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Study area and camera trapping systemThe study area included the northern region of Tochigi Prefecture, Japan (Fig. 2). In Tochigi Prefecture, 54.4% of the land was covered by forest, 19.1% was covered by agricultural land in 2019 (Tochigi Prefecture 2021, https://www.pref.tochigi.lg.jp/a03/documents/keikakusho2267.pdf, accessed on Feb. 10, 2023). The northern region of Tochigi Prefecture has a relatively large area of forest. This area was the home range of the highest density of sika deer in Tochigi Prefecture in 2021. The camera trapping system consisted of 14 cameras (model no. 6210; Ltl-Acorn, Des Moines, IA, USA) that were placed in late April 2018 at 12 sites within the forest interior with two camera sets, namely ID 10–11, and ID 12–13 in neighboring areas (Fig. 2). The 12 sites spanned 84 km from west to east and 39 km from north to south (Fig. 2). The elevation of the sites ranged from 349 to 1033 m. The cameras were set horizontally at 50 cm above the ground and were operated until late November 2018. The cameras were checked every 1 or 2 months and the batteries and memory cards were replaced when necessary. Movements of the sika deer were reordered monthly from May to November. The month of April was excluded because the cameras were placed in late April. The virtual ecological model required the presence/absence of records for validation (described below), thus the number of deer captured in the photos was not considered. Finally, the visit and occupy of sika deer were recorded at 14 sites each month.Figure 2Study area, analytical units, and locations of the camera traps.Full size imageA grid size of approximately 1 km (termed “1-km mesh” hereafter) was used a as the study unit (Fig. 2). The 1-km mesh grid system is a standard Japanese unit used for several types of statistics (https://www.stat.go.jp/english/data/mesh/02.html, accessed on Feb. 10, 2023). To determine the appropriate number of 1-km mesh grids for the simulation study, a 10-km mesh grid, which is the high-order standard Japanese unit (i.e., one 10-km mesh includes 100 1-km meshes), was divided into the minimum number of areas to cover all 14 camera sites as the simulation target area to avoid arbitrary (Fig. 2). Finally, 4200 1-km mesh areas were included for the simulation (Fig. 2).Virtual ecological modelA simple cellular automaton (CA) model can predict the visit and occupy of a target species based on candidate habitats in consideration of the proximity to food resources32. The grid was set to the same size as the unit of the predicted ranges. The model yields a theoretical number of visits (described below) to each cell, which serves as an area preference of the target species. Each cell has two parameters: cell identification (ID) and movement path vector (Fig. 3a). The cell ID indicates the spatial location of the cell within the study area. The movement path involves four variables representing the four directional vectors into adjacent cells (i.e., top, left, bottom, and right) (Fig. 3b). Each variable is a probability value (i.e., 0 to 1) independent of the other three variables that indicates the probability of movement success to the adjacent cells. In this study, the probability value was based on the proximity to availability food resources.Figure 3Basic structure of the cellular automaton model. (a) Two values are associated with each cell: the cell ID “x,” a unique ID for each cell, and the movement probability “mx” indicating four directional vectors into adjacent cells. (b) Values m1, m2, m3, and m4 indicate the probability of movement along a path of the top, left, bottom, and right cells, respectively. If all movement probability values are 0, the virtual population in this cell cannot move to any other cell. If all movement probability values are 1, the virtual population in the cell can move to all adjacent cells.Full size imageA group of sika deer was used as the unit for analysis. The model simulates the capability of movement within the target area. Thus, if a virtual population visited a neighboring cell, the number of visits to the cell is increased without disappearance of the starting cell. The virtual population moves in accordance with the movement probability values.Movement probability between cellsThe term “movement probability” is defined as the probability of movement success into an adjacent cell to the top, left, bottom, or right (Fig. 3b) with four probability values:$$ {text{Movement probability x}} = {text{mx}};({text{m}}1,;{text{m}}2,;{text{m}}3,;{text{m}}4), $$
(1)
