2.1 Human mobility and the spread of diseases

The resumption of international tourism amid the ongoing COVID-19 pandemic has significant implications for disease transmission, which can be understood through epidemiological theory. Epidemiology, as a discipline, provides valuable insights into disease spread dynamics. Key factors include human-to-human transmission, the reproduction number (R0), asymptomatic and presymptomatic transmission, and the occurrence of superspreader events [15]. In line with the observations made by Lim [16] who advocated that globalization in trade and population mobility are significant drivers of the emergence, re-emergence, and transmission of infectious diseases in the modern era, this study delves into the role of international tourism as a key component of population mobility. This perspective aligns with the findings of Iyaniwura et. al. [17], who have reaffirmed the central role of human mobility in the ongoing spread of COVID-19. Against the backdrop of rapid globalization in trade and population mobility in the twenty-first century, densely populated urban centers in highly globalized countries have evolved into focal points for international tourism. These urban centers are intricately connected to the global economy, attracting travelers from diverse regions. As a result, the impact of international tourism on the transmission of COVID-19 may exhibit variations across countries, contingent upon their degree of globalization, as noted by Bickley et al. [18].

Extensive research conducted in the past has consistently demonstrated the pivotal role of human mobility in the dissemination of communicable diseases, providing valuable insights into the mechanisms through which diseases can rapidly propagate across regions and even continents. The findings from these studies highlighted the profound impact of increased human mobility, particularly through trade, migration, and tourism, on the global spread of infectious diseases. Notably, studies by Findlater and Bogoch [5] have shed light on the transmission dynamics of diseases such as Zika virus and MERS-CoV across different regions. Their research highlighted how increased human mobility, facilitated by trade, migration, and tourism, has contributed to the swift dissemination of these diseases. Similarly, investigations by Brownstein, Wolfe, and Mandl [4] have elucidated the association between international air travel and the introduction of influenza cases into the United States, with domestic air travel further exacerbating its spread within the country. These findings emphasize the significant role played by air travel in enabling the movement of infected individuals and the subsequent transmission of infectious diseases. Furthermore, Fang et al. [19] worked on the transmission of SARS in China and identified major highways and air travel as influential factors in the rapid dissemination of the disease to neighboring provinces. Their research demonstrated how the interconnectedness facilitated by transportation routes, particularly air travel, has acted as a catalyst for the swift and extensive transmission of emerging infectious diseases. These studies collectively underscore the global health threat posed by the interconnected nature of our modern world, which amplifies the potential for the rapid and widespread transmission of infectious diseases.

2.2 Tourism on the spread of COVID-19

Extensive research has consistently highlighted the significant impact of human mobility, particularly in the context of tourism, on the spread of COVID-19. Numerous studies have specifically demonstrated the influential role of air travel in the rapid global dissemination of the virus [20, 21].). The sheer volume of tourists, both domestic and international, has been found to be strongly correlated with the number of COVID-19 cases, as observed in countries like Thailand [7]).

Popular tourist destinations and transportation hubs, including airports, have been identified as significant sources of COVID-19 transmission within countries. The concentration of people in these areas, along with the movement of individuals from different regions, greatly amplifies the risk of viral spread. Moreover, government-led domestic tourism campaigns aimed at revitalizing local economies have inadvertently contributed to a surge in COVID-19 cases associated with travel [11, 22]. For instance, Japan’s "Go To Travel" campaign has been linked to an increase in COVID-19 infections [23].. Similarly, initiatives promoting activities like dining out have accelerated the transmission of COVID-19 to neighboring regions [24]. Tamura, Suzuki, and Yamaguchi [22] quantified the impact of the Japanese government’s tourism campaign and found that it raised the rate of cases by 23.7% to 34.4% between July 30 and August 4, 2020. While these endeavors are intended to revive industries and stimulate economic recovery, they have sometimes disregarded the potential risks associated with increased human mobility and social interactions. It is crucial to acknowledge that disease prevalence within a domestic context has implications that extend beyond national borders. Regions with high levels of COVID-19 transmission can significantly affect neighboring areas, underscoring the necessity for international cooperation in mitigating the virus’s spread [10]. Governments have implemented various measures such as border closures, quarantines, travel restrictions, and lockdowns to limit human mobility and reduce COVID-19 transmission. By recognizing the interconnected nature of the pandemic, these measures are crucial for safeguarding public health and facilitating a coordinated global response.

