Assessing the geographic range of classical swine fever vaccinations by spatiotemporal modelling in Japan

Abstract A classical swine fever (CSF) epidemic has been ongoing in Japan since September 2018. The outbreak started in Gifu Prefecture and involved 21 prefectures by the end of October 2020, posing a serious threat to pork industries. The present study was conducted to capture the spatiotemporal dynamics of CSF in Japan and assess the geographic range of the CSF vaccination on pig farms. First infection dates were collected for wild boars and on swine farms by prefecture. A simple statistical model was used to describe the spatiotemporal dynamics of CSF, describing the infection risk in wild boars and the subsequent transmission hazards to swine farms for 47 prefectures. Because the spatial transmission mechanisms and wild boar population dynamics involved substantial uncertainties, 16 models were applied to the empirical data. Estimated hazard parameters were used to predict the risk of infection on swine farms by 15 December 2020 to explicitly evaluate the governmental recommendation for vaccinations on pig farms by prefecture in light of the predicted infection risk in domestic pigs. The best‐fit model for the wild boars indicated that transmission occurred via neighbouring prefectures and involved seasonality. The estimated conditional hazard was 0.008 (95% confidence interval [CI]: 0.001–0.014) per day for infections transmitted from wild boars to swine farms, and the median time from wild boar infection to swine farm infection was 129.4 days (95% CI: 69.5–935.0). Our prediction indicated that prefectures connected by land to those with wild boar infections had a higher risk of infection on swine farms. CSF transmission in Japan likely progressed diffusively via wild boar movement, and tracking wild boar infections may help determine the risk of infection on swine farms. Our risk map highlights the importance of deciding vaccination policies according to predicted risk.

concern over this disease has increased in Japan since its reemergence in September 2018 (Isoda et al., 2020;Ito et al., 2019). As of 27 October 2020, 59 CSF cases have been reported from swine farms in nine prefectures in Japan, resulting in the slaughter of 171,016 domestic pigs (Online Supplementary Figure S1). The spatial spread is thought to have been facilitated by wild boars, and 21 prefectures have reported CSF-positive cases (Ministry of Agriculture, Forestry and Fisheries, 2020). Consequently, the Japanese government had Japan removed from the list of CSF-free countries (World Organisation for Animal Health, 2020) and decided to protect swine farms by vaccinating domestic pigs starting in October 2019. As a consequence of vaccinating domestic pigs and loss of CSF-free status by the OIE (World Organization for Animal Health), pork exportation to the CSF-free countries was cancelled, thus financially damaging the pork industries.
The current epidemic has affected the elimination plan as well as Epidemiological studies have been conducted and published to better understand the CSF transmission dynamics in Japan. Hayama et al. (2020) used high-resolution spatial data and a geographic information system to estimate the risk of wild boars infecting swine farms inside Gifu Prefecture. Similarly, Ito et al. (2019) applied a spatiotemporal model to compute the risk of infection in the swine population within Gifu Prefecture over space and examined possible control of the wild boars. Isoda et al. (2020) demonstrated that wild boars frequently transmitted CSF to swine farms. Transmission dynamics have also been explored for African swine fever, and studies have been conducted on host species of CSF (Andrey et al., 2020;Barongo et al., 2015;Gulenkin et al., 2011;Halasa et al., 2016;Iglesias et al., 2016Iglesias et al., , 2017Iglesias et al., , 2018Korennoy et al., 2014;Kukielka et al., 2016;Lu et al., 2019;O'Neill et al., 2020;Oganesyan et al., 2013;Pautienius et al., 2018). Despite these epidemiological modelling efforts, the future prospects of spatiotemporal dynamics to account for CSF transmission across Japan remains uncertain. Quantifying the infection risk to swine in each prefecture over time will enable better vaccination policies. The present study was conducted to devise a simple mathematical model of CSF for all of Japan, calculating the infection risk in both the swine and wild boar populations for each prefecture. Using the predicted risk, we evaluated the policy advice of the vaccination campaign.

Epidemiological data
We collected datasets on wild boar and swine infections from the Ministry of Agriculture, Forestry and Fisheries (Ministry of Agriculture, Forestry and Fisheries, 2021). Infected wild boars or swine were confirmed via reverse transcriptase polymerase chain reaction (RT-PCR).
We gathered data from reports of infected wild boars and swine farms by prefecture and analysed the data available through December 2019.
In addition to the epidemiological data, we obtained wild boar population estimates from two data sources: reports of damage to agricultural products (e.g., vegetables) (Ministry of Agriculture, Forestry