where m1, m2, m3, and m4 indicate the probability of movement success into the top, left, bottom, and right cells, respectively (Fig. 3b). Since these values are independent of one another, the maximum and minimum sums of m1, m2, m3, and m4 are theoretically 4 and 0, respectively. If all probability of movement success values are 0, the sika deer population in this cell cannot move to any other cell. Moreover, if all probability of movement success values are 1, the population in the cell can move to all adjacent cells.The amount of food resources of deer was acquired from remote sensing measurements35,36. Thus, two variables were used to represent food resource availability: the kernel normalized difference vegetation index (kNDVI)41 and landscape structure (Supplementary Fig. 1).The kNDVI uses remote sensing measurements to assess the components of green vegetation41. As compared to the ordinal NDVI, which is the most widely used index of the condition of vegetation on terrestrial surfaces, the kNDVI has greater resistance to saturation, bias, and complex phenological cycles, and exhibits enhanced robustness to noise and stability across spatial and temporal scales41. The kNDVI appropriately represents the condition of vegetation to reflect the food resource availability for sika deer. The kNDVI was analyzed from the atmospherically corrected surface reflectance observed with the Landsat 8 Operational Land Imager and Thermal Infrared Sensor instruments at approximately 16-day intervals with a spatial resolution of 30 m (data collected in 2018). The mean kNDVI was calculated monthly for each 1-km mesh within the study area. The probability values (m1, m2, m3, and m4) were defined as the proximity to available food resources in a destination cell divided by the maximum value of the target area as relative values throughout the study area. These values reflect the spatial positions of the available food resources in the study area. If the food resources are continuously available, then the sika deer population tend to visit and occupy linearly.The landscape structure is defined as a mixture of forests and grasslands because previous studies suggest that the forest edge has high availability of food resources for sika deer37,38,42,43. The dataset was generated from a current vegetation map that classified the dominant plant species provided by the Biodiversity Center of Japan (Ministry of the Environment, https://www.biodic.go.jp/index_e.html, accessed on Feb. 10, 2023). The types of vegetation of the forests and grasslands were retrieved from the literature, then the original vegetation classes were re-classified44 and overlayed on the 1-km mesh map. In this study, agricultural land types were classified as grassland. For a mesh with both forests and grasslands, the probability of movement was assigned a value of 1, while a mesh with either a forest or grassland was assigned a value of 0.5, because to treat these 2 components fairly. Every mesh of the study area included either a forest or grassland.Movement simulationFirst, simulations were conducted using two independent variables: kNDVI and landscape structure. Each simulation was initiated from one cell with the month, which is referred to as a “trial.” One step is defined as one day, thus the trial conducted in May consisted of 31 steps. A previous study reported that sika deer can travel about 50 km every 2 weeks34. Thus, one step (movement of 1 km) in one day was considered a reasonable distance. Each trial was repeated for all cells i.e., all cells was used as the starting cell of “trial”. The sum of all trials is termed a “run.” Thus, each “run” consisted of n trials, where n is the number of cells in the CA field. In this study, there were 4200 cells. At each step, each attempt to visit a neighboring cell (top, left, bottom, and right) was based on movement probabilities. For each successful movement, the presence/absence value assigned to the cell was increased from 0 to 1, i.e., change from absence to presence. The next step was then initiated from any newly visited cell and the previously visited cells. Cells with high values indicated the possibility of visitation by a virtual population from several other cells. The assigned value was used as a metric of the preference of the visited cell. In this study, 100 runs were conducted each month from May to November.Second, simulations were conducted using a combination of movement-related variables with two types of combination models: kNDVI AND landscape structure and kNDVI OR landscape structure. With both the logical AND and OR models, each step has two processes: probability approach with the kNDVI and landscape structure. With the AND model, if the virtual population passes the probability of the kNDVI to move to a neighboring cell, then the probability of movement to a neighboring cell is based on the landscape structure. In the logical AND model, we used kNDVI first because that could reflect a seasonal change in the availability of food resources. With the OR model, if the virtual population passes the probability of the kNDVI, or passes that of the landscape structure, the virtual population can move to any neighboring cell.Additionally, equivalence model simulation was conducted with all probability values (m1, m2, m3, and m4) set to 0.5.Validation of the simulation results using the camera trap dataThe results of the CA model simulation were validated by the presence/absence of the monthly records of sika deer collected with the cameras. The occurrence of a visit to a camera was determined using a generalized linear model with a binomial distribution (log link) and model selection based on Akaike’s information criterion (AIC). The explanatory variable was the theoretical number of