Main

The spread of many infectious diseases occurs through complex ecological interactions between humans, animals and ecosystems1,2. Distinguishing the contributions of different host types to observed outbreak dynamics is crucial to inform predictions, early detection, preparedness and outbreak response. However, disentangling contributions to disease transmission is notoriously complex. This is especially the case for zoonotic diseases where pathogens are capable of infecting multiple species. In zoonotic wildlife diseases, our ability to unravel these contributions is often hampered by the lack of high-quality information on population distributions, patterns of disease occurrence and the lack of computational tools to integrate a wide range of data sources. Particularly during the emergence phase of a novel zoonotic pathogen, detailed outbreak data may be scarce and biased towards humans.

Contributions of different host species to transmission have been studied for several diseases and settings, such as minks and humans for severe acute respiratory syndrome coronavirus 2 (ref. 3), different bird species for avian influenza4, cattle and wildlife for bovine tuberculosis5 and wildlife reservoir hosts for plague6. Such analyses improve our understanding of the disease system and could also help inform and target surveillance strategies7,8 and interventions, including vaccines where available9,10,11. Depending on each species’ contribution to transmission, interventions may need to target multiple host species as, for example, for brucellosis12 and rabies13. A better understanding of host contributions can also inform risk of geographical expansion of emerging pathogens and future changes in disease burden of established pathogens.

A wide range of approaches for disentangling host contributions have been used, including the use of genetic sequencing3,5 and combining mechanistic models with outbreak data4,6. However, these studies generally focus on the contributions of species that are known to contribute to transmission and use data specifically collected from these species, while it is also possible that relevant hosts are not (yet) identified. Such unidentified host species that influence disease dynamics constitute the “epidemiological dark matter”14,15. Developing approaches capable of assessing the role of this dark matter in shaping transmission has been described as one of the main challenges for understanding multi-host disease dynamics14. Moreover, transmission models are often calibrated to one or two specific outbreak characteristics such as prevalence over time or mortality patterns. Characterization of unobserved reservoir hosts is more robust when models are calibrated to several outbreak patterns.

A prime example of a virus where multiple, unidentified host species may contribute to transmission is Usutu virus (USUV). USUV is a mosquito-borne virus, closely related to West Nile virus, that emerged in the Netherlands in the past decade16. It was first detected in Europe in 2001 following an observed increase in bird deaths17 and has since spread to several European countries18. The first detection of USUV in the Netherlands in April 2016 was followed by a substantial increase of dead Eurasian blackbirds (Turdus merula, hereafter: blackbird)16,19. Multi-year surveillance conducted in the Netherlands revealed striking emergence patterns20,21 (Fig. 1). First, USUV appeared to have spread from the south to the north between 2016 and 2018. Second, this period was followed by several years with fewer detections, after which the incidence increased again in 2022. USUV is transmitted in a cycle between Culex pipiens mosquitoes and birds22. The virus has been detected in many bird species20,22 and serological evidence of past exposure has been found in a wide range of animals18,20. Across Europe, the most affected bird orders are Passeriformes, Accipitriformes, Strigiformes and Columbiformes, with infections occurring in both wild and captive birds18. The virus is also able to infect humans but does generally not lead to symptoms18. Nine countries in the EU have USUV surveillance schemes for animals, but target species vary between countries and available epidemiological and experimental data does not provide sufficient information on the role of bird species or mammals in the USUV life cycle18.

Fig. 1: Spatiotemporal emergence pattern of USUV in the Netherlands, 2016–2022.
Fig. 1: Spatiotemporal emergence pattern of USUV in the Netherlands, 2016–2022.The alternative text for this image may have been generated using AI.
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Pink circles indicate detections in live birds, with sizes proportional to the number of detections. Green hexagons (30 km² in size) indicate detections in dead birds, with shading intensity reflecting the number of detections in dead free-ranging birds in that cell. Provincial borders are shown and are labelled with two-letter abbreviations in the 2016 map: FR, Friesland; GR, Groningen; DR, Drenthe; OV, Overijssel; FL, Flevoland; GE, Gelderland; UT, Utrecht; NH, Noord-Holland; ZH, Zuid-Holland; ZE, Zeeland; NB, Noord-Brabant; LI, Limburg. The figure is adapted from a related figure in ref. 20.