Research has shown that border closures have proven effective in reducing cases and delaying epidemics between regions. However, the effectiveness of travel limitations on domestic tourism diminishes over time [6, 25]). Local factors, including community transmission rates, healthcare capacity, and adherence to preventive measures, should be carefully considered in understanding disease transmission patterns during different stages of outbreaks [26]).

2.3 Factors influencing the spread of diseases

Previous research has yielded substantial evidence demonstrating the significant role of tourism activities and human mobility in the dissemination of various infectious diseases, including the ongoing COVID-19 pandemic. Studies have consistently highlighted the influential contribution of travel-related factors, such as major transportation routes that interconnect regions and the extensive network of air travel, in facilitating the transmission of diseases [5, 27]). Additionally, a growing body of literature has identified several additional determinants that exert an influence on disease spread. These include population density within urban areas, the concentration of older adults within communities, the intensity of public transportation utilization, and various economic parameters encompassing employment rates, retail sales per area, and industrial value, among others. Furthermore, fundamental economic indicators like Gross Domestic Product (GDP) per capita and Gross National Income (GNI) have been consistently associated with the propagation of infectious diseases, with empirical investigations revealing a positive correlation between these indicators and infection rates as well as mortality rates attributed to communicable diseases [28–30]. The convergence of these research findings reveals the intricate interplay among travel patterns, population density dynamics, and socioeconomic circumstances, shaping the intricate landscape of infectious disease transmission.

Another interesting factor is the vulnerability of the population and the number of unskilled laborers, which have been found to be positively associated with the spread of COVID-19. These individuals often face challenges in accessing healthcare services, including limited availability of vaccines, and may find it difficult to adhere to lockdown measures due to their dependence on daily labor for sustenance. As a result, these factors increase the risk of COVID-19 transmission within communities [31]. Conversely, factors related to robust public health infrastructure, such as hospital density, healthcare personnel, hospital capacity, and availability of medical resources, have consistently shown a negative association with infection rates. These factors contribute to effective disease control and mitigation efforts [32].

3.1 Data

The cross-sectional dataset used in this study comprises information from 83 countries worldwide in the year 2022. Specifically, this dataset encompasses data collected from January to December, with our analysis focusing on either the summation of data or the most recent data available at the end of the year. The selected time period is particularly relevant as it coincides with the reopening efforts of many countries following the wave of the pandemic. The sample of countries was chosen to ensure representation from different continents, including 24 countries from Asia, 29 from Europe, 2 from Oceania, and 20 from North and South America, as well as 8 countries from Africa. This diverse selection aimed to capture a range of regional variations and facilitate a comprehensive analysis of the relationship between tourism and disease spread.

In this study, the focus centers on analyzing factors that influence the COVID-19 infection rate within countries. The dependent variable, "COVID-19 infection rate per population" (CASE), serves as a measure of the spread of the disease. The main independent variable of interest is the number of tourists entering each country (ARRIVAL), which is hypothesized to explain variations in the infection rate. To account for potential confounding factors, the analysis encompasses several control variables. These encompass the country’s economic level (GDP), population density (POP), a stringency index that gauges the effectiveness of epidemic control measures (STR), the rate of full vaccination coverage (FULLVAC), the proportion of the elderly population (AGE65), and trade openness (TRADE).