simulated visits to a 1-km cell with a camera trap. If the AIC value of the model was  > 2 points lower than that of the null model45 (i.e., with no explanatory variable), the run was considered “correct”. The data from the kNDVI, landscape structure, AND/OR, and null/equivalence models were used. The number of “correct” runs of every 100 runs with each model was calculated. Therefore, all values could theoretically be 100.Then, the predictive ability of the model was evaluated using the results considered as “correct” with the AIC. The AIC values of all runs were compared, where one simulation set used four variables. If the four models (i.e., kNDVI, landscape, AND, and OR models) were all “correct” in one run, the AIC values were compared and the lowest AIC value of the model was recorded. Notably, differences among the AIC values were not considered because the effectiveness of the model was already evaluated in the first validation procedure. Calculations for all months were conducted. Therefore, the maximum value among the four models was 100, assuming that the run was “correct” with the lowest AIC.Finally, a map was generated of the theoretical number of visits by sika deer in each month based on the best performance among the four simulations. The map included the average number of theoretical visits over 100 runs. The results considered incorrect were not excluded because in real-world applications, simulated results are not evaluated.All statistical analyses were performed using R software (ver. 4.0.2; https://www.r-project.org/, accessed on Feb. 10, 2023). More

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To supplement the limited publicly available information on rabies risk, the US Centers for Disease Control and Prevention (CDC) performs an annual country-by-country qualitative assessment of rabies risks and protective factors. The results of this assessment are released annually in an open-access database of core metrics consisting of the presence of lyssaviruses (specifically canine or wildlife rabies virus variants, or other bat lyssaviruses), access to rabies immunoglobulins and vaccines, rabies surveillance capacity and canine rabies control capacity18. The analysis presented here builds upon the current CDC evaluation and specifically examines publicly available data to better inform the parameter of rabies surveillance capacity. This study found publicly available data regarding rabies animal testing by species, described testing practices in relation to the country’s human and dog populations, as well as by their stage of DMRVV control (defined by WHO), and used this data to calculate a surveillance testing threshold for DMRVV endemic countries.Data sources were categorized into four tiers, with the order reflecting the preference for selecting the most appropriate data for the purposes of this analysis. Tier 1 data sources were considered to be the preferential data source and included any official government data submitted to a Regional or International data repository. Official data repositories included the WHO GHO, Pan-American Health Organization Regional Information System for Epidemiologic Surveillance of Rabies (PAHO SIRVERA), and the European Rabies Bulletin. Tier 1 data sources also included official country reports found through literature search, so long as they were publicly available. Tier 2 data sources consisted of published reports in peer-reviewed literature or on a ministry of health or agriculture site that includes data from the entire country, as well as unofficial data repositories (e.g., Global Alliance on Rabies Control (GARC) Rabies Epidemiologic Bulletin). Tier 3 data consisted of one-time cross-sectional studies or studies describing sub-national testing activities and which could not be reliably extrapolated to an entire country. Tier 4 data sources include any resource not captured in the previous criteria that were obtained during literature searches. The primary data search was conducted in September 2021, with an update in September 2022. Only Tier 1 and Tier 2 data sources were included in the evaluation of animal testing rates. If multiple data sources contained conflicting testing rates, we prioritized data from surveillance repositories, then reports from ministries of health or agriculture, and, finally, peer-reviewed publications.For Tier 1 data (i.e., surveillance repository), data was included in this study if it described rabies testing conducted between the years 2010 and 2019. As political, economic, and epidemiologic factors directly influence the reliability and transparency of surveillance system data, we decided that a ten-year limit would capture any year-to-year variation in data and better characterize current passive surveillance practices. Additionally, the cutoff of 2019 was chosen so that the effects of the COVID-19 pandemic on rabies surveillance capacity would not affect this comprehensive evaluation and would account for lag time in reporting to Tier 1 data sources19,20. This study assumed data from these surveillance repositories is entered secondary to passive surveillance systems. If data was known to be from active surveillance