Ecology

Here, we examine infection dynamics in the four regions of focus to learn more about how various control interventions performed in each region. Since the first documented cases emerged in these regions, the virus was able to spread freely across much of the first and second phases with a gradual increase in the control interventions. In the four regions of Makkah, Madinah, Eastern, and Riyadh, cases peaked on 12th May (6397 cases; 95% CI 5960–9697), 15th May (1967 cases; 95% CI 1625–2308), 23rd June (10367; 95% CI 8948–11785) and 11th June (11273 cases; 95% CI 11068–12491) respectively according to the fitted model shown in Fig. 2. As the epidemic progressed, more measures were adopted to contain the disease, and the disease’s infectiousness sharply decreased after the third period. There are a few factors responsible for the sudden declining trend: first our model is dependent on official data on cases that have been documented, and these data will only ever reflect a portion of the overall number of cases. Second, different regions developed different testing strategies, and some locations altered their approach to testing during the course of the time period that was investigated. It is possible that the beginning of the Hajj term (period 4) was a contributing factor in the decrease in the number of documented cases. Additionally, previous to this time period, the government indicated that it would be increasing the size of its local testing in order to detect new cases. It is possible that the efficacy of interventions would be reduced if increases are found to be occurring during the falling phase of an epidemic. This may result in measures being kept in place for a longer period of time than they would have been had more accurate data been provided.Figure 2With the use of the Delay Rejection Adaptive Metropolis method, the relevant parameters were estimated for each of the four areas of interest by fitting the data from 13th March until 25th September.Full size imageWe estimate the effective reproduction number (R_t) as an indicator of SARS-CoV-2 transmission before and after the interventions. Figure 3 depicts the dramatic shift in the rate of SARS-CoV-2 transmission as a result of decreased social contact and other control measures. At the beginning of the pandemic, (R_t) for SARS-CoV-2 in Saudi regions was between 4 and 6 as illustrated in Tables 6 and 7. In other words, on average each case spread to between four and six others. Considering that each new generation of SARS-CoV-2 cases occurs every five days, it is evident that this pandemic was rapidly expanding out of control. Moreover, we assumed that the transmission rate and the documented infection rate did not change during the first two periods since interventions were carried out gradually until a complete lockdown took place. As more measures were introduced, the spread of the disease began to decrease. Therefore, our data were based on the weekly reported number of documented SARS-CoV-2 cases broken down by region. As a result, it became clear that the reliability of the (R_t) value was relatively high for transmission.Figure 3Distribution of Rt estimates derived from 10000 MCMC samples for Makkah, Madinah, Eastern, and Riyadh, respectively. The black dot in the centre of each violin plot denotes the median, the thick bar in the plot denotes the interquartile range, and the thin bar in the plot denotes the lowest and maximum values. The mean and the credible interval for 95%, which is shown in parentheses, are labelled below or above, respectively.Full size imageThe effects of the events and interventions on the dynamics of SARS-CoV-2 in the regions of interest are considered. First, if the controls remained in phase four in Makkah, our model projects that the total number of documented cases would increase to 81047 (95% CI 79421–82672). In Al-Madinah, the cumulative number of documented cases would have increased to 22997 (95% CI 19578–26415). The number of cumulative documented cases may have reached 80520 (95% CI 78335–82704) if controls stayed steady in the Eastern region at the level they were at in phase four. If the pattern shown during the fourth period is taken into account, we estimate that there would have been 67150 (95% CI 63731–70568) documented infections in the Riyadh region. Figure 4 illustrates these findings.Figure 4The relevant parameters were estimated for each of the four regions of interest by first fitting the data of each region, and then predicting using the parameters from period 4. This was done with each of the four regions of interest separately.Full size imageWe now explore the impact of controls remaining in place at the same level as that implemented in phase three. In that case, the number of documented cases in Makkah would have increased to 116641 (95% CI 105015–128266). Similarly, the total number of