Spatiotemporal modelling
We modelled CSF spatiotemporal dynamics in both wild boars and swine. We first modelled the spatial spread of the infection in wild boars and subsequently used the estimated results to quantify the risk of infection on swine farms. To model the infection hazard in wild boars, we used the relative susceptibility of wild boars: where x measures the relative susceptibility of the wild boars and y is assumed proportional to the wild boar population size (either by using the agricultural damage data or the captured wild boar counts). Both measurements were used independently; n s is the domestic pig population size (Official Statistics of Japan, 2018); L s denotes the prefectural area; and L w denotes either the prefectural area or the forest area inside a prefecture (Forest Coverage/Planted Forest Coverage as of March 31, 2017; Forestry Agency, 2017). We also accounted for seasonality as follows: where ε adjusts for the timing of seasonal variations in time, and the unit of time t is days, starting from 13 September 2019, the date when the first wild boar case was reported in Japan. To model the infection hazard in wild boars, we used two approaches: the gravity model and the neighbourhood model. The gravity model uses the Euclid distance to determine the distance-dependent decay in the transmission risk: where a ij is the hazard rate of transmission from prefecture j to prefecture i, s(t) and x i are as described above, and d ij is the Euclidean distance between prefectures j and i as measured by the location of the prefectural headquarter office. Alternatively, the neighbourhood model is formulated as where θ is the adjacency matrix (θ, {0, 1}), that is, if a land connection exists between prefectures i and j, and if j was infected, ij = 1, otherwise, ij = 0.
Using either hazard function, the daily infection risk from wild boars To estimate the parameters governing the hazard function of wild boar infections in prefecture i, we defined the event time as the date of the first report in the mth prefecture as t m . For example, the date of the first report in Gifu (the first affected prefecture) was t 0 = 0 (13 Septem- December 2019: t w was the event time of prefecture i. Given the previous event on day t w-1 , the conditional likelihood of observing infected wild boars in prefecture i is the product of the risk of infection in prefecture i on t w and the escape probability of all other prefectures j. Thus, the log-likelihood is ) .
The total log-likelihood is then calculated as l = ∑ w l w .

Modelling the hazard for domestic pigs
Subsequently, we modelled the risk of infection in domestic pigs. As was applied to wild boars, the swine population risk was also based on the hazard function. Specifically, we modelled the daily transmission risk in pigs as where represents the hazard for transmission from wild boars to swine farms and was treated as an unknown parameter. That is, we counted the risk from the date of infection in the wild boars. If the first wild boar case was reported in prefecture i on day t si , then the first domestic pig infection was reported on day t ei . Among prefectures with infected swine farms, the likelihood used to estimate the hazard rate was If t n is the latest observation date, using prefectures j with no reports of infected swine farms yields The total likelihood is L 1 L 2 . Maximum likelihood estimation was implemented to optimise the model and obtain parameter estimates.

Estimation scenarios and real-time forecasting
We used the above likelihood functions to estimate unknown parameters. Day zero was the date on which the first wild boar infection was reported from Gifu Prefecture. This yielded 16 scenarios for comparison, which arose from four dichotomous combinations: (i) whether we adopted a gravity model or neighbourhood-transmission model to model the infection risk in wild boars, (ii) whether we accounted for seasonality s(t) in the infection hazards of wild boars, (iii) whether we used the agricultural damage data or the captured wild boar counts to approximate the prefectural variations in the wild boar population size, x, and (iv) whether we used the prefecture area or the forest area to calculate the wild boar density. x axis and the true positive rate as the y axis to evaluate the model's performance and choose the best cut-off value (Hoo et al., 2017). The Youden index was defined as sensitivity + specificity − 1, and the point at which the maximum Youden index was obtained was used as the optimal cut-off point (Ruopp et al., 2008). The predicted infection risk on 15 December 2019 in wild boars or on pig farms was then computed for each prefecture, and prefectures that were predicted to have infections in wild boars or on pig farms were considered 'high-risk' prefectures that may require vaccinations for the wild boars or pig farms.

Data sharing statement
The first reporting dates for the wild boars and swine farms by prefecture are presented in the online supporting material (Supplementary Table S1).  Figure 1D). Note: Parameters β 1 and β 2 are the coefficients for factoring the population impact of the wild boar and swine density in each prefecture in the hazard function. Parameter helped identify the location for the seasonality. Neighbour and gravity refer to the neighbourhood transmission and gravity (distantdependent) models, respectively, for the wild boar infection hazard.   Figure 2B shows the risk map for swine farm infections using the same algorithm as used in Figure 2A.      Figure S1 shows the updated epidemic curve. In addition to Okinawa in January 2020, seven other swine farms became newly infected.

DISCUSSION
To appropriately quantify the spatiotemporal model of CSF transmission in Japan, we analysed both wild boar and swine datasets using a parsimonious approach and compared all possible model combinations.
Sixteen combinations were compared, and the best-fit model indicated that the neighbourhood-transmission model would capture the reality better than would the distance-based model, and the transmission pattern may involve seasonality. Using agricultural damage data for wild boar populations yielded slightly better results than did using ecolog- In our study, we used a spatiotemporal model to address the infection risk on a prefectural scale. Analyzing a finer spatial data scale would be quantitatively more useful. Given the higher resolution data, more targeted approaches, such as targeting a certain spatial unit of swine farms or focusing on specific wild boar habitats, could be considered. Seroepidemiological surveys could also be considered for future investigations. Because vaccine campaigns have been implemented for wild boars and swine, antibodies should be detected in these animals regardless of whether the animals were artificially immunised or naturally infected. Seroepidemiological surveillance may be used to identify spatial hotspots of infection, and local vaccination campaigns could potentially refer to these datasets.
Our study had three limitations.