Theoretical explanations regarding the influence of various indicators on the spread of COVID-19 are both intricate and crucial. A higher Gross Domestic Product (GDP) typically signifies greater economic resources, leading to improvements in healthcare infrastructure, medical facilities, and treatment accessibility. Consequently, this aids in reducing the virus’s transmission [29, 30]. The stringency index, which reflects the imposition of strict epidemic control measures such as lockdowns, mask mandates, and travel restrictions, plays a pivotal role in mitigating virus transmission by reducing opportunities for contagion and preventing super-spreader events [29]. In terms of population density, it has been observed to increase coronavirus transmission in various contexts. Given that face-to-face contact is a primary mode of virus transmission, areas with higher population densities tend to exhibit higher infection rates. A preliminary literature review has shown that density is a statistically significant and positive predictor of COVID-19 [28]. Furthermore, achieving a higher rate of full vaccination coverage is instrumental in attaining herd immunity, effectively dampening the virus’s spread, reducing the severity of outbreaks, and alleviating the strain on healthcare systems. The proportion of the elderly population significantly influences the virus’s impact since the elderly are more susceptible to severe illness and fatalities [33]. Regions with a larger elderly demographic face heightened risks, emphasizing the necessity of stringent protective measures [34].

Additionally, trade openness can impact the spread of COVID-19 due to global interconnectedness. While it may facilitate the importation of the virus, it can also expedite the procurement of essential medical supplies, vaccines, and information sharing. Trade openness can also influence child health through government spending on healthcare, fueled by tax revenues generated from trade activities [35]. This suggests that increased trade activities in the economy lead to higher government revenues, subsequently increasing healthcare spending on child health. These variables emphasize their significance as predictors of COVID-19 spread. By incorporating these control variables, our objective is to mitigate potential biases and gain a more comprehensive understanding of the relationship between tourism and COVID-19 transmission.

Table 1 presents the descriptive statistics of the data used in this study, and the lsit of sample countries is laid out Table A1 in S1 Appendix.

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Table 1. Basic statistics and descriptions of variables.

https://doi.org/10.1371/journal.pone.0295249.t001

3.2 Methodology

To account for the spatial impact of tourism on the spread of the pandemic, this study employs the spatial quantile Regression model. This model allows for the analysis of spatial effects at different quantile levels. By considering different quantiles, we can obtain distinct coefficients for factors, thus offering a more comprehensive understanding of the relationship between factors and the spread of COVID-19. Building upon the work of Kostov [36], this study combines a spatial model with quantile regression, as proposed by Koenker and Hallock [37], to investigate the influence of tourism on the spread of COVID-19. This approach does not impose assumptions on data distribution, allows for the heterogeneity of influential characteristics on the dependent variable, and accounts for spatial dependence [38]. To our knowledge, the application of the spatial quantile model to this topic remains unexplored in existing literature.

Three specifications of the spatial quantile regression model are utilized: the spatial quantile lag model (SQLM), the spatial quantile error model (SQEM), and the spatial quantile durbin model (SQDM). Each model offers unique insights into the spatial relationship between tourism and the spread of COVID-19. Furthermore, to validate the presence of spatial correlation in the variables of interest, the researcher conducts a test using the Moran I statistic. This statistical test provides an indication of whether spatial autocorrelation exists among the variables, which suggests the presence of spatial dependence. By examining the Moran I statistic, we confirm the presence of spatial correlation and ensure that the spatial nature of the data is appropriately accounted for in the analysis.

3.3 Spatial autocorrelation

When evaluating the spatial correlation of each variable considered in this study, the analysis focuses on assessing the extent to which each variable exhibits spatial influence within its own geographical area and neighboring regions. To conduct this examination, the Moran I test statistic is employed. This statistical test allows for the assessment of spatial autocorrelation and helps determine the presence of spatial dependence among the variables under investigation. The Moran I test statistic can be written as (1) where x_i and x_j represent the variables of country i and country j, respectively. represents the average of the studied variables (both independent and dependent variables). n represents the number of countries. The spatial weight, denoted as w_ij, measures the spatial influence between countries i and j. We assign a value of spatial weight as 1 if country i and country j are adjacent and 0 if country i and country j are not adjacent. In this study, the interpretation of Moran’s I statistic is as follows: If the value of Moran’s I is greater than 0, it indicates that the variable exhibits positive spatial autocorrelation, meaning it has a similar pattern within its own area and neighboring areas. Conversely, if Moran’s I is less than 0, it suggests negative spatial autocorrelation, indicating that the variable has a dissimilar pattern within its own area and neighboring areas. When Moran’s I is equal to 0, it implies no spatial correlation, indicating the absence of a spatial pattern or spatial dependence.