documented cases in Al-Madinah would have increased to 53877 (95% CI 50458-57295) if the outbreak had been allowed to continue at the same level. If the controls had remained unchanged from how they were in phase three in the Eastern region, the total number of documented cases would have been 310459 (95% CI 298362–334981). Finally, in Riyadh this would have resulted in 665241 documented cases (95% CI 651822 to 678659). Figure 5 highlights these findings.Figure 5For each of the four areas of interest, the relevant parameters were estimated by first fitting the data of each region and then predicting using the parameters from period 3. This was carried out for each of the four areas of interest independently.Full size imageWe now investigate the impact of second-period controls remaining in place. In that case, the number of documented cases would increase to 1236642 (95% 1218314–1251626), 442865 (95% CI 439446–456283), 454031 (95% CI 441846–466215), and 2322624 (95% CI 1919206-3026042) in the regions of Makkah, Madinah, Eastern, and Riyadh, respectively (see Fig. 6).Figure 6For each of the four regions of interest, the relevant variables were identified by first fitting the data from each area and then making predictions using the parameters from period 2. Each of the four regions of interest was done separately.Full size imageThe efficacy of NPIs is dependent on when they are adopted, with earlier adoption resulting in greater success in lowering transmission rates of infectious diseases. In the early stages of COVID-19, Saudi regions made the decision to gradually implement measures in order to understand the severity of the disease and reduce the economic and social costs of lockdowns, as well as the political costs. In Fig. 6, if the government were to rely on the interventions of the second phase, then the number of cases of infection would considerably rise owing to the ineffectiveness of the measures. In the third period as in Fig. 5, the government made it possible to relax some of the control measures, but it is ultimately up to each area to decide whether they will maintain the same level of control or whether they will increase or decrease it. In comparison to the control measures carried out during the third and fourth periods, this led to significantly improved outcomes. The reason that these time periods were chosen is that there was no stiffening of the NPI response in most Saudi regions during the first two periods and control interventions were improved later on.Significant undetected infections resulted in the fast spread of new coronaviruses (SARS-CoV-2) which is illustrated in Fig. 7. The proportion of undocumented infections, including asymptomatic cases and undocumented symptomatic individuals who did not seek medical treatment or be tested for mild symptoms, was greater than that of Wuhan at the onset of the pandemic26, which may be a result of the following factors: first, the medical configuration was not optimal and public awareness was limited during the onset of the pandemic while the undocumented rate progressively increased; Second, contact tracing procedures employed in Saudi regions may have become overwhelmed if the number of early-stage cases in Saudi regions rises substantially. The discrepancy between the predicted proportions of asymptomatic (undocumented) cases may be attributable to the difficulty in the un-identifiability of parameters in epidemiological models. There were a substantial number of asymptomatic infected individuals with high infectivity in Saudi regions, where the epidemic situation escalated rapidly. Our research emphasises the frequency of asymptomatic SARS-CoV-2 cases and their role in transmission in order to increase people’s knowledge of asymptomatic cases and to serve as a guide for the prevention and control of SARS-CoV-2.Table 3 Estimated transmission rate in Saudi Regions.Full size tableTable 4 Estimated ascertainable infection rate.Full size tableIn this model, we fitted dynamic transmission rates because of varied preventable measures by the Saudi government at the level of the country or region. After a series of actions taken by the government, regions and cities went into lockdown, resulting in a decrease in the transmission rate as in Table 3. Before the interventions were introduced, in the first two periods of our study, we assumed the transmission rate did not change since individual and community responses had not effectively taken place. After severe interventions were implemented, the transmission rates were allowed to vary in later periods and reduced gradually due to the control measures that reduced the spread of disease27. Estimates of documented infection rates are presented in Table 4. Our model estimates show the documented infection rate has continued to decrease in the last two periods. Thus, the parameters we fit across periods are a measure