Regardless of whether the global navigation satellite system (GNSS)/inertial navigation system (INS) is integrated or the INS operates independently during GNSS outages, the stochastic error of the inertial sensor has an important impact on the navigation performance. The structure of stochastic error in low-cost inertial sensors is quite complex; therefore, it is difficult to identify and separate errors in the spectral domain using classical stochastic error methods such as the Allan variance (AV) method and power spectral density (PSD) analysis. However, a recently proposed estimation, based on generalized wavelet moment estimation (GMWM), is applied to the stochastic error modeling of inertial sensors, giving significant advantages. Focusing on the online implementation of GMWM and its integration within a general navigation filter, this paper proposes an algorithm for online stochastic error calibration of inertial sensors in urban cities. We further develop the autonomous stochastic error model by constructing a complete stochastic error model and determining model ranking criterion. Then, a detecting module is designed to work together with the autonomous stochastic error model as feedback for the INS/GNSS integration. Finally, two experiments are conducted to compare the positioning performance of this algorithm with other classical methods. The results validate the capability of this algorithm to improve navigation accuracy and achieve the online realization of complex stochastic models. Modeling and estimation of inertial sensor errors are generally challenging tasks, especially for low-cost inertial micro-electromechanical system (MEMS) sensors, since the error model has complex spectral structures. For a global navigation satellite system (GNSS) and inertial navigation system (INS) integrated system, it is usually performed through a general Kalman filter, e.g., an extended Kalman filter (EKF), which is closely related to the inertial sensor modeling. When the GNSS signals are partially or completely unavailable, the INS operates in coasting mode, i.e., the navigation parameters can be estimated completely independently of the GNSS. Consequently, the overall navigation performance depends greatly on the accuracy of the inertial signal, or more precisely, on the errors of the inertial signal. These errors are integrated into the INS, and their impact increases dramatically over time. In conclusion, accurate modeling and estimation of the error of inertial signals are crucial for improving the quality of navigation performance.The errors of inertial sensors can generally be divided into deterministic errors and stochastic errors. Most deterministic errors can be compensated for by physical models and have been widely studied ,2,3, whiThe algorithm in this work is designed under the frame of INS/GNSS integration within KF. The main contributions of this paper are as follows: Firstly, this paper realizes autonomous stochastic error modeling by constructing a complete stochastic error model and a model ranking criterion. Secondly, this paper proposes a static state detecting algorithm with an adaptive threshold. It collects and accumulates static data when the vehicle stops. Finally, the frame of INS/GNSS integration is developed, combining autonomous stochastic error modeling and detecting module as feedback within the EKF. It realizes online modeling of the stochastic errors and provides a more accurate navigation solution as the vehicle runs. Two experiments, the GNSS denial experiment and GNSS available experiment, are designed to validate the feasibility of the proposed algorithm.The rest of the paper is organized as follows: Generally, measurements of inertial sensors have various errors which contaminate the true measurements from the gyroscopes and the accelerators, decreasing the performance of the navigation solutions. For inertial sensors, the angular rate of the gyroscope and the specific force observation equation of the accelerometer are calculated as follows:GMWM is a recently proposed technique to model the sensor noise When GNSS signal is received, the INS/GNSS integration within EFK obtains the navigation solution. Differing from traditional INS/GNSS integration, this system has an additional feedback to the EKF and has a stochastic error model as an augmented error vector in the EKF. When GNSS signal is blocked, the INS works in coasting mode;The feedback consists of autonomous stochastic error modeling of inertial sensors and the detecting module. The raw observations from the IMU will go to the detecting module. The static state detecting with adaptive threshold judges the motion state of the vehicle. If the vehicle is static, e.g., waiting before traffic lights or temporarily avoiding pedestrians or other vehicles, the IMU data accumulate during this static duration. After bias removal, accumulations will go to autonomous stochastic error modeling where the GMWM will prepare the best model of inertial stochastic error. Meanwhile, the angular rate detector will judge if the angular rate of the vehicle is higher than 30°/s. If not, the best model can work as an augmented vector together with the navigation error models in a Kalman filter. The Kalman filter outputs the bias of gyros and accelerators fed to autonomous stochastic error modeling in return;The IMU data for autonomous stochastic error modeling only accumulate during the static duration; therefore, the amount of data is quite small, and the calculation is generally completed within a few seconds. As the vehicle runs, the IMU data accumulation increases with extension of the static duration; consequently, the accuracy of the stochastic model improves.GMWM is an estimation method based on the idea of generalized method of moments (GMM) estimators and the wavelet variance (WV) . The GMWThe wavelet coefficients are built using wavelet filters WV is defined as the variance of the wavelet coefficients, For a finite observed process, the MODWT-estimated WV can be calculated as follows:The PSD of the wavelet coefficient, found in ,14.The next step is the parameter estimation of the possible model, Within our research interests, the problem of modeling and estimation focuses on the stochastic error components affecting gyroscopes and accelerators. Hence, we restricted the possible models, del (AR) ,21,22,23In order to cover as many basic stochastic processes as possible, this paper defines the complete model of IMU stochastic error asThe complete model consisting of these basic stochastic processes is universally suitable to a variety of inertial sensors. When identifying the structure of the stochastic error, all the combinations of these basic stochastic processes within the complete model are regarded as the candidate models. Then, parameters of all the candidate models are estimated by GMWM and later, the best or most suitable model is selected by a designed model ranking criterion.After using GMWM to estimate the parameters of all candidate models, it is necessary to establish a model ranking criterion according to the actual requirements of noise modeling and estimation in the practice appliance. According to this criterion, candidate models are evaluated and ranked to select the most suitable one. Ref.  gave a rThe objective function given by Equation (6) can be regarded as a mismatch between the WV calculated by the model After the parameter estimation of all candidate models is completed by GMWM, all candidate models are evaluated by the GOF criterion, and the model with the smallest GOF value is selected as the optimal model.A summary of the overall flow of autonomous stochastic error modeling of inertial sensors is shown in For the vehicle navigation system, the inertial outputs contain some specific constraint information under different motion states. Under the premise of adding no extra cost and devices, the information can provide additional constraints for the navigation system, which is helpful to improve the accuracy and stability of the integrated navigation system. In particular, when the vehicle is in a static state, the inertial sensor is not affected by vehicle maneuvers, so the accelerations kept stable and the velocity remains close to zero. Nevertheless, the stability analysis of the accelerometer output can be performed to detect the static states. A common method is to use the standard deviation of the accelerometer output in a fixed time window as the test statistic :(9){Ti physically means that when the standard deviation of the data is smaller than the test threshold, it is more inclined to assume that the vehicle stays in a continuous static state, so the detection threshold increases to make it easier to detect the static state. The second item physically means that if the standard deviation of the data between the current epoch and the previous epoch is quite large, the motion state of the vehicle has changed. It is more inclined to assume that the vehicle is not in the static state, so the detection threshold decreases to make it more difficult to detect the static state. The effect of this static state detection method with adaptive threshold will be experimentally verified in The static state detection with an adaptive threshold works together with the angular rate detection as the detecting module to provide extra guidance for autonomous stochastic error modeling. The detecting module is supported by two important conclusions given in . One is In practical applications, ranking all candidate models to identify the error structure will take up the most majority of the calculation time. However, identifying the structure will be conducted only once, i.e., after the first static duration, since the structure will not differ with the dynamic variations. Once the error structure is determined, only the parameter estimation of this fixed model structure will be conducted later through the experiment, and it can be processed within several seconds. It means that the autonomous stochastic error modeling lasts only a few seconds after the vehicle starts moving, then the KF will be able to adopt the stochastic error to obtain the navigation solution.