Blackbirds were the most commonly sampled species in the Dutch surveillance data between 2016 and 2022, showed the highest USUV prevalence among live birds and showed the highest number of USUV-related deaths20. High viral RNA loads detected in multiple organs suggests blackbirds also contribute to onwards transmission23,24. However, several other animal species can experience infections with USUV. In this study, we first aimed to explore whether, and to what extent, non-blackbird reservoir hosts played a role in shaping spatiotemporal patterns of USUV emergence and spread. Second, we aimed to reconstruct the emergence and spread of USUV in the Netherlands and quantify the contributions of different host populations to this. To characterize the role of host populations other than blackbirds in transmission dynamics, we developed a Bayesian inference framework in which mechanistic USUV transmission models were fitted to several sources of blackbird surveillance data. Through comparing these models, we disentangled the characteristics of a potential unobserved reservoir population. Using the best-fitting model we reconstructed the emergence over time and space and quantified each population’s contribution to transmission over time.

Results

Trends in epidemiological surveillance data

Five sources of blackbird surveillance data were used to study USUV emergence between 2016 and 202220,21. Observations were filtered to align with the modelled transmission season (April to October). Surveillance data included infection prevalence (based on real-time polymerase chain reactions (PCRs); n = 2,499) and seroprevalence in live blackbirds (n = 1,091), infection prevalence in dead blackbirds (n = 284), blackbird population size and reported dead blackbirds (n = 3,505). Infection prevalence in live blackbirds varied between years with the lowest observed prevalence in 2021 (0 positive cases) and highest in 2018 (0.09, n = 25/291, 95% confidence interval (CI) 0.05–0.12). Prevalence in dead blackbirds was much higher and ranged from 0.10 (n = 2/21, 95% CI 0–0.22) in 2021 to 0.87 (n = 61/70, 95% CI 0.79–0.95) in 2018. Seroprevalence peaked in 2018 (0.23, n = 44/194, 95% CI 0.17–0.29), which coincided with the lowest blackbird population size being observed in the following spring. Most dead birds were reported in 2016 (29% of the total across 2016 to 2022, n = 1,014/3,505) (Supplementary Fig. 9).

Characterizing hidden reservoir populations

To explore the potential role of host populations other than blackbirds in the emergence of USUV we developed four compartmental transmission models with different reservoir population characteristics (Table 1) on the basis of empirical data of mosquito and bird abundance25,26, bird movement and local temperature27, using a 5 km × 5 km grid cell structure (Fig. 2). These models were fitted to the five surveillance datasets using approximate Bayesian computation by aggregating the grid cells into three regions (north, middle and south). Models were compared on the basis of the (normalized) distances between model predictions and observed data across the five datasets. Models that included a reservoir population (mean normalized distances of 0.52–0.80) consistently outperformed the blackbird-only model (model A, a mean normalized distance of 0.97) (Fig. 3e). Comparison of different reservoir population characteristics revealed that the observed patterns in blackbirds were best described by the presence of a reservoir population that does not die from infection and disperses further than blackbirds (model D). This model estimated high seroprevalence levels in the reservoir population (Supplementary Fig. 12) and was able to capture both the south-to-north patterns and the reduced transmission in later years (reflected in a stabilization of blackbird population size) (Fig. 3a–d). It showed the best fit to the data across four out of five datasets (mean normalized distance of 0.52, compared with 0.60 for model B and 0.80 for model C) (Fig. 3e).

Fig. 2: Model overview.
Fig. 2: Model overview.The alternative text for this image may have been generated using AI.
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a, The country is divided into equally sized 5 km × 5 km grid cells, which vary with respect to bird (green) and mosquito (red) abundance as well as temperature (yellow). b, Birds disperse between cells. Transmission occurs within a grid cell. c, In the model, solid arrows represent transitions between infection states, while dashed arrows represent the link to the source of transmission (red for mosquitoes and green for birds). Non-connected outward pointing arrows represent a natural death of the animal. Non-connected inward pointing arrows represent births. S, susceptible; E, exposed; I, infectious; R, recovered; DI, dead from infection.

Fig. 3: Comparison of model versions.
Fig. 3: Comparison of model versions.The alternative text for this image may have been generated using AI.
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a–d, A visual fit of simulated data (dashed lines) to observed data (solid lines) for the blackbird population size for model A (a), model B (b), model C (c) and model D (d). Simulated data are presented as mean values with 95% prediction intervals. e, A comparison of model fits between main model versions. Comparisons were on the basis of distances between observed and simulated data for each dataset. For each dataset, distances were normalized by dividing each model’s distance by the maximum across all model versions. A normalized distance of ‘1’ thus indicates that the model showed the largest distance between observed and simulated data (that is, the worst fit). Lower normalized distances indicate a better fit to the data.