of how effective the lockdown was in bringing down the documented infection rate28.Risk of resurgenceThe risk of resurgence in Saudi Arabia’s four regions has been examined in this section after the relaxation of intervention measures. There will be a rise in disease activity if control measures are relaxed without taking into account increases in the number of cases being detected, isolated, and/or traced. We predict the first week of no new cases of infection and the week when all current infections in Saudi Arabia will be eradicated.In the Makkah region, had the trend continued into the fourth period, the number of documented infections would have dropped to zero on average by the 6th September (23rd August to 27th September), and all infections would have been eradicated by the 26th of October (7th October to 14th November). On the 28th June, the number of weekly active infections (including presymptomatic, symptomatic, and asymptomatic cases) reached its highest point of 230,230 (95% CI 226811–234364), and on 8th September, that number dropped to 44023 (95% CI 40604–47441).Therefore, the number of documented infections would have reached zero in Al-Madinah region on average on 6th November (23rd October to 22nd November), and all infections would have been eliminated by 1st December (27th November to 14th December). On 23rd June, weekly active infections (including presymptomatic, symptomatic, and asymptomatic cases) peaked at 130,134 (95% CI 126715–133552) and then declined to 60023 (95% CI 58604–63441) on 25th September.If the trend had continued as it did in the fourth period in the Eastern region, the average number of documented infections would have reached zero on 2nd November (from 23rd October to 18th November), and the total eradication of infections would have happened on 1st December (26th November to 22nd December). The number of weekly active infections (including presymptomatic, symptomatic, and asymptomatic cases) peaked at 65000 (95% CI 61581–68418) during the week of July 23rd and subsequently decreased to 800 (95% CI 765–834) on 8th of September.Lastly, the model predicted that the number of weekly active infections in the Riyadh region (including presymptomatic, symptomatic, and asymptomatic infections) peaked on 28th June at 562332 (95% CI 513379–619542) and then decreased to 188215 (95% CI 174796–191633) on 18th September. On average, we expected that the number of documented infections would have decreased to zero on 18th October (7th October to 14th November) and that the total number of infections would have been eliminated on 1st December if the trend continued as it did in the fourth period (20th November to 23rd December). Figure 7 illustrates these findings. We found that if control measures were lifted 30 days following the first day of zero documented cases.Figure 7The estimated number of infected cases that were active (presymptomatic, symptomatic, and asymptomatic) during the research period in the areas of Makkah, Madinah, Eastern, and Riyadh respectively.Full size imageThe probability of resurgence, which we define as the number of active documented cases greater than 100 could be as high as 0.96 in Eastern, 0.95 in Madinah, 0.97 in Makkah, and 0.96 in Riyadh. If we adopt more stringent conditions of lifting controls after observing no confirmed cases for a continuous period of 30 days, the probability of resurgence decreases to 0.31, 0.28, 0.30, and 0.30, with probable resurgence occurring on 13th February, 7th February, 2nd January, and 8th January for Eastern, Makkah, Madinah and Riyadh, respectively (Fig. 8). Despite the use of a simplified model, these results emphasize the hazards of ignoring undetermined occurrences when modifying intervention techniques.Figure 8Figure demonstrating the effect of relaxing all control measures in all four regions 30 days following the first day without confirmed cases.Full size imageSensitivity analysisFor the purpose of testing the robustness of our research results, we conducted a series of sensitivity analyses by varying the durations of the latent and infectious periods, the ratio of transmissibility in asymptomatic (undocumented) cases to symptomatic (documented) cases, and the initial documented infection rate. We conduct eight sensitivity analyses (S1 to S8) within each model for each region of Saudi Arabia to assess the robustness of our model results. For instance, the sensitivity analysis performed for S1 was based on the changes of the latent period and pre-symptomatic infectious period, respectively, and other parameters remain the same. These modifications were carried out with the help of reference15,29, and the same approaches were used for the other parts of the sensitivity analysis, which is summarised in Table 5.Table 5 Description of essential model parameters that were not fitted in the MCMC, where (D_e) refers to the latent