(1)GNSS denial experiments, which are designed to verify the feasibility of the autonomous stochastic error modeling based on GMWM;(2)GNSS available experiments, which are designed to verify the feasibility of the proposed algorithm for online stochastic error modeling of inertial sensors. We compare the navigation performance of the proposed algorithm with the other traditional methods and further analyze the performance of the proposed algorithm in different trajectory sections as the car runs.This section is split into two main parts:As previously mentioned, AV is probably the most commonly used method for model identification and sensor calibration. In 1998, the IEEE standard officially put forward this technique as a noise identification method to determine the characteristics of the underlying random processes that perturb data. In general, AV only considers five basic stochastic processes: QN, WN, BI, RW, and DR. These processes correspond to the linear regions in a log–log plot, which will present a typical U/V-shaped curve in ideal circumstances. Therefore, parameters are usually estimated by performing linear regression of  identified linear regions in such log–log plots. Further research on this principle can be found in ,25,26. AThe trajectory was produced by a car with SPAN NovAtel-CPT driving around an urban area of Beijing on 18 June 2021. The reference is provided by SPAN NovAtel-CPT under the post-processed solution. The raw IMU data were collected statically for 2 h at 125 Hz by SPAN NovAtel-CPT, as shown in Based on the optimal model autonomous selection method proposed in The five gyro stochastic models to be validated are as follows:Model 1: Loosely coupled navigation solution;Model 2: AV-based model;Model 3–5: GMWM-based model with three minimum GOF values .The navigation drifts of the five models at the end of three GNSS outages are shown in As mentioned above, human judgment in the identification of five noise terms will absolutely cause deviation in estimation parameters when performing Allan variance. Aiming to solve this problem, reference  providedIn this experiment, the trajectory was produced by a car with SPAN NovAtel-CPT driving around an urban area of Xuzhou on 16 April 2018. The reference trajectory was provided by SPAN NovAtel-CPT under the post-processed solution, as shown in The result of static state detection with adaptive threshold for the X axis during the whole trajectory is shown in Based on the detection results of static states, raw IMU data accumulate during the static epochs, reaching a duration of 318 s. The accumulation of static data was fed to the GMWM-based model, the AV-based model, and the EM-based model. For a clear view of the estimation results of these two methods, It is worth mentioning that AV plot-plot of X axis and Y axis does not present a typical U- or V-shaped curve. Only WN and RW can be identified from the X axis and only WN and BI can be identified from the Y axis. The amount of data accumulation is quite small; therefore, it requires a much larger amount of data to present the specific characteristics of other processes. Moreover, the human identification in each process is probably unreliable, then the parameters estimated by performing linear regression of these visually identified linear regions may have significant deviations. The EM-based approach is very sensitive to the initial values of parameters. When the initial values are “far” from the true values, the EM-based approach is likely to converge to a local minima. Hence, the initial values are set to the results estimated by AV.Based on the stochastic error model generated above, three models were compared as follows:Model 1: INS/GNSS integration within EKF;Model 2: EKF with AV-based model;Model 3: EKF with EM based model;Model 4: EKF with an online GMWM-based model.The reference trajectory is shown in the left column in Moreover, the stochastic error model become more and more accurate with the accumulation of the static data. Particular attention should be given to the time-taken for the online algorithm. All the static epochs detected take up 318 s in the whole trajectory. Due to the relatively small amount of data accumulation, calculations with the online algorithm take little time. After the first relatively long stop, identifying the model structure and estimating the parameters takes 1.4 min. After that, only the estimation of the fixed model structure will be performed, which takes much less time, i.e., it is finished within 3 s. This paper proposes a new method for online modeling of stochastic errors of inertial sensors, which combines static state detection with an adaptive threshold and the autonomous stochastic error model based on GMWM. Firstly, the limitations of other widely used stochastic modeling methods including AV and PSD are analyzed. Then, two experiments are designed to compare the online GMWM algorithm with the AV-based method and the EM-based method. The GNSS denial experiment proves the feasibility of the proposed autonomous stochastic error model based on GMWM. Meanwhile, it reveals the capability of the online GMWM algorithm to estimate the stochastic error and limit the navigation drift. The GNSS available experiment demonstrates that the online GMWM can significantly improve the navigation accuracy as the vehicle runs. Moreover, it validates the online performance as well.This paper mainly focuses on exploring the stochastic error of inertial sensors, which is related to the natural characteristics of the sensor itself. Meanwhile, for vehicle-mounted sensors, the dynamic environment of the vehicle may affect the error behavior of the sensor as well. Given the conclusions of our research, a stochastic error model in a static environment can work instead of a model at low speed. Therefore, further study is warranted on how to construct the error models and estimate the parameters based on dynamic characteristics. We will focus on how the inertial error model changes with vehicle maneuvers at high speed. Future work aims to set up and conduct experiments which enable the construction and analysis of error signals acquired in dynamic environments. Therefore, the observability of some processes and the justification of employing complex stochastic models for MEMS inertial sensors can only then be fully verified.


Content-centric vehicular networks (CCVNs) have considered distributed proactive caching as an attractive approach for the timely provision of emerging services. The naïve caching schemes cache all of the contents to only one selected roadside unit (RSU) for requested vehicles to decrease the data acquisition delay between the data source and the vehicles. Due to the high deployment cost for RSUs and their limited capacity of caching, the vehicular networks could support only a limited number of vehicles and a limited amount of content and thus decrease the cache hit ratio. This paper proposes a mobility-aware distributed proactive caching protocol (MDPC) in CCVNs. MDPC caches contents to the selected RSUs according to the movement of vehicles. To reduce the redundancy and the burden of caching for each RSU, MDPC distributes to cache partial contents by the movement pattern, the probability to predict the next locations (RSUs) on the Markov model based on the current RSU. For recovery of prediction failures, MDPC allows each RSU to request partial missing contents to relatively closer neighbor RSUs with a short delay. Next, we expand the protocol with traffic optimization called MDPC_TO to minimize the amount of traffic for achieving proactive caching in CCVNs. In proportion to the mobility probability of a vehicle toward each of the next RSUs, MDPC_TO controls the amount of pre-cached contents in each of the next RSUs. Then, MDPC_TO has constraints to provide enough content from other next RSUs through backhaul links to remove the delay due to prediction failures. Simulation results verify that MDPC_TO produces less traffic than MDPC. With the emerging demand for content-based applications, content-centric networking (CCN) has attracted attention for the next-generation communication paradigm . In partIn the existing vehicular networks, each vehicle has its own on-board units (OBUs) so that it has a wireless networking function and can be provided content via the nearest roadside unit (RSU). The vehicles can connect with RSUs through vehicle-to-infrastructure (V2I) communication. The vehicles send their interests to obtain requested contents; then the RSUs could relay the requested contents provided from the remote content server(s). In the communication between the vehicles and the RSUs, the networks should support mobility as the vehicles are moving continuously and requesting a seamless content service. In other words, the requester vehicle should be provided contents from RSUs continuously. In spite of supporting mobility, the delay in receiving data from the RSU could increase when a vehicle sends a request for content because of a disconnection or moving to a new location before receiving the requested content. For the continuously moving vehicle, in-network caching has been considered an attractive approach for the CCVNs. It has two approaches to cache data in the networks: reactive and proactive approaches. In the reactive approach ,6, if thProactive caching ,8,9 is aThis paper proposes a mobility-aware distributed proactive caching strategy in content-centric vehicular networks. To reduce the redundancy and the burden of caching for each RSUs, our previous work ,11 distrThe rest of this paper is organized as follows. With the rapid development of mobile communication and intelligent transportation technologies, vehicular networks have emerged as a new paradigm ,13. VehiCCNs are communicated by request customers through the exchange of two kinds of packets: interest packets and data packets. When a consumer needs specific content, the consumer broadcasts an interest packet over the available network. A node holding required data responds to it with the data packet. The CCNs reduce packet collisions to prevent broadcast storm symptoms and provide a simple routine for retransmission when a packet is lost. The CCN network model also has three data structures: content store (CS), pending interest table (PIT), and forwarding information base (FIB). The CS is the space to store the content and the PIT is the table for interface tracking where the interest packets sent/received are delivered. The FIB is used for forwarding interest packets. The node that receives the interest packet checks if the requested content is in the CS list. If the content exists in the list, the data packet is transferred to the requester. Otherwise, the node searches the PIT for an interface that has transmitted an interest packet containing the same content name as the content name included in the interest packet and discards the interest packet. If not, a new PIT list including the interface on which the interest packet is received and the content name of the interest packet is included is created, and the interest packet is transferred to a node with data by using the FIB. When a node with matched data is found, the data packet is communicated to the requester through the PIT, and the node receiving the interest packet is utilized as a node for content distribution.In the past few decades, the current Internet has evolved from an academic network into a global cyberinfrastructure. It is estimated that the annual network traffic of the Internet will surpass the zettabyte  threshold in 2016, and video traffic would account for 79 percent of all consumer Internet traffic . HoweverRecently, most studies try to integrate vehicular networks and content-centric networks as CCNs ,22 have In content-centric vehicular networks, caching is to place storage in the data path to store data temporarily so that subsequent requests of the data network nodes simplify the data access mechanism by eliminating node addresses and facilitating caching at any network element such as routers and end-user devices. However, the main research challenges are defined by where and how to cache data. Ref.  describeMany studies have been conducted on