Table 1 Specification of model versions
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Sensitivity analyses showed that results of the best-fitting model (model D) were robust to assumptions regarding the location of virus introductions (mean normalized distance of 0.53) and the spatial distribution of the reservoir population (mean normalized distance of 0.54) (Supplementary Fig. 13). Sensitivity analyses exploring the impact of uncertainty in blackbird movement distances (that is, equal movement in breeding and post-breeding seasons) suggested that the increased dispersal required to explain the data falls within the uncertainty range of our blackbird movement estimates (mean normalized distance of 0.55). Leaving out PCR data during model calibration resulted in posterior estimates that were similar to those obtained from the best-fitting model using all data (Supplementary Material I). All further analyses are on the basis of the best-fitting main model: model D. Inspection of model fits showed that this model was able to capture the trends in population size and immunity levels in blackbirds, but underestimated prevalence in 2017 and 2022 and did not capture trends in reported dead blackbirds (Supplementary Fig. 14). Model fits to within-year trends are shown in Supplementary Fig. 15, model fits of all other models are shown in Supplementary Figs. 16–21, and further inference diagnostics can be found in Supplementary Material G.

Posterior estimates showed that the average adult lifespan of the modelled reservoir population was 5.8 years (95% CI 1.1–12.7 years). This population received 42 times (95% CI 32–50 times) more bites than the blackbird population per day owing to differences in population size and/or mosquito biting preference. Posterior distributions were largely robust across model versions, showing a high degree of overlap in 95% highest density intervals, especially across models D and S1–3 (Supplementary Table 8).

Reconstruction of USUV emergence

In addition to the role of reservoir populations, we also examined other determinants of the USUV outbreak. The best-fitting model showed an estimated infection mortality risk for blackbirds of 74% (95% CI 66–78%). While the first PCR-positive bird was found in 2016, undetected transmission before 2016 cannot be ruled out. We therefore aimed to estimate the level of immunity in 2016, but found that evidence of transmission before 2016 using our model was inconclusive (historical force of infection (FOI) 0.14, 95% CI 0.01–0.28). In addition, we quantified the annual USUV re-emergence rate, representing the possibility of local overwintering and/or re-introductions from migratory birds. This rate was estimated at 18.0% (95% CI 6.5–29.6%), indicating that USUV prevalence in mosquitoes at the start of the new season (April) is around 80% lower than at the end of the previous season (mid-September). Posterior distributions for all parameters and model versions are available in Supplementary Table 8.

We used our best-fitting model to reconstruct the emergence of USUV into the Netherlands. Prevalence in live and dead blackbirds generally peaked in August and September, matching the trends in observed data (Fig. 4a,b). In our model, the highest monthly average prevalence was estimated in August 2018 at 3.0% (95% CI 2.3–3.7%) in live birds and 67.1% (95% CI 60.6–72.5%) in dead blackbirds. While the mean prevalence in live blackbirds tended to be highest in juveniles (0.7%, 95% CI 0.5–0.9%; adults 0.5%, 95% CI 0.3–0.7%), prevalence in dead blackbirds was highest in adults (30.4%, 95% CI 23.4–37.6%; juveniles 17.1%, 95% CI 13.5–20.6%). Seroprevalence generally peaked in October and was on average 5.1 times higher in the modelled reservoir population (68.1%, 95% CI 56.1–74.8%) compared with seroprevalence in blackbirds (13.4%, 95% CI 9.7–17.9%) (Supplementary Fig. 12), highlighting the role of reservoir population immunity in shaping transmission patterns.

Fig. 4: Model outputs generated from 100 simulations using random draws from parameter sets from posterior distributions.
Fig. 4: Model outputs generated from 100 simulations using random draws from parameter sets from posterior distributions.The alternative text for this image may have been generated using AI.
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a, The infection prevalence during the transmission season in dead blackbirds split by age group. b, The infection prevalence during the transmission season in live blackbirds split by age group. c, R0 and Re during the transmission season. d, The partial effective reproduction numbers per transmission route averaged over the transmission season. Results are shown per transmission season from April to October while averaging across all locations. In a–c, solid lines indicate mean values and shaded areas show 95% prediction intervals.