3.4 Spatial quantile regression models

The three aforementioned models can be explained as follows:

1. 1) Spatial quantile lag model (SQLM)

The model considers the spatial effect in the dependent variable, which in this study is denoted as CASE_i. This model takes into account the spatial dependence and examines how the spatial lag of the dependent variable influences the quantiles of the response variable. By incorporating the spatial lag term, the model captures the influence of neighboring areas on the spread of the pandemic, providing insights into the spatial dynamics of the disease transmission. The model can be written as follows: (2) where lnCASE_i represents the value of the dependent variable for country i, i = 1, …, n, the independent variables consist of lnARRIVAL_i, lnAGE65_i, lnSTR_i, lnFULLVAC_i, lnGDP_i, lnPOP_i and lnTRADE_i for country i. In the above model, we can observe the inclusion of the spatial influence term in the varible CASE_i denoted as w_ijCASE_i and it corresponding spatial lag parameter, denoted as ρ(τ). If the coefficient of ρ(τ) at a certain quantile level is not equal to zero, it indicates that spatial influence is affecting the variable due to spatial spread. For the error term ε_i, it follows a normal distribution with a mean of zero and a variance of σ²(τ). Note that τ is the corresponding quantile of the model, which ranges from 0 to 1.

1. 2) Spatial quantile error model (SEQM)

This model is proposed to analyze the potential spatial impact that may exist in the error term, even when the spatial influence is not present in the explanatory and independent variables. In traditional regression models, the assumption is that the error terms are independently and identically distributed. However, in the presence of spatial autocorrelation, this assumption may be violated, leading to biased and inefficient parameter estimates. The SEQM accounts for spatial autocorrelation by introducing a spatial error term into the quantile regression framework. This spatial error term captures the spatial dependence in the model residuals, allowing for the estimation of robust quantile regression coefficients. By incorporating the spatial error term, the SEQM enables the identification of spatially varying effects on the quantiles of the response variable, providing valuable insights into the spatial patterns of the relationship between tourism and the spread of the pandemic. The model can be written as follows: (3) where λ(τ) represents the coefficient of spatial autocorrelation in the error term (w_iju_i) and u_i the disturbance term or error term that exhibits spatial dependence or spatial impact.

1. 3) Spatial quantile durbin model (SQDM)

This model takes into account the presence of spatial effects in both the explanatory variables and the response variable. In simpler terms, it considers that the variables being analyzed are not only influenced by their own values but also by the values of neighboring or nearby locations. The model can be presented as (4) where θ(τ) coefficient for the explanatory variables with spatial influence. In the estimation of SQDM, the parameters β₁(τ) and θ(τ) cannot be directly interpreted due to the presence of bias in the estimation results [13]. Therefore, it is necessary to analyze and separate the effects of the explanatory variables into direct effects and indirect effects in order to determine their spatial impact. The direct effect would involve assessing how changes in international tourist arrivals in one country directly impact its own COVID-19 transmission rate. This provides insights into the immediate consequences of international tourism on a country’s public health situation. In contrast, the indirect effect explores how changes in international tourism in one country indirectly influence the COVID-19 transmission rates in neighboring countries. This indirect impact takes into account the spatial dependencies between countries, whereby the actions or conditions in one country may affect others through a network of spatial relationships. By considering both direct and indirect effects, this study can provide a comprehensive view of how international tourism potentially heightens COVID-19 transmission, not only within individual countries but also across borders, considering the interconnectedness of neighboring regions.

To obtain the direct and indirect effects, let Eq (4) be rewritten as the reduced form as follows: (5) where I is the n order identity matrix, X_i represents the set of the independent variables. According to LeSage and Pace[13], the partial derivatives of E(lnCASE_i)with respect to each independent variable k is employed in this analysis. The general form is observed to be: (6)

Then the direct effect can be obtained from the mean diagonal element multiplied by (I − ρW)⁻¹, while the indirect effect is calculated as the mean row sum of off-diagonal elements times (I − ρW)⁻¹.