period, (D_p) refers to the pre-symptomatic infectious period, (D_i) refers to the symptomatic infectious period, (gamma _0) refers to the initial ascertain rate and (alpha) refers to the ratio of the transmission rate for P and A to I.Full size tableIn particular, for (S1), we raised the incubation period to 7 days (upper 95% CI based on ref15) and the pre-symptomatic infectious period to 3 days (upper 95% CI based on ref29). Therefore we set (D_e = 4) and (D_p=3), and modified (E_0) and (P_0) as needed. The transmissibility of the undocumented cases was assumed to be 0.46 (lower 95 % CI according to ref.31) of the infection cases for (S2); for (S3), the transmissibility of the asymptomatic (undocumented) cases was assumed to be 0.62 (upper 95 % CI according to ref31). We assumed that in (S4), the initial documented infection rate was (gamma _0) = 0.14 (lower 95 % CI according to ref13) and adjusted (A_0), (P_0) and E(0) accordingly. Similarly for (S5) we assumed the initial documented infection rate was (gamma _0) = 0.42 (upper 95 % CI according to ref13) and adjusted (P_0), (A_0), and (E_0) accordingly. In (S6) we set the variables (D_ e=3) and (D_p=1.1), and altered the values of (P_0) and (E_ 0) as necessary in accordance with13. In (S7) we assumed that the transmission rate of asymptomatic (undocumented) cases was half that of documented cases by setting 0.5. Finally, in (S8) we assumed that the infectious period ((D_i)) was double that of symptomatic cases by setting 6 days. Both (S7) and (S8) were based on30. The results of our sensitivity analysis are summarised in Tables 6 and 7. We note that the variation in the model predictions of (R_t) varies from setting to setting. However, these variations appear to be fairly small, proposing the robustness of the results to the specification of associated values in fairly realistic ranges13,13. Our sensitivity analysis provides information about the importance of each parameter to the model representing the transmission of SARS-CoV-2. An increase (or decrease) in parameter values, while other parameters’ values remain the same, contributes to an increase (or decrease) in effective reproduction numbers. For example, an increase in infectious period would result in a higher effective reproduction number at the beginning of the epidemic and a longer time required to clear all infections in Saudi regions32. Our sensitivity analysis indicates that almost all model parameters may have an important role in spreading this virus among susceptible people. In particular, the contact rate from person-to-person and the transition rate of asymptomatic (undetected) individuals play a significant role in disease spread. Our important findings, of a significant decrease in (R_t) after interventions and the existence of a substantial number of presymptomatic and asymptomatic cases, were found to be robust. This highlights that Saudi authorities should pay attention to intervention strategies in the event of a resurgence of cases and quarantining those who were in contact with active cases can effectively reduce the disease33. In Tables 6 and 7 we show the estimated effective reproduction number (R_t) associated with 95% CIs obtained from those eight sensitivity analyses for all four regions and all five time periods.Table 6 Sensitivity analysis of the effective reproduction number (R_t) for Eastern and Madinah.Full size tableTable 7 Sensitivity analysis of estimated effective reproduction number (R_t) for Makkah and Riyadh.Full size table More

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Study areaWe focused on hiking activity in the four main islands of Japan (Honshu, Hokkaido, Kyushu, and Shikoku) and nearby small islands connected to the main islands by a bridge (Fig. 1a). These islands lie between latitudes 31.0° and 45.5°N, and the total area is 361,000 km2. The islands are generally mountainous and tallest mountains in central Honshu exceed 3000 m a.s.l. (Fig. 1c). In Tokyo, mean monthly temperatures range between 5.2 °C in January and 26.4 °C in August, while they range between − 18.4 °C in January and 6.2 °C in August at the summit of the highest mountain, Mt. Fuji (3776 m a.s.l., Japan Meteorological Agency). In northern Honshu and Hokkaido, snow depth can exceed 1 m even at low elevations and high mountains are covered with snow even in southern Japan.Vegetation excluding farmland and pasture covers 70.9% of the study area and the 93.9% is forest. Plantations of mostly evergreen conifers such as Japanese cedar (Cryptomeria japonica) occupy 37.6% of the vegetation area (National Surveys on the Natural Environment by the Biodiversity Center of Japan 2nd–7th; http://www.biodic.go.jp/trialSystem/top_en.html). Secondary vegetation after past human disturbances occupies 39.4% of the total vegetation and the remaining 23.0% is primary vegetation. The typical primary vegetation