proactive caching schemes. Ref.  proposedWork in ,32,33 aiIn ,34,35, tIn ,37,38, tThis paper considers the content-centric networking model  for the Recently, as the size of content increases on the Internet, vehicles may not be able to receive the entire content with one RSU. The proposed strategy calculates the content size as much as possible that a vehicle can receive with one RSU, divides the obtained content by the chunk level, and caches some chunks of the content. In addition, content chunks are distributed and cached through transition probabilities derived by the Markov model . The pron. Therefore, There are various ways to predict the next location where a vehicle will arrive soon. For example, vehicle navigation GPS, providing the path to a destination, can be used to predict the next location. However, the drivers might follow the preferred road rather than the pre-determined path information from the navigation system. Additionally, when driving on a familiar road, most drivers do not enter destination information in the navigation. Therefore, vehicle navigation could not guarantee the transition probability that a vehicle will arrive soon. The Markov model uses historical information about the vehicle to predict the next arrival location from the current location. Deriving transition probability based on the Markov model is a well-known method to predict mobility . The MarAdditionally, the probability of the vehicle moving from Therefore, Currently, in order to cache contents for moving vehicles in the vehicular network, the existing studies consider either caching in the RSU with the highest transition probability or caching to all RSUs with the transition probability. However, such caching methods cause caching redundancy problems for the same contents in many RSUs as well as increasing backhaul traffic for content delivery to the many RSUs concurrently. In this paper, we partially cache content chunks based on transition probability to reduce the burden of caching in RSUs backhaul traffic. The existing studies focus only on who caches content and assume that the selected node predicts cache whole chunks of specific content. So, if the prediction fails, an additional cost is required for recovery. For instance, let us assume that there are RSUs This subsection explains the details of our proposed strategy. We explain the process for MDPC and MDPC with entropy. MDPC calculates the amount of content that will be proactive to the RSU in that direction based on the transition probability. Based on the vehicle’s movement record, the probability of moving the vehicle was calculated using the Markov model. The Markov model is a cumulative recording method that records the number of times a vehicle has veered in a particular direction from that road relative to the number of times it has entered that road. Thus, the longer the learning time, the more accurate the probability can be.interest packet calculates the content-chunk size that the vehicle can receive within the RSU’s communication range through the vehicle’s speed and communication range. We can calculate the maximum number of chunks This subsection shows the proposed chunk-level caching strategy based on the transition probability matrix as shown in The distributed point is calculated as follows:Therefore, the next H is calculated asEntropy is a measure of uncertainty introduced by Claude Shannon in his paper . With a When the entropy value exceeds 0.5, it is estimated to be an inaccurate prediction. To support our use of entropy value as an inaccuracy, we simulated the correlation between prediction accuracy and entropy. The accuracy of the probabilities was calculated by setting success as if the vehicle had moved to the highest probability and fail if not. p = {0.85, 0.10, 0.05}, the entropy H is −0.85 × logWith the given example This subsection describes the procedure for content delivery between RSUs and a vehicle. The vehicle In our strategy as shown in MDPC with optimization is a measure to minimize backhaul traffic by optimization using the transition probability in the intersection. Based on the transition probability of a vehicle, the MDPC_TO optimized the amount of pre-caching in a way that minimizes backhaul traffic. The RSU, where the vehicle enters next, brings content from other pre-cached RSUs while delivering optimized pre-cached content to the vehicle, providing the vehicle with a maximum amount of content.v is staying in Let The first constraint in Equation (10) means the limitation that the current RSU Equation (11) describes that the The last two constraints in Equations (12) and (13) calculate the maximum content amount that the vehicle can receive from the We compare the MDPC with the existing caching schemes by a simulation for performance evaluation. The simulation is implemented on the network simulator NS-3.2.7 . In our We vary the hit ratio from 0% to 50% by 10%. In this simulation, the hit ratio could be defined as the probability to move to the highest RSU. In other words, that means the ratio that the prediction is successful. We measure the backhaul traffic by the hit ratio as shown in Content should be cached efficiently due to the limited storage space of the RSUs. To measure the content availability, we have more request vehicles in the networks. The 63 vehicles send a content request message for storage availability. When a car sends a content request message, the RSU is defined as a hit when caching can be performed compared to the content request size contained in its content storage and content request message. In this section, we compare the backhaul traffic and delay time performance of MDPC and MDPC_TO. The MDPC strategy caches content in proportion to the transition probability derived from the Markov probability of the vehicles. As the next step, the MDPC_TO strategy optimizes the transition probability derived from the Markov model from the perspective of backhaul traffic.When the vehicle sends a request to the RSU, the RSU downloads the content on the content server. When requesting content from an RSU adjacent to the RSU, the content is distributed through a backhaul link. Backhaul traffic occurs in this case. This paper proposes a distributed pre-caching strategy (MDPC) in a content-centric vehicular network for increasing vehicles and contents. To reduce the redundancy of contents on the networks, we exploit the transition probability for the distribution of contents to the next roadside units (RSUs). In order to decrease the delay time, the RSUs share the distribution information for the content; then they are able to request the missing content chunks to the other adjacent RSUs rather than the original content server. Via the simulation, we evaluate the performance in terms of delay time, backhaul traffic, and content availability. Further, as a result of comparing the MDPC and the MDPC when the entropy is 0.5 or less, it is proved that it is more efficient not to cache the content to the RSU having the lowest probability. We optimized MDPC (MDPC_TO) to reduce backhaul traffic. The overall performance was increased, but the optimization constraint did not include transition probability, so backhaul traffic was higher than MDPC when the entropy value was lower. In order to solve these problems, a transition probability will be added when setting a constraint condition.


Background: The sudden and unpredictable changes caused by the COVID-19 pandemic are a serious threat to the occupational stress and mental health of referees worldwide, which has not attracted widespread attention. The mental health of football referees has a certain influence on their job satisfaction or the accuracy of judgments. Methods: This study constructed a moderated mediation model to explore the buffer factors between occupational stress and mental health in Chinese soccer referees in the early stage of reopening soccer matches during the COVID-19 pandemic outbreak. Data from 317 Chinese soccer referees (aged 19–45) were collected through an online questionnaire in September–October 2022. Occupational stress, mental health, job burnout and perceived social support were measured, and moderated mediation model was analyzed. Results: The results of this study showed that occupational stress was negatively correlated with mental health through the mediating effect of job burnout and the moderated effect of perceived social support after controlling for demographic variables. Specifically, the association between occupational stress and mental health was weaker when perceived social support was higher and stronger. Conclusions: The results demonstrate that job burnout and perceived social support played important roles in buffering the negative effects of occupational stress on the mental health of Chinese soccer referees in the early stage of reopening soccer matches during the COVID-19 pandemic outbreak. The findings provide implications for mental health interventions in soccer referees during the public health crises. The novel coronavirus COVID-19), which broke out in late 2019, has seriously threatened the physical and mental health of the global population 9, which . In addiIn the early days of the COVID-19 outbreak, most provinces activated public health emergency response measures and suspended some sports competitions . As the The theoretical basis of the present study is the job demands–resources model (JD-R) . The JD-Occupational stress adopted in this study refers to the stress caused by a particular individual in a particular job position , which cJob burnout refers to the state of physical and mental fatigue and exhaustion of individuals under the pressure of work, which is the result of an individual’s failure to cope with pressure . AccordiAlthough the mediating effect can reveal the internal mechanism of how the independent variable affects the dependent variable, it fails to explain how the association changes under different conditions. The association between occupational stress and mental health has been supported by a large amount of evidence; however, knowledge about the moderating variables between them is still limited. Therefore, it is important to explore the moderating variables between occupational stress and mental health. In addition, in the current context, it helps to understand the psychological characteristics of referees in the early stage of reopening soccer matches during the COVID-19 pandemic. The perspective of positive psychology emphasizes the role of positive intrinsic factors in challenging situations, where the perception of the protective effect of social support is widely supported, especially in studies of adults . PerceivResearch on the mental health status of soccer referees is limited and mainly concentrated in Europe and Egypt. In addition, the relatively late resumption of soccer matches in China could have a worse effect on referees’ mental health. Therefore, it may be valuable to conduct research on the mental health of soccer referees in China. Based on empirical and theoretical evidence, this study constructed a moderated mediation model to examine the mediating effect of job burnout on the relationship between