The estimation will be conducted for quantiles ranging from the 10th to the 90th percentile. Each quantile has the following interpretations:

1. 10th, 20th, 30th percentiles: The impact of tourism on infection rates in countries with low infection levels.
2. 40th, 50th, 60th percentiles: The impact of tourism on infection rates in countries with moderate infection levels.
3. 70th, 80th, 90th percentiles: The impact of tourism on infection rates in countries with high infection levels.

4.1 Moran I spatial autocorrelation test

In the initial part of this study, the researcher conducted a spatial autocorrelation test using the Moran I method. The study results are presented in Table 2, which shows that all variables have Moran I values greater than 0. This indicates significant positive spatial correlation, implying that there is a statistically significant and geographically influential relationship. Based on these test results, it can be concluded that changes in epidemic spread, population density, economic level, intensity of control measures, vaccination rates, tourism, and elderly population in one country will affect neighboring countries in the same direction. Therefore, the preliminary test confirms that spatial impact should be considered in this study.

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Table 2. The Moran I test for each variable.

https://doi.org/10.1371/journal.pone.0295249.t002

4.2 Comparison of spatial models’ performance

In this study, three spatial models are presented to obtain the best results at each quantile level. Therefore, it is necessary to compare the performance of each model. For this test, the Bayesian Information Criteria (BIC) will be considered, where the model with the lowest BIC value indicates the best model. Furthermore, to confirm the existence of spatial effects, this study also includes a comparison with the Quantile Regression model, which does not incorporate spatial effects. The results of the comparison are shown in Table 3, indicating that the spatial quantile durbin model (SQDM) performs the best at all quantile levels. This is evident from its lowest BIC value, suggesting that spatial influence is crucial in studying the impact of tourism on the spread.

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Table 3. Test model identification.

https://doi.org/10.1371/journal.pone.0295249.t003

Moreover, it confirms that the spatial effects influence both the spread and the number of tourists, along with other control variables. Therefore, the SDQM model will be used to analyze the spatial impact of international tourists on the spread in the subsequent analysis.

4.3 Estimation results of SQDM

Based on the findings presented in the previous section, it is evident that the SDQM proves to be the most appropriate model for the data utilized in this study. Furthermore, it is essential to apply the Likelihood ratio (LR) test to validate that the spatial correlation pattern is adequately captured by the SDQM. The results of the LR test, displayed in the final two rows of Table 4, indicate significant outcomes at the 0.01 significance level. Additionally, it is evident that the SDQM cannot be simplified or reduced to either the SQLM or SEQM.

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Table 4. Estimated results of the SDQM.

https://doi.org/10.1371/journal.pone.0295249.t004

The estimated results from the SDQM model are presented in Table 4, demonstrating the impacts of tourism and other relevant factors on the spread at different quantile levels. The study’s findings can be divided into two parts: direct impacts and indirect impacts. The direct impacts refer to the effects of various factors that directly influence the country itself. On the other hand, the indirect impacts represent the influences of different factors that spill over to neighboring countries.

Table 4 reveals compelling findings regarding the direct impacts. Firstly, it highlights that the influx of international tourists (ARRIVAL) significantly influences the COVID-19 infection rate within countries experiencing high infection rates, specifically in the 70th-90th quantile range. This emphasizes the role of tourism as a contributing factor to the spread of the virus within heavily affected regions. Moreover, when considering other pertinent variables, we find that the population (POP) variable exhibits a noteworthy impact on the infection rate in countries with a relatively lower to moderate infection rate, within the 20th-40th quantile range, as well as in countries with high infection rates, falling within the 70th-90th quantile range. This highlights the population size as a crucial determinant of the spread in both moderately affected and highly impacted regions.