We calculated basic reproduction numbers (R0), indicating the number of secondary infections resulting from one infectious individual in a fully susceptible population, and effective reproduction numbers (Re), indicating the number of secondary infections when accounting for immunity in the population. The annual mean Re was highest in 2016, when immunity was still limited, and lowest in 2019 (Fig. 4c). The Re tended to get above 1 at the end of May, peak in July and drop below 1 in early September, when mosquitoes started entering diapause. Differences in Re between regions were small (north 3.4, 95% CI 2.6–4.8; middle 3.0, 95% CI 2.5–4.9; south 2.9, 95% CI 2.4–4.7) (Supplementary Figs. 26 and 27).

Contributions of different host populations to transmission

To disentangle contributions to transmission from the different host populations, we calculated reproduction numbers for each transmission cycle, so-called partial reproduction numbers (Supplementary Fig. 28). We found that the reservoir–mosquito cycle contributed more to overall transmission than the blackbird–mosquito cycle. The Re of the blackbird–mosquito cycle during the transmission season was 0.07 (95% CI 0.05–0.11), meaning that USUV could not persist in blackbirds alone. With an Re of 3.0 (95% CI 2.3–4.3), USUV could persist in the reservoir–mosquito cycle (Fig. 4d). Juvenile blackbirds contributed about 1.5 times more to transmission than adult blackbirds (juvenile Re 0.06, 95% CI 0.04–0.10; adult Re 0.04, 95% CI 0.02–0.05) (Fig. 4d).

Discussion

In this study, we integrated five sources of surveillance data with data-driven transmission models in a Bayesian framework to assess drivers of spatiotemporal wildlife disease emergence. Using USUV as a case study, we showed that ignoring the multi-host context of transmission strongly impacts estimated outbreak dynamics. Specifically, failing to account for the build-up of immunity in reservoir populations hampers the model’s ability to accurately capture multi-annual trends. We found that, while blackbirds were strongly impacted by the virus, they could not by themselves contribute sufficiently to the population-level build-up of immunity, nor to the spread needed to explain the spatial and multi-annual patterns of emergence. We used the inference framework to characterize the unobserved reservoir population as having a longer lifespan, low infection mortality and probably a larger home range than blackbirds.

Contributions from different host populations

We found that, during the first recorded outbreak of USUV in the Netherlands, one or more host species, in addition to blackbirds, played a role in transmission. Previous studies highlighted evidence of exposure in a wide range of animal hosts, most commonly in birds but also in mammals such as horses, dogs and wolves18,20,22. Several papers have explored contributions of and interactions between host stages and/or species for the closely related West Nile virus from a theoretical perspective, highlighting the large impact that such interactions can have on outbreak dynamics28,29,30,31,32,33. However, this impact has not been demonstrated from real-life West Nile virus outbreak data. We found that the reproduction number for the blackbird–mosquito cycle was below 1 (maximum value 0.28, 95% CI 0.19–0.42) during the whole transmission season, suggesting that USUV persisted because of host competence (that is, the ability to transmit USUV onwards) and the abundance of other populations. An important driver of the difference in contribution between the two host groups was the estimated distribution of mosquito bites. The proportion of bites on each host is a consequence of both host preference and relative abundance, which we could not disentangle in our analysis. Our estimated distribution of bites (1–2% on blackbirds) is consistent with observations in the field (0–9% of bites on blackbirds)34. However, this model-based estimate is sensitive to assumptions around transmission probabilities, which we assumed to be the same for the reservoir population as for blackbirds. It is important to note that these findings do not imply that USUV transmission can only be sustained in the presence of other competent bird species but that this depends on how many mosquito bites blackbirds receive, which is a function of the composition of the total population mosquitoes feed on34,35.

Immunity in the reservoir population

A high level of immunity (reflected by high seroprevalence levels) in the reservoir population was found to be an important explanation of the observed transmission dynamics in blackbirds. While the basic reproduction number remained high each year, the effective reproduction number, which accounts for immunity in the host population, reduced as the outbreak spread across the country. The strong decline in the effective reproduction number in the (adult) reservoir population in the first 3 years indicates that high immunity in this population reduced USUV transmission in later years and thereby protected the blackbird population from further decline. This is an example of the ecological concept of population immunity36, that is, for instance, used in measles control, where high population immunity is achieved through vaccinations to protect vulnerable populations, such as those unable to develop protective immunity37. Seroprevalence could reach high levels in the reservoir population owing to their longer lifespan. In accordance with life-history theory38, longer lifespans were modelled to be associated with a lower annual birth rate (for example, through smaller clutch sizes) and therefore a smaller number of naive individuals that enter the population each year. Following ecological theory, if only a limited number of susceptible individuals enter the population each year, the resulting increase in effective reproduction number is limited. An Austrian study reported an USUV seroprevalence of 8.5% across several wild bird species in 2003–2004, but seroprevalence had increased to 54% even before the transmission seasons of 2005–2006 (ref. 39). In Spain, mean annual West Nile virus seropositivity levels ranged from 5% to 69% (ref. 40), in line with end-of-season seroprevalence levels estimated in Italy (7.8–89.1%)41. These studies show that heterogeneity in reported seroprevalence levels is large, with estimates varying both between and within years. Observational studies showed large variation in USUV antibody waning rates42,43. The lifespan of the reservoir population also affects immune dynamics. Seroprevalence and reservoir population lifespan estimates (which showed large uncertainty in this study) could be improved as longer time series of surveillance data become available.