occupational stress and mental health of referees, and to examine the moderating effect of perceived social support in the direct effect path. From a positive psychology perspective, this model could further influence the reduction of the negative impact of environment-related stress on referees’ mental health, and help to develop effective interventions to promote referees’ mental health during the gradual opening of matches in a pandemic. The following are the hypotheses of this study:Hypothesis (H1): Occupational stress is negatively correlated with referees’ mental health.Hypothesis (H2): Job burnout plays a mediating role in the association between occupational stress and mental health.Hypothesis (H3): The association between occupational stress and mental health was moderated by perceived social support and the relationship was weaker among referees with higher levels of perceptive social support.The conceptual model is shown in www.wjx.com, accessed on 1 August 2022), which is a commonly used online survey channel in China during the pandemic. For referees who could conduct face-to-face surveys, the researchers conducted a questionnaire survey by showing the link of the questionnaire on-site in a face-to-face manner, and explained the questions that were not thoroughly understood by the participants. For the online survey, the researchers used telephone communication to address questions that participants faced.The study protocol, which included a series of questionnaires for Chinese soccer referees in the early stage of reopening soccer matches during the COVID-19 pandemic outbreak, was approved by the Ethics Committee of Shandong University (No. ECSBMSSDU2022-1-086). Cross-sectional surveys were conducted across China from September to October 2022. During the study period, the COVID-19 epidemic in China was brought under certain control, but new confirmed cases of COVID-19 and the negative impact of the epidemic still existed. Due to pandemic control measures, face-to-face interviews with all referees scattered across the country were not possible during the survey. This study was conducted through an online questionnaire platform  participants voluntarily participated in the survey after reading the instructions; (2) the entire investigation was completed as required; (3) the respondents qualified as Chinese football referee Level 3 or above; (4) the time to complete the questionnaire was consistent with the estimate . The final sample included 317 respondents, 265 of whom were male (54.1%) and 52 of whom were female (45.9%), indicating a high proportion of male soccer referees in China. Participants ranged in age from 19 to 45. Although there has been no large-scale study based on a representative sample of global soccer referees, the sample in this study is from a wide range of coverage in China. Our sample seems comparable to previous studies on referees, healthcare workers or other groups with relatively high occupational stress levels. Therefore, the sample is highly representative of the target population (referees).The Chinese version of the Effort–Reward Imbalance Scale (ERI) was used to investigate the occupational stress of Chinese football referees . The ERIThe Chinese version of the Depression Anxiety Stress Scale-21   was selected to measure the level of perceived social support . The orin = 5000). Moreover, we used the structural equation model (SEM) made by AMOS 22.0 software to verify the proposed model. Descriptive fit indices were utilized to determine model fit in our research. The descriptive fit indices consist of the CFI, the TLI, RMSEA and the SRMR, which have most commonly been studied as indicators of structural equation modeling and confirmatory factor analyses [IBM SPSS version 22.0  and plug-in PROCESS Macro version 3.3 for SPSS   were useanalyses . If threUnivariate tests were used to test for common methodological bias due to self-reporting in this study. The results showed that the common factor explained 26.265% of the total variance, which was lower than the threshold of 40%. Therefore, to a certain extent, there is no common method bias in this study.All variables are described and correlated in After the data were standardized, Model 59 in the PROCESS was used to test the moderated mediation model, in which occupational stress was the independent variable, job burnout was the mediating variable, and the three dimensions of mental health were the dependent variable. In addition, perceived social support was incorporated into a three-dimensional pathway from occupational stress to mental health. The structural equation model was used to verify the model, and the fitting index was: χ²/df = 4.7. CFI = 0.97; TLI = 0.92; SRMR = 0.06; RMSEA = 0.11, indicating that the model had an acceptable fitting effect. The results are consistent with H1 and H2. Occupational stress had a negative predictive effect on perceived social support, and a positive predictive effect on job burnout, depression, anxiety and pressure. The interaction between occupational stress and perceived social support negatively predicted mental health. In addition, job burnout was positively correlated with the dimensions of depression, anxiety and stress . These rThe combination of the three dimensions of mental health reflects the overall mental health status of the individual. The current study focused on the association between occupational stress and mental health among Chinese soccer referees during the resumption of soccer matches following the outbreak of the COVID-19 pandemic. A model with job burnout as the mediating variable of the relationship between occupational stress and mental health and perceived social support as the moderating variable was constructed. Analysis based on data from an online survey of 371 Chinese soccer referees supports the model. Our findings suggest that occupational stress during the resumption of football matches following the outbreak of the COVID-19 pandemic had a negative impact on the mental health of Chinese football referees. At the same time, job burnout mediated the relationship between occupational stress and mental health, while perceived social support moderated the relationship between occupational stress and mental health, both of which could serve as a buffer.The results of correlation analysis showed that occupational stress was positively correlated with poor mental health conditions . Therefore, the occupational stress associated with the pandemic can positively predict the adverse psychological status of Chinese football referees, that is, the positive prediction of mental health, which supports H1. As a special occupational group, referees may be more vulnerable to the negative psychological consequences of insecurity caused by the pandemic as COVID-19 has negatively impacted the mental health and well-being of adults . During According to the Person–environment Fit Theory (P-E Fit Theory) , stress In addition to the cushioning effect of job burnout, the important role of social support as internal resource satisfaction cannot be ignored, especially in the unpredictable and adverse circumstances of a pandemic that has only recently allowed football matches to be re-opened. Less research has been conducted to understand the moderating effects of social support  on the rThe findings of this study have important theoretical implications. First, the study aims to investigate football referees in the early stage of reopening soccer matches during the specific phase of the COVID-19 pandemic, and to extend the study to occupational stress in the wider population. Previous studies mainly focused on the occupational stress of medical staff, teachers, police and other groups, but there are few studies to understand the impact of occupational stress on referees’ mental health ,14,15. SIn addition to the important theoretical and practical significance, this study also has some limitations, which need to be further explored in the future. Firstly, this study mainly explored the moderated mediation model based on the data of Chinese soccer referees collected during the first football competition period after the outbreak of the COVID-19 pandemic. Therefore, the generalizability of these findings in other areas remains to be explored. According to the WHO data, during the period of our investigation, China overcame the critical phase of the worst of the COVID-19 pandemic, with the national outbreak under initial control. However, cases are still increasing in other countries around the world. Previous studies have shown that cultural background or the severity of the epidemic can have an important impact on an individual’s mental health or feelings of burnout. Therefore, considering the development trend of worldwide COVID-19 in different countries of different cultural background and related measures, some countries may not be able to resume football matches, people of different areas are likely to experience different levels of occupational stress or mental stress reactions, and psychological health is not affected to the same degree. Therefore, considering the above factors, the applicability of this model in other fields in Asia or globally still needs to be further verified. Secondly, this study mainly explored the mediating effect of job burnout and the moderating effect of perceived social support between occupational stress and mental health of Chinese football referees, which was supported by existing evidence and data analysis. However, a review of previous studies suggests that other variables may mediate or moderate the relationship between occupational stress and mental health. Therefore, it is of interest to further investigate the role of hope in future studies of different groups and cultural contexts. Considering that the average occupational stress level of referees in this study is not high, it is likely that there are other pathways through which increased job burnout influences mental health. Finally, it is difficult to identify causal effects with cross-sectional designs, and longitudinal investigations may help to improve the understanding of changes in referees’ mental health throughout the outbreak of different pandemics and enhance the reference value of theoretical applications.The study was conducted starting in September 2022, during the reopening of football matches after a suspension due to COVID-19 lockdowns, using data from an online questionnaire conducted with 317 Chinese football referees. As for the study’s main findings, first, occupational stress during the post-pandemic resumption of football had a negative predictive effect on referees’ mental health. The negative relationship between job stress and mental health was mediated by job burnout, and perceived social support can moderate the direct path of the mediation model. The higher the level of social support perceived by football referees, the weaker the link between occupational stress and mental health, and the higher their mental health. The findings suggest that burnout and perceived social support play an important role in cushioning the negative effects of occupational stress on the mental health of soccer referees.