Furthermore, the analysis indicates that the GDP variable influences the infection rate in countries with a lower to moderate infection rate, encompassing the 10th-70th quantile range. This suggests that economic factors play a role in shaping the spread of COVID-19 in regions with varying infection levels. The FULLVAC variable demonstrates a substantial impact on the COVID-19 infection rate in countries across different quantile ranges. Specifically, it affects the infection rate in countries with low infection rates (10th-20th quantile range), moderate infection rates (50th quantile range), and high infection rates (80th-90th quantile range). This emphasizes the importance of vaccination coverage in mitigating the transmission of the virus across diverse settings. Regarding the AGE65 variable, it is observed to have a significant influence on the infection rate in countries with lower to moderate infection rates, within the 10th-60th quantile range. This highlights the vulnerability of elderly populations to COVID-19 and underscores the importance of considering age-related factors in pandemic management strategies. Importantly, the analysis reveals that the STR variable does not exhibit a statistically significant impact on the COVID-19 infection rate. This suggests that the stringency of containment measures alone may not be a significant determinant in the spread of the virus. In term of TRADE, a significant impact of trade openness on the COVID-19 infection rate is observed at the 30th, 40th, 70th, and 90th quantiles.

In addition to the direct impacts mentioned earlier, Table 4 also provides insights into the indirect impacts. It reveals that the variable "WARRIVAL" has an influence on the spread of the infection to neighboring countries, particularly in countries with high infection rates at the 70th-90th quantile level. Among other related variables, "WGDP" has a significant impact on neighboring countries, especially in countries with high infection rates at the 80th quantile level. The variable "WSTR" affects neighboring countries in countries with moderate infection rates at the 40th-60th quantile level. Lastly, the variable "WFULLVAC" impacts neighboring countries in countries with low infection rates at the 10th-30th quantile level.

Based on the above results, only the significant direct and indirect impacts are presented. However, it is not yet possible to interpret the estimated coefficients obtained from the estimation process. This is because the estimated results may still be biased, and the interpretation does not have economic significance. Therefore, it is necessary to transform the estimated results using the spatial-weighted derivative method, which compares the expected value of the weighted spread of the infection with the explanatory variables within the same and different areas[13]). The estimated results of both direct and indirect impacts will be presented in the subsequent section.

4.4 Robustness checks

To validate the findings of this study, it is essential to account for the endogeneity problem. This concern arises due to the potential bidirectional causation between tourism arrivals and COVID-19 transmission, as well as the possibility that omitted variables can contribute to the endogeneity problem in the economic model [27]. Following the approach recommended by Lee and Yu [39], the Two-Stage Least Squares (2SLS) technique is employed to mitigate the endogeneity problem when estimating the SDQM. In this methodology, the real effective exchange rate (REER) is considered a suitable instrumental variable. The choice is based on the fact that the REER is not only used as a viable proxy for tourism arrivals but is also intricately linked to personal travel patterns, which are more relevant to tourism than to the transmission of COVID-19 [40, 41]. In the first stage, tourism arrivals are estimated using the instrumental variable as a regressor. Subsequently, the expected tourism arrivals are utilized as a regressor in the SDQM equation. It is crucial to note that the REER data utilized in our analysis were sourced from the reputable World Bank database.

To ensure the robustness of the real effective exchange rate (REER) as the chosen instrumental variable, the F-statistics test was performed during the initial stage of estimation. When the F-statistic exceeds 10, as per the "rule of thumb" critical value recommended by Wang and Zivot [42], the null hypothesis of a weak instrument is rejected, thereby indicating the strength of our chosen instrument. Additionally, the Durbin-Wu-Hausman test, as outlined by Hausman [43], is employed to assess whether the one-step estimation of the SDQM is both efficient and consistent. The rejection of the null hypothesis in this test implies that the one-step estimation of the SDQM is inconsistent, suggesting the presence of endogeneity.

Table 5 presents the results for the SDQM model employing the instrumental variable (REER), along with the results of the endogeneity tests in the final two rows. It is observed that the statistical values of the Durbin-Wu-Hausman test are all insignificant, while the F-statistics significantly exceed the critical value of the test (i.e., 10). This implication establishes the robustness of the chosen instrumental variable and indicates the absence of an endogeneity issue in our empirical model. Furthermore, it is noted that the coefficients of tourism arrival remain consistent with the results presented in Table 4. The results of the robustness tests, as displayed in Table 5, reveal that the positive effect of tourism arrival on COVID-19 transmission remained significant at higher quantile levels, thus affirming the robustness of the benchmark regression results presented in Table 4.