types are, from north to south, boreal mixed forest, deciduous broad leaved forest, and evergreen broad leaved forest.Grid squaresRecords of hiking activity were summarized for 4244 secondary grid squares based on Standard Grid Square System, which was defined by the Minister’s Order of Administrative Management Agency in 1973. In the system, the secondary grid was defined as a grid of 5′ in latitude and 7′ 30″ in longitude, which roughly corresponds to a 10 km grid in the study area. This is the standard grid system of the government and we adopted the system for convenience in future application uses and communication with practitioners. The grids, which are defined by latitude and longitude, are different in the area up to 22% between the north and south ends. Therefore, area of each grid was included in a model as an offset term.Hiking activityAccording to a government survey in 2016, (the Survey on Time Use and Leisure Activities by the Statistics Bureau of Japan, http://www.stat.go.jp/english/data/shakai/index.htm), 10.0% (about 10.7 million people) of Japan’s population age 15 or over enjoyed hiking/mountaineering in the last year. The census showed also that hiking is more popular among urban residents in the metropolitan areas. Both multi-day expedition to high mountains and day trek to low mountains in suburban areas are popular. Because of the severe winter climate, unskilled hikers use the high mountains in summer and early autumn only. During a summer vacation, whose peak time in Japan is August, many hikers enjoy multi-day trips to distant mountains. Spring and autumn are also popular seasons because of the mild weather and the scenic beauty of the fresh green or autumn colors.Data collectionIn this study, we used number of hiking records accumulated on the most popular social networking service for hikers in Japan (Yamareco; https://www.yamareco.com) as a surrogate for flow of recreation service. For all the registered destinations in the study area, the number of hiking records for each month and the latitude and longitude of the destination were collected from the service in September 2016 with the rvest28 package in R software29. This service launched in October 2005 hosts records of the hiking route, photos, participants, and impressions of a hiking trip and facilitates communication among users. Although monthly number of records for each destination is always available on the site, the exact date of each hiking record is not always public information for privacy reasons; therefore, all of the records from the almost 11 years since the start of the service were lumped together in our analysis. Hikers may record multiple places in a single trip, so the total number of records must be larger than the number of unique trips. Users of the service sometime record a place that is not a destination, e.g. start points and stations of trails, parking areas, stations of transports, and bus stops. Such records were excluded before analyses as far as it can be judged from the name of the place. As a result, the total number of hiking records was 4,708,229 records for 16,179 destinations. Finally, these records were assigned to the 4244 grids based on the latitude and longitude of each destination and then total number of records for each grid was used as a surrogate of the recreation service flow in our analysis. Not only total number but also monthly number was used in our analysis to examine seasonal changes in associations between the service and vegetation. Total record number of the grids was strongly right-skewed; no record (handled as 0 in our analysis) was found in 2036 grids while mean and maximum record number were 1109 and 350,384, respectively.Explanation variablesFifty ecological, environmental, and social/infrastructural variables (Table S1) were prepared for each grid by using ArcGIS version 10.5 (ESRI, Redlands, CA, USA). For vegetation and land-use attributes, National Surveys on the Natural Environment by the Biodiversity Center of Japan (2nd–7th; http://www.biodic.go.jp/trialSystem/top_en.html) and National Land Numerical Information (http://nlftp.mlit.go.jp/ksj-e/index.html) were used. The proportion of sea, that of total vegetation cover (excluding agricultural land and pasture) to land area, that of agricultural land (including pasture) to land area, that of natural vegetation (vegetation excluding plantations) to total vegetated area, and that of primary vegetation (vegetation with no record or evidence of a disturbance) to natural vegetation were summarized at four spatial scales: a radius of 10 km, 20 km, 50 km, and 100 km from the center of each grid. Spatial patterns of the three vegetation variables in 10 km radius were summarized in Fig. 1d–f.Maximum elevation, minimum elevation, and ruggedness (index of topographic heterogeneity30) were summarized at the four spatial scales based