Identifying the reservoir population

Existing literature can be combined with surveillance data available on other bird species to start identifying which species are represented in the reservoir population. Results indicated that a high seroprevalence level was an important characteristic of the reservoir population. Of the four species with more than ten samples in 2005 in an Austrian study39, all showed USUV seroprevalence estimates of around 50% or higher (blackbirds, Eurasian blackcaps (Sylvia atricapilla), Ural owls (Strix uralensis) and European robins (Erithacus rubecula)). However, only a subset of these birds were live captured wild birds and a substantial proportion were captive birds and/or sick, injured or dead. In the Netherlands, annual seroprevalence levels of that order of magnitude were not observed in any species, but species-specific sample sizes were often limited and estimates are sensitive to the timing of sampling. The highest seroprevalence levels among commonly sampled species in 2016–2022 were found in Carrion crows (Corvus corone) (13.7%, n = 51, some of which were sick), Eurasian magpies (Pica pica) (14.1%, n = 64) and Eurasian collared doves (Streptopelia decaoto) (11.1%, n = 36)20, of which the first two are relatively highly abundant in north-western Europe44. Another important characteristic of the reservoir population was limited infection mortality and further dispersal. While the impact of USUV infection is unknown for most of these species, studies indicated that magpies do not show clinical symptoms after USUV infection45. Magpies also live somewhat longer than blackbirds, typically 5 years after reaching breeding age46. Other species found positive for USUV in the Netherlands disperse further, such as crows and doves47,48. Finally, to act as a reservoir host, species should be able to transmit the virus to mosquitoes and contribute to persistence. Experimental studies have shown that house sparrows can transmit USUV to mosquitoes, and domestic canaries develop high viral RNA loads after infection, suggesting these species could act as reservoir hosts provided their transmission cycle is sufficiently efficient49,50. In conclusion, enhancing sampling in species with high seropositivity levels, as well as experimental infections to assess competence and infection responses, supplemented by demographic characteristics, could shed more light on the identity of species constituting the reservoir population.

Temporal trends in transmission

We were able to reproduce the large outbreaks observed during the first 3 years of emergence, after which transmission was sustained at a lower intensity. Our model captured the observations that the virus spread from south to north in a period of 3 years. This spatiotemporal pattern was a result of the location of virus introduction, dispersal distances and duration of the transmission season. We estimated that the effective reproduction number generally dropped below 1 after early September. Variation in basic reproduction numbers within and between years were mainly driven by mosquito population size and mean daily temperature, and to a smaller extent by bird population size. Spatial heterogeneity in reproduction numbers was limited and we did not identify clear transmission hotspots. Reproduction numbers were estimated to be highest in 2016 and 2018, coinciding with the highest estimated mosquito abundance in 2016 and the highest spring and summer temperatures in 2018. In 2016, a large USUV outbreak was observed in Germany, during which the virus spread towards North Rhine-Westphalia51,52, a region to the southeast of the Netherlands. The high reproduction numbers in 2018 coincided with the largest observed West Nile virus outbreak to that date in Europe53. Transmission season was shortest in 2021, where the reproduction number was not consistently above 1 until June, coinciding with the coldest spring of the study period. While some of the surveillance data sources showed increased transmission in 2022 compared with the previous years, this was not captured by the model, mostly because the predicted mosquito abundance was lowest during this year. Limitations that may have impacted the predicted annual variation in transmission include the simplifying assumption of a constant number of newborn birds each year, while variation might occur because of environmental conditions54, the assumption of a constant virus re-emergence rate each year and remaining biases in surveillance data. We estimated the re-emergence rate (around 20%) as the proportion of USUV prevalence in mosquitoes that persists to the next spring, representing the possibility of local overwintering and/or re-introductions from migratory birds. While we estimated a constant rate, this may be affected by winter temperatures55 and variation in bird migration patterns, among others. The quality of model fit varied between datasets. While this could reflect epidemiological or ecological processes that were not captured in the model, such as those mentioned above, this was probably largely driven by imperfect observation processes such as non-constant sampling intensity and varying detection probabilities, especially because the observation process was sometimes linked to circulation levels.