The global distribution of COVID-19 vaccinations remains highly unequal. We examine public preferences in six European countries regarding the allocation of COVID-19 vaccines between the Global South and Global North.We conducted online discrete choice experiments with adult participants in France (n=766), Germany (n=1964), Italy (n=767), Poland (n=670), Spain (n=925), and Sweden (n=938). Respondents were asked to decide which one of two candidates should receive the vaccine first. The candidates varied on four attributes: age, mortality risk, employment, and living in a low- or high-income country. We analysed the relevance of each attribute in allocation decisions using conditional logit regressions.In all six countries, respondents prioritised candidates with a high mortality and infection risk, irrespective of whether the candidate lived in the respondent’s own country. All else equal, respondents in Italy, France, Spain, and Sweden gave priority to a candidate from a low-income country, whereas German respondents were significantly more likely to choose the candidate from their own country. Female, younger, and more educated respondents were more favourable to an equitable vaccine distribution.Given these preferences for global solidarity, European governments should promote vaccine transfers to poorer world regions.Funding was provided by the European Union’s Horizon H2020 research and innovation programme under grant agreement 101016233 (PERISCOPE). Over 90 percent of Africans are still waiting for their first dose. This is a moral indictment of the state of our world. It is an obscenity”  countries joining the agreement, (ii) distribution rules, and (iii) cost per German household. The authors found that participants displayed a strong preference for an alliance exclusively composed of EU states. More importantly, the authors found that participants were more supportive of vaccine alliances if the national cost of participation was lower and national vaccine coverage higher, suggesting that participants’ preferences were significantly shaped by self-interest .In contrast, in a discrete choice experiment conducted in Germany and the US, participants in both countries expressed a strong preference for prioritising vaccine allocation to countries with a higher number of COVID-19 deaths and fewer intensive care unit beds, even when they were asked to imagine that they or a vulnerable family member were still waiting for the COVID-19 vaccine . NotablyIn this paper, we analyse new experimental evidence from six EU countries on citizens’ preferences for the distribution of COVID-19 vaccines between the Global South and North. We advance the literature in three ways. First, by covering six countries, we implement the largest survey experiment on international vaccine allocation preferences to date and are thus able to examine differences in citizens’ preferences across EU member states. Second, we conduct a discrete choice experiment among participants who are themselves not yet vaccinated, asking them to allocate a COVID-19 vaccine to either a person in their own country or to a person in a country in the Global South. This places specific salience on the notion that donating a vaccine dose to a person in the Global South might mean sacrificing one’s own dose or that of a fellow citizen, thus leveraging self-interest-based and nationalistic considerations. Third, we specifically examine heterogeneity in participants’ preferences along key sociodemographic characteristics as well as in terms of regional COVID-19 case numbers. Policymakers can use these insights to anticipate which groups will be most supportive of vaccine donations and might thus be at the heart of a supporting coalition - and to which groups political leaders, epidemiological experts, or civil society groups might still need to provide better information about the benefits for the donating country.Bilendi-Respondi. We sampled participants based on quotas that were matched to the census population of each target country in terms of (1) gender, (2) age, (3) education, and (4) geographic location (e.g. state or province within each country)  are used to measure the relative importance of different characteristics that respondents weigh against each other when making certain choices . DCEs haWe used the DCE methodology to elicit participants’ preferences on the allocation of a COVID-19 vaccine dose to a person in the Global North or to a person in the Global South. We presented eight different choice sets and asked respondents to choose whether Person A or Person B should receive the COVID-19 vaccine first. Respondents were told that the other candidate in each pair would have to wait substantially longer to receive their first vaccine dose. In each of the eight choice sets, one candidate was described as living in the country of residence of the respondent – i.e. a high-income country with high healthcare system capacity, - and the other candidate was described as living in a low-income country with a low healthcare system capacity. The healthcare system capacity was explicitly mentioned in the two candidate profiles. Across choice sets, candidates varied along three additional attributes, namely (1) age , (2) individual COVID-19 mortality risk due to comorbidity and/or lifestyle , and (3) employment status .The specific combination of candidate profiles in the eight choice sets, that is the experimental design, was selected for statistical efficiency (referred to as ‘D-efficiency’), which is accomplished by minimising the asymptotic variance-covariance matrix of the parameter estimates  . A sampland were themselves still waiting to receive their first dose.Participants were only eligible to participate in the survey experiment if they (1) had not yet been vaccinated against COVID-19 at the time of the survey and (2) indicated that they were willing to get vaccinated. We employed these two criteria to elicit prioritisation preferences on how to distribute scarce COVID-19 vaccine doses among individuals who perceived the vaccine as beneficial Power calculations for the discrete choice experiment indicated an optimal sample size of n=2,061 respondents per country . HoweverSimilar to previous studies , we examown characteristics was controlled for and absorbed by the fixed effects, given that respondents’ characteristics do not vary across the eight choice sets of the DCE.The empirical analysis comprised two steps. First, we estimated the main effects model for each country separately to assess the impact of the four candidate attributes  on the probability of choosing a specific candidate. The statistical model we utilised was a conditional logit model (with respondent fixed-effects) with standard errors clustered at the respondent level. Thus, in the main effects model, we regressed respondents’ vaccine allocation choice on the attribute levels of the respective candidate in each scenario. The potential impact of respondents’ https://osf.io/72jrq/.Second, we examined heterogeneity in the effect of the candidates-country-of-residence attribute by adding interaction terms between country of residence and heterogeneity variables to the above regression. Thus, the interaction of the respective heterogeneity variable (e.g. sex or age category) with the country of residence attribute - which varies across choice sets - allows us to examine the importance of respondents’ characteristics, while still using a fixed-effects model. A pre-analysis plan along with justifications of any deviations thereof is accessible via The study received approvals from the ethics committees of the medical faculty at the Technical University of Munich  and the ethics board at the University of Trento . Participants were given an individual link to the survey, where they first received information about the study’s purpose, data protection regulations, and voluntary participation. All participants provided written electronic consent to participate in the study prior to commencing the survey. Personally identifying information such as names and contact details were not collected and data is thus fully anonymised. After completing the survey, participants received a voucher worth three to five Euros, which was distributed by the survey company.A total of 6030 eligible participants across all six countries completed the DCE. For the attribute of COVID-19 mortality risk, we observe a similar pattern in all surveyed countries: The odds of being chosen to receive the vaccine were between two and almost six times higher for a candidate with an increased COVID-19 mortality risk, relative to a candidate with an average risk. The effect was even more pronounced for a candidate with a strongly increased mortality risk .For employment status and age, we also observed largely similar patterns across countries: First, employed candidates who lost income due to the pandemic and candidates who were employed in essential services were significantly more likely to be chosen to receive the vaccine when compared to unemployed candidates. Second, in all countries, 40-year-old candidates had slightly higher odds of being chosen to receive the vaccine than 20- or 60-year-old candidates.Moving beyond the main attribute effects, within a country and between countries. For example, they prioritise the candidate with the higher mortality risk but a foreign nationality over the candidate with a lower mortality risk but with the same nationality.In our DCE conducted online in six EU countries, we found widespread global solidarity and support for a more equitable distribution of COVID-19 vaccines between the Global North and South. Our results suggest that vaccine allocation preferences are largely driven by the assessed vulnerability of possible recipients, irrespective of whether the recipient lives in the respondents’ own country or in the Global South. Our respondents – who are themselves not yet vaccinated against COVID-19 but do favour vaccination – appear to rely upon the same solidarity considerations when deciding how vaccines should be distributed Interestingly, we found that respondents apply similar vulnerability considerations with regards to a candidate’s employment status. Specifically, employed candidates who endured income losses due to the pandemic were significantly more likely to be chosen to receive the vaccine compared to candidates not employed. Thus, respondents seem to prioritise vaccine receipt according to the extent at which a candidate’s employment status – and income generation – is affected by the pandemic situation. This is a finding, which, to the best of our knowledge, has not yet been identified explicitly by any of the other studies examining vaccine distribution preferences.in the context of previous pandemics – revealed largely positive attitudes towards vaccine donations to poorer countries ountries . Yet, weAt the same time, our DCE findings were inconclusive for the Polish and diverged for the German respondents: German survey participants were significantly less willing to allocate the COVID-19 vaccine to a person living in the Global South than to a person living in their own country, thus revealing preferences consistent with vaccine nationalism.There are several possible explanations for the strikingly contrasting findings in Germany. First, studies have repeatedly found in-group bias  in distributional