activities, it was removed from analyses.For Tier 2 data (i.e., peer-reviewed publications), certain publications presented aggregated testing data that included years prior to the Tier 1 cutoff (i.e., 2010). To increase inclusivity of eligible data and keep the findings from this evaluation representative of current practices, eligible data must have had an end year ≥ 2012, regardless of the starting year of data (Table S1). The literature search was conducted on PubMed, Scopus, and Google for “rabies” AND “[country name]” from 2010 to December 2021. “Publicly available” was defined as any result appearing in PubMed or Scopus, or within the first three pages of a Google search. Exceptions to the first three pages were made for similar country names (e.g., Guinea, Congo). The first 10% of Spanish- and French-speaking countries were also searched for “rabia” and “raj,” respectively, to potentially capture any other sources of surveillance data. However, after no additional data was found, this was discontinued. If an article or resource quantifying animal testing capacity within these criteria was not found, the country was deemed to not have readily available data for analysis.For any countries that were part of the surveillance threshold calculation for DMRVV endemic countries, the preferred tiered data was compared to all other data sources. For one country (i.e., Brazil), there was a notable lack of dog testing data and known discrepancies in data reporting between their two reporting systems (i.e., SINAN, SIRVERA)21. In this situation, a median rate was calculated between a Tier 1 and Tier 3 data source. No other such discrepancies were noted. The type of surveillance (active or passive) was noted for each data source; we assumed passive surveillance with Tier 1 data unless compelling evidence existed to display that this was not the case. A strictly active surveillance program was excluded from all analyses. A summary of overall testing practices was performed and standardized according to the number of years each data source contained.As evaluations of rabies testing rates spanned over multiple years, population estimates were obtained to reflect the most recent year in the available data. Three separate testing rates were calculated and standardized based on the human population within the country: [1] All animal, [2] Domestic animal, and [3] Wildlife. There are different social and cultural behaviors that affect the human to dog ratio and interactions between people and animals. These differences can impact the susceptibility of dogs to rabies virus infection and the likelihood of human interactions with rabid animals. Therefore, we additionally calculated country testing rates standardized by the estimated dog population, to provide an additional indicator value of adequate surveillance capacity. Estimated dog populations were obtained from a previous study22. This resulted in up to four calculated rabies testing rates per country, depending upon available data.Equation 1: All-animal per human testing rate (AAHR)$$frac{Average,number,of,all,animals,tested/year}{{Estimated,human,population}} times 100,000$$
(1)
Equation 2: Domestic animal per human testing rate (DAHR)$$frac{Average, number, of, domestic, animals, tested/year}{{Estimated, human, population}} times 100,000$$
(2)
Equation 3: Domestic animal per dog testing rate (DADR)$$frac{Average, number, of, domestic ,animals, tested/year}{{Estimated ,dog, population}} times 100,000$$
(3)
Equation 4: Wildlife per human testing rate (WHR)$$frac{Average, number ,of, wildlife, animals, tested/year}{{Estimated ,human, population}} times 100,000$$
(4)
The WHO rabies epidemiologic Status is divided into five categories in escalating levels of dog rabies control: [1] Endemic dog-transmitted human rabies, [2] Endemic dog rabies, [3] Sporadic dog-transmitted rabies, [4] Controlled dog rabies, and [5] No dog rabies. The WHO Status was established based on existing data and expert knowledge to help better define the level of rabies control for each country23. In addition to these five WHO Statuses, countries in Status [5] were further sub-categorized into [5a] (rabies virus free), and [5b] (wildlife rabies enzootic) based on CDC’s wildlife rabies status; the CDC rabies status was also used for any country without a WHO Status (n = 11)24. Average testing rates for the aforementioned equations were calculated for each WHO Rabies Status category, treating each country as an equally weighted value in the rate calculation. Only descriptive analyses were conducted to describe surveillance and testing data, as data quality was not deemed acceptable for multi-variable statistical analysis and testing rates were heavily left-skewed. Data is presented as median and IQR as the data was noted to not reflect a parametric distribution.Ethics approvalThis activity was reviewed by CDC and was conducted consistent with applicable federal law and CDC policy. (See e.g., 45 C.F.R. part 46, 21 C.F.R. part 56; 42 U.S.C. §241(d); 5 U.S.C. §552a; 44 U.S.C. §3501 et seq.) The views and opinions of the manuscript are of the authors alone and do not represent those of CDC or any other federal agency. More