Implications for surveillance and predictions

Our findings indicate that blackbirds are useful as a target species for USUV surveillance because of their high infection mortality rate, which makes it possible to detect signals indicating large outbreaks in the absence of live bird surveillance schemes. The high prevalence in dead blackbirds makes sampling of dead blackbirds an efficient surveillance strategy to detect circulation. However, to better identify which other species can contribute to transmission, frequent sampling of a wider range of species is necessary. Longitudinal serological surveillance would be the most appropriate starting point to identify reservoir species, as they might not display increased mortality. However, to distinguish reservoir species (that is, those capable of transmitting the virus onwards) from dead-end host species (that is, those unable to further transmit), infectiousness would have to be confirmed, for example, using proxies such as viral RNA loads. Such information could be useful when making projections about future transmission risks and when predicting the suitability for USUV circulation. The large contribution of non-blackbird host species implies that regions with low blackbird density may also be suitable for USUV transmission, but this might remain undetected if surveillance is focused on dead bird reporting, as is the case in many other European countries. In addition, the model could be employed to evaluate current surveillance strategies by adding these into the model to provide recommendations regarding sampling intensity, timing and location for different surveillance systems.

Importance of multiple data sources

Using multiple sources of data for inference is one of the key challenges in epidemiological modelling56. We addressed several obstacles related to synthesizing diverse datasets. A common challenge in the use of multiple datasets for inference is weighing observations that are not on the same scale. We addressed this by defining acceptance thresholds for each dataset individually, thereby placing equal weight on each dataset and only accepting parameters that simultaneously met the threshold for all datasets. This allowed for the model to be fitted to multiple aspects of an outbreak, representing different characteristics of the disease system, including population impact, infection levels in both live and dead hosts and immunity build-up. In addition, these data sources represented varying levels of temporal aggregation of the system. By simultaneously calibrating to multiple datasets, the impact of bias in one of the datasets and the risk of overfitting is reduced. This is illustrated by the observation that removing PCR data from the model inference had little impact on parameter estimates, probably because parameters were sufficiently informed by patterns in other datasets, although the effect of removing datasets likely varies between datasets. As a consequence of calibrating to diverse datasets simultaneously, the resulting model could not capture all individual observations when these were not consistent across all datasets. The use of summary statistics, in contrast to likelihood functions, increased flexibility in the definition of optimization function and these could therefore be designed such that they are more robust to imperfect sampling compared with the full dataset. The inference validation analysis showed that our framework was able to correctly estimate unknown parameters from simulated data. These approaches enhance the usability of datasets, which would be insufficient on their own to address specific epidemiological questions. While more complete and larger datasets would be recommended for such analyses, this is unrealistic in the context of wildlife surveillance. With the increasing availability of novel surveillance data streams, possibilities to collect multiple types of data on the same outbreak are expanding. This highlights the importance of developing and evaluating computational approaches capable of integrating different data types.

Our results emphasize the importance of considering multiple host populations to understand outbreak dynamics. Ignoring the multi-host context of disease transmission can have implications for the projected effectiveness of intervention strategies or accuracy of future predictions. Advances in novel data streams and modelling techniques present highly promising developments in our ability to unravel transmission processes and characterize ‘epidemiological dark matter’.

Methods

Surveillance data

Five sources of USUV surveillance data were collected on blackbirds: (1) PCR and (2) seroprevalence in live blackbirds, (3) reported dead blackbirds, (4) PCR prevalence in a subset of these dead blackbirds and (5) annual blackbird population size. We used these to calibrate mechanistic transmission models to better understand the emergence and spread of USUV in the Netherlands. Further details of these data sources can be found in Supplementary Material C and in refs. 20,21.