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Table 5. Estimated results of the SDQM with instrument variable (REER).

https://doi.org/10.1371/journal.pone.0295249.t005

Furthermore, a comparison between the full model, presented in Table 4, and the model that excludes control variables, depicted in Table 6, allows for an assessment of the impact of controlling for potential endogeneity and omitted variable bias. Notably, in the absence of control variables, the results from the model in Table 6 reveal consistent and robust relationships between the variables across all quantile levels. The sizes, signs, and levels of significance of the coefficients remain largely unchanged, underscoring the stability and validity of the findings. This comparative analysis suggests that accounting for potential endogeneity and omitted variable bias through control variables does not substantially alter the observed relationships between the variables. Consequently, it can be inferred that the direct relationship between the variables of interest remains robust and unaffected by the inclusion or exclusion of control variables, further enhancing the reliability of this study.

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Table 6. Estimated results of the SDQM without control variables.

https://doi.org/10.1371/journal.pone.0295249.t006

4.5 Factors affecting direct and indirect impacts on the COVID-19 infection rate

Table 7 presents the factors directly impacting the COVID-19 infection rate. Specifically, the number of international tourists (ARRIVAL) is found to be statistically significant in relation to the COVID-19 infection rate, particularly in countries with high infection rates at the 70th-90th quantile level. The estimation results indicate that a 1%increase in ARRIVAL is associated with an increase in the infection rate per population by 0.117–0.436%. This study provides insights into the concept that tourism involves the movement of people between different locations, and tourists can act as carriers of diseases. Consequently, they have the potential to spread the disease to the local population at their destination.

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Table 7. Direct effects.

https://doi.org/10.1371/journal.pone.0295249.t007

Regarding other related factors, population density (POP) has been found to have an impact on the COVID-19 infection rate in countries with low to moderate infection rates (quantiles 20th-50th) and countries with high infection rates (quantiles 70th-90th). If the population increases by 1%, it leads to an increase in the infection rate per population by 0.209–0.381% in the former group and by 0.105–1.034% in the latter group. These results are in line with the anticipated outcomes and the natural transmission of infectious diseases. In other words, higher population density contributes to population congestion, which facilitates the spread of the virus. Several studies from the past to the present support these findings. For example, Fang et al. [19] found that population density was a key factor influencing the SARS infection in Beijing. The latest study by Ehlert [30] also demonstrated the positive association between population density and COVID-19 infection. Therefore, it can be concluded that population density plays a role in the COVID-19 infection rate, covering almost all groups of countries.

Regarding the variable of Gross Domestic Product (GDP), it has an impact on the COVID-19 infection rate in countries with low to moderate infection rates (quantiles 10th-30th) and countries with moderate to high infection rates (quantiles 40th-70th). If GDP increases by 1%, it leads to an increase in the infection rate per population by 0.502–1.384% in the former group and by 0.475–0.899% in the latter group. These findings align with the research conducted by You, Wu, and Guo [44] and Ehlert [30], which stated that economic activities such as employment, retail sales per unit area, and industrial value have a positive impact on infection and mortality rates from contagious diseases. This is because the level of economic activities in a country often involves the gathering of individuals, which can lead to easy transmission of infectious diseases.

The variable of full vaccination rate per population (FULLVAC) also has an impact on the COVID-19 infection rate in countries with low, moderate, and high infection rates. In the quantiles 10th-20th, an increase of 1% in FULLVAC results in a percentage decrease of 0.309–0.330 in the infection rate per population. At the 50th quantile, a 1% increase in FULLVAC leads to a percentage decrease of 0.904 in the infection rate per population. In the quantiles 80th-90th, a 1% increase in FULLVAC causes a percentage decrease of 0.741–0.923 in the infection rate per population. These findings are consistent with the expected outcomes. It is worth noting that in the group of countries with a moderate infection rate, an increase in vaccination rate leads to a greater reduction in the infection rate per population compared to other country groups.