preferences . Such inSecond, respondents might have been influenced by heterogeneities in the pandemic situation across countries. In Germany, our experiment was implemented as the third pandemic wave peaked, whereas in the other countries, our DCEs were launched two months later, during a phase of relatively low daily case numbers. German respondents might therefore have felt a greater urgency about having faster access to vaccination. The evidence for this explanation is mixed, as our data does not show evidence of a substantially higher reported COVID-19 threat perception among German respondents see . NeverthThird, the findings could be a function of the differences in the timing of the surveys relative to the progress of national vaccination campaigns. A recent survey experiment found that individuals with a higher perceived rank in the global income distribution feel stronger pressure to donate . ExtrapoIn view of the above, the differential findings for Germany are most likely driven by a combination of (i) higher infection and (ii) lower vaccination rates at the time of the German data collection and (iii) a higher proportion of older, high-risk and lower educated respondents in the German sample. While we are able to provide empirical support in favor of (i) and (iii), our analysis did not allow for any in-depth investigation of (ii), not least due to a lack of publicly available data on subnational vaccination rates for some of the countries.A number of limitations are worth noting. First, in addition to the cross-country differences in COVID-19 infection and vaccination rates discussed above, participants’ preferences may partly also be driven by cross-country variation in the pandemic trajectory over time. Given that our study utilises only cross-sectional survey data, we are not able to empirically examine any changes in public perceptions regarding the pandemic over time. Yet, the pronounced temporal nature of the pandemic needs to be kept in mind when reflecting on our findings. This includes, for instance, (i) notions of scarcity in the early phases of the vaccination campaigns, which may have affected perceptions about their value, (ii) a potential erosion of public trust during the suspension of the AstraZeneca/Johnson&Johnson vaccines, and (iii) increases in conspiracy beliefs related to vaccination through increasing spread of misinformation via social media channels . More gePolicymakers and global health scholars have condemned the unequitable distribution of COVID-19 vaccines between high- and low-income countries as ‘vaccine apartheid’ . Still,  Despite all efforts, the global distribution, developed versus developing economies, of Covid-19 vaccines and immunisation with them remains highly unequal. This rigorous and well-designed study addresses the question of what are the public preferences for vaccine allocation globally in 6 European countries. The results documented in this paper show that overall the public preference is for equitable distribution and provide important evidence and insights for policymakers. public reviews designed to be posted alongside the preprint for the benefit of readers; (ii) feedback on the manuscript for the authors, including requests for revisions, shown below. We also include an acceptance summary that explains what the editors found interesting or important about the work.Our editorial process produces two outputs: (i) Decision letter after peer review:eLife. Your article has been reviewed by 1 peer reviewer, and the evaluation has been overseen by a Reviewing Editor and a Senior Editor. The reviewers have opted to remain anonymous.Thank you for submitting your article "How Should COVID-19 Vaccines be Distributed between the Global North and South? A Discrete Choice Experiment in Six European Countries" for consideration by eLife, the reviewers have discussed their critiques with one another and with the Reviewing and Senior Editors. The decision was reached by consensus. What follows below is the Reviewing Editor's edited compilation of the essential and ancillary points provided by reviewers in their critiques and in their interaction post-review. Please submit a revised version that addresses these concerns directly. Although we expect that you will address these comments in your response letter, we also need to see the corresponding revision clearly marked in the text of the manuscript. Some of the reviewers' comments may seem to be simple queries or challenges that do not prompt revisions to the text. Please keep in mind, however, that readers may have the same perspective as the reviewers. Therefore, it is essential that you amend or expand the text to clarify the narrative accordingly.As is customary in Essential revisions:1) The sample from Germany is noticeably different from the rest of the countries (particularly in terms of having a higher ratio of those who are in the high-risk category). This might have impacted the results and needs to be reflected in the study discussion. Also, there is heterogeneity between studies in terms of the time of the fieldwork and each country's conditions in regards to the vaccination roll-out and the number of infections at that time. A study limitation that needs to be noted is that despite the large sample sizes and the inclusion criterion of not being vaccinated, the samples are not nationally representative of the population profile of each country, hence, the results are not representative of the views of the entire population.2. The manuscript narrative needs to be updated to reflect the present conditions in terms of inoculation campaigns, their success rate, and their disparities across the world. While the sense of urgency at the beginning of the global inoculation campaign seems to be passed, the inequity between the global north and south has remained persistent.3. There is space for more discussions on an interesting finding of the study that is prioritizing the vaccines according to employment status, and in particular income loss.4. The temporal nature of the public views at various stages of the pandemic and vaccination campaigns should also be noted.5. During the analysis of the main results (Table 2), were respondents' characteristics, including being in a high-risk group, controlled for? It will be helpful to clarify this in the paper. Yet even with the inclusion of such controls, it is likely that the characteristics of the sample from Germany and the timing of the fieldwork during which Germany had high infection rates while being behind the rest of the EU countries in vaccination rates play a role in the study findings from Germany. A stark difference between country samples e.g. is the high rate of those respondents who were in the high-risk group in Germany. This factor, even after being controlled for, very much likely has influenced respondents' attitudes towards sharing the vaccines with the rest of the world.6. It will be interesting to see a chart using the pooled data depicting the ratio of responses to the 8 choice sets of the DCE (as shown in Table 4).7) This paper provides solid evidence on public opinion from six European countries on key attributes according to which they believe COVID-19 vaccines should be prioritized. The paper has valuable policy implications.Reviewer #1 (Recommendations for the authors):1. Given that the events since the start of the pandemic have rapidly evolved, the introduction and Discussion sections require updates. While the sense of urgency at the beginning of the global inoculation campaign seems to be passed, the inequity between the global north and south has remained persistent. I believe the narrative of the entire manuscript needs to be changed and perhaps it can be tailored in the context of the possibility of future pandemics when another global campaign becomes essential.2. I trust that during the analysis of the main results (Table 2), respondents' characteristics, including being in a high-risk group, were controlled for? It will be helpful to clarify this in the paper.3. Yet even with the inclusion of such controls, I believe that the characteristics of the sample from Germany and the timing of the fieldwork during which Germany had high infection rates while being behind the rest of the EU countries in vaccination rates play a role in the study findings from Germany. A stark difference between countries' samples e.g. is the high rate of those respondents who were in the high-risk group in Germany. This factor, even after being controlled for, very much likely has influenced respondents' attitudes towards sharing the vaccines with the rest of the world.4. A study limitation that needs to be noted is that despite the large sample sizes and the inclusion criterion of not being vaccinated, the samples are not nationally representative of the population profile of each country, hence, the results are not representative of the views of the entire population.5. It will be interesting to see a chart using the pooled data depicting the ratio of responses to the 8 choice sets of the DCE (as shown in Table 4). Essential revisions:1) The sample from Germany is noticeably different from the rest of the countries (particularly in terms of having a higher ratio of those who are in the high-risk category). This might have impacted the results and needs to be reflected in the study discussion. Also, there is heterogeneity between studies in terms of the time of the fieldwork and each country's conditions in regards to the vaccination roll-out and the number of infections at that time. A study limitation that needs to be noted is that despite the large sample sizes and the inclusion criterion of not being vaccinated, the samples are not nationally representative of the population profile of each country, hence, the results are not representative of the views of the entire population.Thank you very much for the important suggestion to address the divergent findings for the German sample more fully. We agree that the notably different composition of the German sample has likely impacted the study findings, i.e. the much lower support among German respondents for distributing vaccines to the Global South. Combining the information regarding the differences in the sample compositions across countries (Table 1) with the findings from the heterogeneity analysis within the German sample  suggests that especially the higher proportions of older, high medical-risk and lower educated respondents might explain why we observe substantially lower global solidarity among German respondents. We moreover agree that the differences in infection and vaccination rates across countries, and especially between Germany and the rest of the sampled countries , likely also contributed to the differential results for Germany. In addition, both points are probably related, as the much lower vaccination rate in Germany, at the time at which the survey was fielded, allowed for the inclusion of a larger proportion of older and high-risk respondents, given our eligibility criterium of not yet having been vaccinated against COVID-19.To address the above points, we have (i) extended our empirical analysis by adding an additional heterogeneity analysis and (ii) notably expanded the Discussion section of the paper to incorporate the above points in more detail.Regarding (i): The additional heterogeneity analysis uses subnational data from the