Model overview

We created a stochastic, compartmental, metapopulation model to simulate transmission of USUV between Culex pipiens mosquitoes and blackbirds in the Netherlands from 2016 to 2022 (Fig. 2). Both the host and vector populations were divided into compartments on the basis of their infection status: ‘susceptible’, ‘exposed’, ‘infected’, ‘recovered’ and ‘dead’ compartments for birds, and ‘susceptible’, ‘exposed’ and ‘infected’ compartments for mosquitoes. Blackbirds were chosen as the main host species for this study because they showed the highest USUV prevalence among live birds20 and showed high mortality following USUV transmission16,19. To explore the potential role of reservoir hosts, we also created model variants that included an additional host population, representing unidentified USUV-competent species (that is, species that can transmit USUV onwards). Birds can get infected when they get bitten by an infectious mosquito. Mosquitoes can get infected when they bite an infectious bird. We assumed host frequency-dependent transmission. This follows from the assumption that the vector biting rate is independent of host density, and the biting rate experienced by hosts increases with vector density57,58. The mosquito population dynamics, extrinsic incubation period and biting rate were temperature-dependent. The model’s starting conditions were determined by the historical FOI (‘Estimated parameters’ section in Methods). The full set of equations and parameter values are described in Supplementary Material A.

The temporal resolution of the model was 1 day. We used a 5 km by 5 km grid structure with bird and mosquito abundance varying between grid cells (‘Input layers’ section in Methods). Virus transmission occurred within a grid cell, and cells were connected through bird movements. The transmission season was set from April to mid-October, with no transmission occurring outside this period. We distinguished daily foraging movement patterns from seasonal natal and breeding dispersal59,60. To allow for different movement patterns across life stages and seasons, we divided the transmission year into breeding season (April–July) and post-breeding (July–October), and the bird populations into juveniles (from fledging until the next breeding season) and adults (birds older than 1 year). Only bird movement during the virus transmission season was included, as movement outside this season was assumed not to affect transmission. Similarly, blackbird spring and autumn migration was not included, explicitly because this largely occurs outside the transmission season and Dutch blackbirds have almost completely stopped migrating over the past decades61. Movement of mosquitoes between cells was ignored owing to a lack of high-quality evidence available for parameterization62. The model was run continuously from April 2016 to the end of 2022, with the virus re-emerging in the mosquito population each year, representing the possibility of local overwintering and/or re-introductions from migratory birds. All analyses were performed in R (version 4.2.1).

Input layers

Bird and mosquito abundance

Relative blackbird abundance was obtained for each grid cell from the study by Dellar et al.26. In this Article, random forest models were fitted to blackbird point count data (n = 183,123 observations) from the Netherlands (Meetnet Urbane Soorten63, Meetnet Agrarische Soorten64 and Common Bird Census65 from Sovon Vogelonderzoek Nederland (Dutch Centre for Field Ornithology)) and France (Common Bird Monitoring Scheme66) in the period 2001–2016, using a set of environmental and climatic predictors. Relative Culex pipiens abundance was obtained for each day and each grid cell from the study by Krol et al.25. Here, data on female mosquito trap counts was obtained from the National Mosquito Survey 2010–201367 and the MODIRISK project68. Random forest models were fitted to female mosquito count data including a set of land cover, environmental and climatic predictors. Estimates for both blackbird and mosquitoes reflect relative abundance and were scaled proportionally to each other using a scaling parameter (‘Estimated parameters’ section in Methods).

Bird movements

Two movement patterns were distinguished in the model, representing daily movements and seasonal dispersal. Daily movements include foraging-type movements often within the bird’s home range, that is, the area the bird regularly traverses around in its territory. In the model this is reflected as a contribution to the FOI experienced in other grid cells. In addition to daily movements, we included seasonal dispersal, which represents the search for a new nest location. Seasonal dispersal takes place during the change from the breeding to the post-breeding season in early July, whereby birds can move to a different grid cell. We quantified both the daily and seasonal blackbird movement patterns by fitting dispersal kernels to ringing and recovery data of blackbirds ringed and recovered in the Netherlands collected by Vogeltrekstation NIOO-KNAW. This resulted in a median daily movement distance of 143 m (interquartile range 19–692 m) during the breeding season and 29 m (interquartile range 4–129 m) during the post-breeding season. Seasonal dispersal distances were larger and estimated at a median distance of 377 m (interquartile range 95–1,114 m) for juveniles and 180 m (interquartile range 19–1,062 m) for adults. We constructed movement matrices by sampling from these dispersal kernels assuming rotational symmetry (Supplementary Material B). For the additional reservoir population we explored an additional movement scenario with a median distance of 1,016 m for the breeding season and 323 m for the post-breeding season (Supplementary Material B), seasonal movement was not included.

Temperature data

Average daily temperature data in the period 2016–2022 were obtained from the Royal Meteorological Institute, with a 1 km × 1 km spatial resolution27.