on a digital elevation model (10-m resolution) provided by the Geospatial Information Authority of Japan (https://fgd.gsi.go.jp/download/menu.php). For climatic variables (annual and monthly mean temperature, annual and monthly precipitation, annual and monthly hours of sunshine, and annual maximum snow depth), the National Land Numeric Information provided by the Ministry of Land, Infrastructure, Transport and Tourism of Japan (http://nlftp.mlit.go.jp/ksj-e/index.html) was referenced. Densities of population and roads at the four spatial scales were prepared from population census data from the Statistics Bureau of Japan (http://e-stat.go.jp/SG2/eStatGIS/page/download.html) and the National Land Numeric Information. For calculation of these densities, the sea surface was excluded. In addition, latitude and longitude of center of each grid were also used as explanatory variables to average effects of spatial coordinates.Statistical analysisIn this study, we employed BRT, a machine-learning method based on regression trees31 for modeling the complex relationship between a CES flow and landscape attributes12. BRT is an ensemble learning method where multiple regression trees are sequentially combined to minimize the loss function by means of gradient descent. This technique has advantage in the development of a model with a high predictive performance, in which high-dimensional interactions among explanatory variables and nonlinear responses are fully accounted for. In ecology, BRT has been frequently used for modeling of a species distribution32.Total and monthly numbers of hiking records were modeled as a function of the 50 variables described above under the assumption of a Poisson response. For temperature, precipitation, and hours of sunshine, annual and monthly average were used for the analysis of total and monthly records, respectively. In modeling by BRT, parameters for building of each learner and assembly of the learners must be carefully chosen to maximize generalization ability of a model31. In our case, candidate parameters were 2, 5, and 10 for the maximum depth of variable interactions for each learner; 2, 5, 10, and 20 for the minimum number of observations in the terminal nodes for each learner; 0.5 and 0.75 for the proportion of training data used for building each learner; and 1000, 2000, 4000, 6000, 8000 and 10,000 for the total number of learners (Table S2). In the model assembling process, the value of 0.01 was used as a shrinkage parameter. Ten-fold cross validation was used to obtain the best suites of parameters. R2 based on sum of squares:$${R}^{2}=1-frac{{sum ({y}_{i}-widehat{{y}_{i}})}^{2}}{{sum ({y}_{i}-overline{{y }_{i}})}^{2}}$$
was used for evaluation of the model’s prediction performance. The importance of explanatory variables was evaluated as an increase of mean absolute error after 100-times permutation of a variable33.Effects of each explanatory variable (a landscape attribute) on the response variable (record number) and the context dependence were visually inspected by individual conditional expectation (ICE) plot34. ICE plot visualizes the effect of a given explanatory variable for each observation by connecting outcome of a model for shifting values of the focal explanatory variable throughout the range while keeping other explanatory variables as the original value. Predictions were performed in log-scale and each line was centered to be zero at the left end of the x-axis to show relative effects of explanatory variables (c-ICE plot sensu Goltstein et al.34). Each line in ICE plot can be colored based on value of the second explanatory variable to assist assessment of the interactive effects of the two predictors. Friedman’s H statistic35 was used to detect explanatory variables whose interaction with the vegetation variables are important and therefore should be used for color-coding of an ICE plot. Friedman’s H is defined as a proportion of variance of partial dependence estimates explained by interactive effects for arbitrary suites of explanatory variables.Then, expected impacts of 0.1 decrease in the three local vegetation variables were assessed by the trained model and mapped. Although vegetation variables were sometimes more important at larger spatial scales (see “Results”), we focused on vegetation at a local (10 km radius) scale because most changes in vegetation occur at the scale in Japan (National Surveys on the Natural Environment by the Biodiversity Center of Japan, https://www.biodic.go.jp/kiso/fnd_list_h.html).All statistical analyses were performed using the R software packag29. The gbm36 package was used for BRT, the iml37 package was used for calculation of Friedman’s H statistic, and the cv.models (Oguro, https://github.com/Marchen/cv.models) packages was used for cross validation and parameter tuning. More

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