end{aligned}$$
(3)
where T is the available time horizon and (w_i) is the binary variable indicating whether (T_i) is right-censored (that is, (T_iwedge T =T)) in which case (w_i = 0) and otherwise (w_i = 1). For the remaining (n_1+n_2) records that are partially incomplete, the wave-specific DSA likelihood function is$$begin{aligned} begin{aligned} {mathcal {L}}_I(theta vert t_1ldots ,t_{n_1},T_1,ldots ,T_{n_2},T)= (s_T-1)^{-(n_1+n_2)} gamma ^{n_2}prod _{i=1}^{n_1} {dot{s}}_{t_i} prod _{i=1}^{n_2} (rho e^{-gamma T_i }-iota _{T_i}) end{aligned} end{aligned}$$
(4)
where we assume that (T_i1). Given the wave-specific time horizons (T’s), the set of parameters for each epidemic wave was estimated independently using 2 independent chains of 3000 iterations, with a burn-in period of 1000 iterations. The chains’ convergence assessed using Rubin’s R statistic28. The analysis resulted in approximate samples from the posterior distribution of (theta) for each of the three waves of the epidemic (see e.g., Fig. 4).Ethics statement on human subjects and methodsThe research was conducted in accordance with the relevant guidelines and regulations of the US law and OSU Institutional Review Board. The research activities involving human subjects discussed in the paper meet the US federal exemption criteria under 45 CFR 46 and 21 CFR 56. More