Abundance and temperature data were resampled into the model grid using bilinear interpolation. A visual overview of bird and mosquito abundance, as well as monthly temperature values, can be found in Supplementary Fig. 1.

Inference

Approach

We used an approximate Bayesian computation approach using a sequential Monte Carlo sampler (ABC-SMC) to calibrate our model to surveillance data69. This approach allows for complex transmission models to be fitted to data using summary statistics, thereby avoiding having to explicitly define likelihood functions70,71. In ABC-SMC, the estimation of the posterior distribution is achieved sequentially by constructing intermediate distributions in each generation, converging towards the final posterior distribution. After each model iteration, using proposed parameters, model output is compared with the data using summary statistics. Summary statistics each represent different epidemiological aspects of the outbreak. The parameter set is accepted if the distances between the model and data summary statistics are below their respective thresholds, where the thresholds become progressively stricter each generation on the basis of results from the previous generation. For each model, we ran three chains of 200 particles and stopped when the acceptance rate reached 5% or less.

We used five summary statistics, one for each type of surveillance data: seroprevalence in live blackbirds, PCR prevalence in live blackbirds, and PCR prevalence in dead blackbirds for each month and region (north, middle and south) (Supplementary Fig. 8), as well as the annual blackbird population size relative to 2016 and the relative number of reported dead blackbirds per year within each region (Supplementary Fig. 9). In the model, regions were created by aggregating the grid cells. More details on the inference approach can be found in Supplementary Material D.

Estimated parameters

The following parameters were estimated: (1) the abundance scaling parameter to convert the host and vector abundance, allowing them to be on the same scale, meaning that their ratio reflects the vector-to-host ratio; (2) the re-emergence rate, that is, the fraction of the USUV prevalence in mosquitoes in September that persists to the subsequent spring; (3) the infection mortality rate in blackbirds (ν); (4) the transmission probability bird-to-mosquito (pmb); and (5) the historical FOI, to quantify transmission before the first detection leading to non-zero immunity levels in 2016. For the model versions including a reservoir population, the population’s natural mortality rate (μAR) and the distribution of mosquito bites between blackbirds and the reservoir population (ω) were also estimated. For a more detailed description of the parameters, including the priors, see Supplementary Material D.

Validation of inference approach

To validate the ability and accuracy of our inference algorithm, we simulated data mimicking the surveillance data available with known parameter values using the blackbird-only model. We evaluated the ability of our model framework to estimate these parameter values using five simulated datasets (Supplementary Material E). We found good agreement between true values and posterior medians (concordance coefficients 0.55–0.97) for the re-emergence rate, abundance scaling parameter, transmission probability bird-to-mosquito and infection mortality rate. The identifiability of historical FOI was poor (concordance coefficient <0.1). This parameter was still kept to ensure that the uncertainty around historical transmission is reflected in the model’s results.

Model comparisons and analyses

Four models (A–D) were created, which differed with respect to the presence and characteristics of a reservoir population (Table 1). Because there is no general consensus on the definition of reservoirs, we use a broad definition encompassing a population of animal species capable of (indirectly) transmitting infections to a target species (here: blackbirds) and enabling persistence of the virus in the ecosystem. We assumed the virus was introduced in the south as that appeared to be the first region where transmission occurred. In addition, we developed three sensitivity analyses (models S1–S3) on the basis of the best-fitting model to explore sensitivity to the location of initial virus introductions (S1), to the spatial distribution of the reservoir populations (S2) and to uncertainty in our blackbird dispersal estimates (S3). In model S1, the virus was successfully introduced (that is, leading to an infected mosquito) each day between April and mid-October in 2016 in randomly chosen locations throughout the country. In all other models, introductions happened at one-third this rate to keep the number of introductions in the south equal between all models. We also explored the impact of removing the PCR data from the surveillance data and only fitting to the remaining three datasets (Supplementary Material I). Models were compared on the basis of their distances between observed and simulated summary statistics calculated in the last generation of the ABC-SMC algorithm, where accepted particles represent the best approximation of the posterior distribution. To ensure all summary statistics’ distances were on the same scale, for each summary statistic we separately normalized the summed distances by dividing these by the maximum summed distances across all model versions.

Using the best-fitting model, we ran 100 simulations using sampled parameter sets from the posterior distributions and calculated the prevalence, seroprevalence and (partial) basic (R0) and effective (Re) reproduction numbers for each day and grid cell. Reproduction numbers were calculated using the Next Generation Matrix approach72 (Supplementary Material H).

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.