In the case of the variable representing the proportion of the population aged 65 and above (AGE65), it is found to have a positive impact on the COVID-19 infection rate in countries with low to moderate infection rates. In the quantiles 10th-30th, a 1% increase in AGE65 leads to a percentage increase of 0.812–2.149 in the infection rate per population. At the 40th-60th quantiles, a 1% increase in AGE65 results in a percentage increase of 1.137–1.360 in the infection rate per population. Likewise, at the 70th-90th quantiles, a 1% increase in AGE65 results in a percentage increase of 0.638–0.903 in the infection rate per population. This could be because the elderly population is more susceptible to contracting infectious diseases due to their lower immune defenses compared to other age groups [45]. The finding that the stringency index of control measures (STR) had a statistically significant impact on the COVID-19 infection rate at multiple quantiles signifies its versatile influence. Notably, this impact is observed at the 10th, 20th, 50th, 80th, and 90th quantiles, indicating that the stringency of control measures effectively influence infection rates across a wide range of conditions. This means that stricter control measures are associated with significant changes in infection rates not only when rates are low but also when they are moderate or high. Furthermore, trade openness is found to positively influence the infection rate at the 30th, 40th, and 70th quantiles.

Indirect effects analysis considers the impact between the different regions or countries, particularly those that share borders or are in close proximity. This is shown in Table 8, where it is found that the number of international tourists (ARRIVAL) affects the spread of the infection to neighboring countries, especially in countries with high infection rates at the 70^th and 90^th percentiles. This is consistent with the direct effects observed. However, it is interesting to note that the impact of the number of international tourists from one country can have a negative effect on neighboring countries. In other words, an increase of 1% ARRIVAL can lead to a decrease in the infection rate per population in neighboring countries by 0.063–0.127%.

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Table 8. Indirect effects.

https://doi.org/10.1371/journal.pone.0295249.t008

For other control variables, it is found that Gross Domestic Product (GDP) per capita has an impact on the spread of the infection to neighboring countries in the group of countries with high infection rates at the 80th percentile. Specifically, if GDP increases by 1%, it leads to an increase in the infection rate per population in neighboring countries by 0.532%. However, this effect is observed only in the group of countries with high infection rates. It can be said that when a country increases its GDP per capita, it attracts foreign labor from neighboring countries. However, countries with such characteristics are those with high infection rates within the country (at the 80th percentile). Therefore, the incoming foreign workforce in these countries is at risk of contracting the infection. When these foreign workers travel back to their home countries, they may carry the disease with them.

In addition to that, the Stringency Index (STR) is found to have an impact on the spread of the infection to neighboring countries in the group of countries with moderate infection rates at the 40th-60th percentile. Specifically, if the STR increases by 1%, it leads to a decrease in the infection rate per population in neighboring countries by 0.112–0.710%. This indicates that the intensity of controlling the spread of the infection in one country has a positive effect on neighboring countries. This finding is consistent with the study by Gordon, Grafton, and Steinshamn [46], which explained that stringent control measures in one country make neighboring countries more vigilant and reduce cross-border activities, resulting in a significant reduction in the spread of the infection.

Lastly, the full vaccination rate per population (FULLVAC) has an influence on the spread of the infection to neighboring countries in the group of countries with low infection rates at the 10th-30th percentile. Specifically, if the FULLVAC increases by 1%, it leads to a decrease in the infection rate per population in neighboring countries by 0.118–0.268%. This finding is in line with the control and prevention measures (STR) and demonstrates that increasing the vaccination rate significantly reduces the spread of the infection to neighboring countries.

To demonstrate the clear findings of this study, the overall analysis results are illustrated in Fig 2, which includes both direct and indirect effects, as well as the overall impact. The results for each variable studied are as follows

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Fig 2. Impact of different variables on the rate of COVID-19 infection from the 10th to the 90th quantiles.

Note: Blue bars represent the direct impact on the rate of COVID-19 infection. Orange bars represent the indirect impact on the rate of COVID-19 infection. Gray lines represent the overall impact on the rate of COVID-19 infection.

https://doi.org/10.1371/journal.pone.0295249.g002