European Centre for Disease Prevention and Control on COVID-19 infection rates during the time of data collection in each included country. The analysis reveals that respondents residing in regions with a higher infection rate have on average a lower preference for distributing the vaccine to a candidate from the Global South. This provides some support for the supposition that the higher infection rates in Germany compared to the other countries might have played a crucial role also for the observed country-level differences in global solidarity. We would have liked to also include an additional heterogeneity analysis for subnational vaccination rates at the respective points in time, but, unfortunately, such data is not available for all of the six countries in our sample . To properly incorporate these additions into the empirical analysis, we added Figure 5 to the main manuscript, Supplementary Files 1j-k to the Supplementary Material, and new paragraphs to the Material and Methods section and to the Results sections of the main manuscript:Additions to: Materials and Methods “Moreover, we conducted an additional heterogeneity analysis to explore the relevance of the varying COVID-19 infection rates across countries at the time of the data collection. Specifically, we utilised subnational data from the European Centre for Disease Prevention and Control about the number of notified COVID-19 cases and assessed whether it predicts differences in respondents’ vaccine allocation choices in the DCE.”Additions to: Results“Figure 5 and Supplementary Files 1j-k present the results of the additional, pooled heterogeneity analysis using subnational data from the European Centre for Disease Prevention and Control on the number of notified COVID-19 cases during the time of data collection. When including the subnational COVID-19 incidence as a continuous heterogeneity variable, we found that respondents living in a region with a higher case incidence were on average slightly less supportive of distributing the vaccine to a candidate from the Global South . This effect is small in magnitude, but highly statistically significant. Based on an alternative specification, using a five-interval categorical variable for the incidence rate, we found that this heterogeneity seemed to be driven by a threshold incidence rate of more than 200-300 notified cases per 100.000 people, whereas it was less pronounced in the lower incidence regions and even showed an opposite pattern (i.e. more support with rising COVID-19 cases) when the case incidence is below 100. This finding remained stable both when using self-constructed intervals for the categorical variable  and when using quintiles informed by distribution of the case incidence data itself (see Supplementary Files 1jk).”Regarding (ii): We have notably expanded the Discussion section of the paper in order to provide a more thorough reflection on the differential findings for Germany, now including all the points mentioned above as well as the new findings from the additional heterogeneity analysis of the COVID-19 case incidence. In line with this, we have also made the within country heterogeneity analyses a bit more prominent in the manuscript by moving the corresponding figure from the supplementary materials to the main manuscript . We hope that this will make it easier for the reader to see why and which differences in the sample composition are likely driving the lower support among German citizens for distributing vaccines to the Global South. Please find below the additions made in the Discussion section of the paper:Additions to: Discussion“Second, respondents might have been influenced by heterogeneities in the pandemic situation across countries. In Germany, our experiment was implemented as the third pandemic wave peaked, whereas in the other countries, our DCEs were launched two months later, during a phase of relatively low daily case numbers. German respondents might therefore have felt a greater urgency about having faster access to vaccination – though our data does not show evidence of a substantially higher reported COVID-19 threat perception among German respondents . Nevertheless, results from our subnational heterogeneity analysis provide some support for this explanation by suggesting that respondents residing in regions with a higher COVID-19 incidence rate during the time of data collection showed, on average, relatively less support for distributing the vaccine to a candidate from the Global South. Interestingly, this heterogeneity partly exhibits a quadratic functional form: respondents’ support for distributing vaccine doses to the Global South slightly increases with COVID-19 case numbers in the lower parts of its distribution (<100 cases/100.000 people), but then more strongly decreases in the upper distribution, leading to an overall small though statistically significant negative interaction effect, which points to a decline in vaccine solidarity with low-income countries.Third, the findings could be a function of the differences in the timing of the surveys relative to the progress of national vaccination campaigns. A recent survey experiment found that individuals with a higher perceived rank in the global income distribution feel stronger pressure to donate.  Extrapolating this dynamic to the context of our study, we might expect to see a higher individual inclination for vaccine donations in countries where the (perceived) vaccination rate is high by international standards. When the survey was fielded in Italy, France, Spain, Poland, and Sweden, the vaccination rate in those countries exceeded 50% (30%) for the first (second) doses, whereas in Germany it was only at 25% (8%) (see Supplementary File 1j). This difference in domestic conditions may have affected the perceived scarcity of the COVID-19 vaccines between countries and the normative assessment thereof. In addition, the differential vaccination roll-out was likely also the reason for having been able to include a much higher proportion of older as well as high-medical-risk respondents in the German sample. Our separate heterogeneity analysis for Germany shows that especially the larger proportion of older respondents and high-risk respondents (the former more so than the latter), in combination with the German sample having a higher proportion of lower educated respondents, may have resulted in the lower global vaccine solidarity among German respondents .In view of the above, the differential findings for Germany are most likely driven by a combination of (i) higher infection and (ii) lower vaccination rates at the time of the German data collection and (iii) a higher proportion of older, high-risk, and lower educated respondents in the German sample. While we are able to provide empirical support in favor of (i) and (iii), our analysis did not allow for any in-depth investigation of (ii), not least due to a lack of publicly available data on subnational vaccination rates for some of the countries.”Finally, we also agree with your final point in this comment, i.e. that our samples are likely not representative of the national population in the sampled countries. We agree that it should be explicitly mentioned in the limitations of the paper. Accordingly, we have included the following note in our Discussion section:Additions to: Discussion“Finally, as a consequence of the two eligibility criteria of (1) not yet having been vaccinated against COVID-19 and (2) being willing to get vaccinated, our samples are not nationally representative of the population profile of each country (compare Table 1 with the census data in Supplementary File 1a). However, since we initially sampled participants based on quotas that were matched to the census population of each target country in terms of gender, age, education, and geographic location, our samples should be representative of each country’s unvaccinated and willing-to-get-vaccinated population at the time of the data collection regarding these quotas. In view of this, our suggested estimates of citizens’ support for global solidarity in distributing the COVID19 vaccines are most likely lower bound estimates – assuming that already vaccinated citizens and those less interested in getting vaccinated would be even more willing to donate vaccine doses to the Global South.”2. The manuscript narrative needs to be updated to reflect the present conditions in terms of inoculation campaigns, their success rate, and their disparities across the world. While the sense of urgency at the beginning of the global inoculation campaign seems to be passed, the inequity between the global north and south has remained persistent.Thank you very much for this important comment and we agree that the manuscript needs to be updated regarding these points, given that it reflected the current pandemic situation and state of the inoculation campaign at the time the initial manuscript was written (i.e. end of 2021). We have now updated the manuscript’s narrative by revising the introduction as well as the conclusion and have put a specific focus on the persistence of the global inequality in inoculation campaigns as well as in the more recent booster campaigns and expected future campaigns for an Omicron-specific vaccine.Additions to: Introduction“In his opening speech to address the United Nations General Assembly in September 2021, Secretary General António Guterres expressed stark discontent with the highly unequal global distribution of COVID-19 vaccines: “A majority of the wealthier world is vaccinated. Over 90 percent of Africans are still waiting for their first dose. This is a moral indictment of the state of our world. It is an obscenity”. . At the time of writing, and a year after Guterres gave his speech, 80% of the citizens of low-income countries are still waiting for their first dose of a COVID-19 vaccine, whereas in high-income countries, almost 80% of citizens are vaccinated. While the initial sense of urgency at the onset of the pandemic may have passed, this blatant inequity in access to COVID-19 vaccines prevails, continuing also throughout the more recent booster campaigns: In the past twelve months, the total number of vaccine doses administered per 100 people amounts to almost 100 in high-income countries and to only 27 in low-income countries. It therefore also seems likely that we will observe this same pattern again with the new Omicron-specific vaccine.[…]The globally unequal distribution of COVID-19 vaccines, including the stockpiling of vaccine doses for their own citizens, is partly a consequence of widespread vaccine nationalism in high-income countries. To ensure “fair and equitable access” to COVID-19 vaccines for all countries and achieve high vaccination rates everywhere, the World Health Organisation (WHO), the Vaccine Alliance (Gavi), and the Coalition for Epidemic Preparedness Innovations (CEPI) formed a multilateral initiative named “COVID-19 Vaccines Global Access”, COVAX. However, several governments have resorted to making bilateral purchasing agreements with vaccine manufacturers outside of COVAX, which has substantially weakened the initiatives’ collective purchasing power. Moreover, out of those vaccine doses that were initially announced as donations to COVAX by high-income countries, substantial proportions – 25% of announced EU doses and almost 50% of announced US doses – have in fact not yet been donated . The WHO’s pledges for a more equitable COVID-19 vaccine distribution have thus still not been fulfilled.”Additions to: Discussion“The emergence of the Omicron and its various subvariants throughout 2022, as well as ongoing concerns about potential future variants, emphasise once again the transboundary nature of the COVID-19 pandemic. Acknowledging this characteristic of pandemic, governments in high-income countries should discard mitigation strategies that are guided by the premise of vaccine nationalism.  Findings from our study suggest that governments of European countries can rely on solid public approval for a more equitable vaccine distribution – especially among female, younger and more educated citizens. Public support for vaccine donations to the Global South may be even more pronounced at the time of writing, since COVID-19 risk groups have now already received their first (or even second) booster vaccination. Moreover, our finding regarding prioritising candidates according to employment status, and particularly potential income losses, may also indirectly point to a pronounced public support for vaccine donations to the Global South: Employment security is much lower in low- and middle-income countries, especially in view of the high share of workers in the informal sector, where substantial income losses are more likely to occur during a lockdown or pandemic-induced economic downturns. More effective international policy initiatives to ensure efficient, adequate, and timely COVID-19 vaccine transfers to low-income countries are therefore urgently needed. They likely remain highly relevant and timely in view of the ongoing development of new, variant-specific vaccine updates such as those for the Omicron variant.”3. There is space for more discussions on an interesting finding of the study that is prioritizing the vaccines according to employment status, and in particular income loss.Thank you very much for this very helpful suggestion. We agree that this is an interesting and important finding, and also a rather novel one, which has not yet been extensively assessed or discussed in previous studies. We have revised the Discussion section in two places to make this finding more prominent, discuss its relevance against the existing literature, and emphasise its importance with regards to the overall narrative of the study:Additions to: Discussion (first part)“Interestingly, we found that respondents apply similar vulnerability considerations with regards to a candidate’s employment status. Specifically, employed candidates who endured income losses due to the pandemic were significantly more likely to be chosen to receive the vaccine compared to candidates not employed. Thus, respondents seem to prioritise vaccine receipt according to the extent at which a candidate’s employment status – and income generation – is affected by the pandemic situation. This is a finding, which, to the best of our knowledge, has not yet been identified by any of the other studies examining vaccine distribution preferences.”Additions to: Discussion (later part)“Moreover, our finding regarding prioritising candidates according to employment status, and particularly potential income losses, may also indirectly point to a pronounced public support for vaccine donations to the Global South: Employment security is much lower in low- and middle-income countries, especially because of the high share of workers in the informal sector where substantial income losses are more likely to occur during a lockdown or pandemic-induced economic downturns.”4. The temporal nature of the public views at various stages of the pandemic and vaccination campaigns should also be noted.Thank you very much for this important comment. We agree that there is an important temporal element to public opinion during the different stages of the pandemic and that this should be acknowledged accordingly when reflecting on our findings. We have now included an additional paragraph in the Discussion section of the paper, where we had already stated a somewhat related point, i.e. the relevance of the pandemic trajectory over time across sampled countries.Additions to: Discussion“A number of limitations are worth noting. First, in addition to the cross-country differences in COVID-19 infection and vaccination rates discussed above, participants’ preferences may partly also be driven by cross-country variation in the pandemic trajectory over time. Given that our study utilises only cross-sectional survey data, we are not able to empirically examine any changes in public perceptions regarding the pandemic over time. Yet, the pronounced temporal nature of the pandemic needs to be kept in mind when reflecting on our findings. This includes, for instance, (i) notions of scarcity in the early phases of the vaccination campaigns, which may have affected perceptions about their value, (ii) potential erosion of public trust in COVID-19 vaccines during the suspension of the AstraZeneca/Johnson and Johnson vaccines, and (iii) increases in conspiracy beliefs related to vaccination through increasing spread of misinformation via social media channels . More generally, however, citizens’ overall assessment of the pandemic situation likely varies strongly with the various stages of the pandemic, which we are at least partly able to capture by exploiting the different timing of our survey launches and thus some country  differences in infection rates at the time of data collection.”5. During the analysis of the main results (Table 2), were respondents' characteristics, including being in a high-risk group, controlled for? It will be helpful to clarify this in the paper. Yet even with the inclusion of such controls, it is likely that the characteristics of the sample from Germany and the timing of the fieldwork during which Germany had high infection rates while being behind the rest of the EU countries in vaccination rates play a role in the study findings from Germany. A stark difference between country samples e.g. is the high rate of those respondents who were in the high-risk group in Germany. This factor, even after being controlled for, very much likely has influenced respondents' attitudes towards sharing the vaccines with the rest of the world.Thank you very much for highlighting these important points. We are utilising a conditional logit model, which includes respondent-fixed effects, and are moreover clustering standard errors at the respondent level. Thus, respondents’ socioeconomic characteristics, such as their COVID-19 risk status, are always controlled for, but are absorbed by the fixed effects and, thus, not measurable. Since respondents’ characteristics do not vary across the eight choice sets of the DCE, it is not possible to ‘control’ for their impact in the traditional sense because there is no variance to exploit within respondents across choice sets. The attributes of the candidates in the DCE, however – whose impact we are mainly interested in – do vary across choice sets. In view of this, a conditional logit with fixed effects at the respondent level seemed to be the most robust approach and is commonly used in the DCE literature. However, we do take a closer look at the potential impacts of respondents’ socioeconomic characteristics by means of our heterogeneity analysis. Here, the interaction of respondents’ (fixed/time-invariant) characteristics with the (varying) attributes of the candidates in the DCE allows us to measure the impact of respondents’ characteristics  on the probability of choosing a candidate from the Global South .Nevertheless, we agree with your concern that the high proportion of high-risk respondents in the German sample probably played a role for the differential findings revealed for Germany. As we stated in our response to comment (1), the discrepancies in the findings from Germany compared to those from the other countries most likely resulted from the different composition of the German sample on the one hand , and the high infection rates and low vaccination rates during the data collection in Germany on the other hand. Regarding this point, we would like to kindly ask you to refer to our detailed response and additional analyses outlined in relation to comment (1) above. Given that this point about the sample composition, vaccination and infection rates was raised both in comments (1) and (5), we will here only list the additional changes not yet addressed in our response to comment (1).To improve clarity and transparency regarding the utilised model and the way in which it accounts for respondents’ characteristics, we have included additional explanations in the methods section:Additions to: Materials and Methods :“The empirical analysis comprised two steps. First, we estimated the main effects model for each country separately to assess the impact of the four candidate attributes  on the probability of choosing a specific candidate. The statistical model we utilised was a conditional logit model (with respondent fixed-effects) with standard errors clustered at the respondent level. Thus, in the main effects model, we regressed respondents’ vaccine allocation choice on the attribute levels of the respective candidate in each scenario. The potential impact of respondents’ own characteristics was controlled for and absorbed by the fixed effects, given that respondents’ characteristics do not vary across the eight choice sets of the DCE..”Second, we examined heterogeneity in the effect of the country of residence attribute by adding interaction terms between the country of residence and heterogeneity variables to the above regression. Thus, the interaction of the respective heterogeneity variable (e.g. sex or age category) with the country of residence attribute – which varies across choice sets – allows us to examine the importance of respondents’ characteristics while still using a fixed-effects model. A pre-analysis plan along with justifications of any deviations thereof is accessible via https://osf.io/72jrq/Moreover, the notes accompanying all tables and figures that present regression outputs have been extended by the following small addition:“Coefficients are odds ratios based on conditional logit estimations (respondent-level fixed effects) with standard errors clustered at the respondent level.”6. It will be interesting to see a chart using the pooled data depicting the ratio of responses to the 8 choice sets of the DCE (as shown in Table 4).Thank you for bringing this to our attention. We agree that such a chart is indeed highly informative and useful as an initial presentation of the DCE results. We have now extended Table 4 by adding seven more columns containing the ratio of responses to the eight choice sets of the DCE, both for the pooled sample and for each country individually. We have moreover moved the table from the Methods section to the main manuscript . These additions to the table show how respondents decided to distribute the vaccine in each of the eight choice sets and allow us to identify in a descriptive manner where and how, for example, German respondents decided differently than Spanish respondents. The observed proportions confirm the same patterns identified in the main effects model of the empirical analysis (now Table 3) and moreover reveal in which choice sets country differences were particularly dominant .