1. Introduction
In response to the outbreak of coronavirus disease 2019 (COVID-19) in late 2019, governments around the world strove to prevent the spread of infection through various non-pharmaceutical interventions (NPIs), which included providing advice on personal hygiene measures and encouraging social distancing. For indoor spaces, an even more cautious approach was necessary, as the risk of being infected through contact is higher indoors. Most pandemic policies introduced for indoor spaces focused on restricting the use of spaces, such as by placing restrictions on business hours or closing spaces. While these measures were necessary to effectively respond to the pandemic, the duration of the pandemic was prolonged, causing such measures to lead to various types of socioeconomic damage
[1],
[2]. This negative consequence highlighted the need for a scientific approach to prevent excessive social costs by identifying relatively ineffective NPIs
[3],
[4].
Existing studies have used simulations to understand how the spread of infection occurs. For facility-level transmission risk analysis, pedestrian simulation is regarded as a suitable method, as it can reproduce pedestrian movements by means of modeling. Prior studies have applied pedestrian simulation to various types of facilities, including schools
[5],
[6], airports
[7], restaurants
[8], and hospitals
[9], measuring the risk of transmission before and after implementing NPIs in order to assess the NPIs’ effectiveness.
To evaluate the effectiveness of different NPIs, metrics for evaluating transmission risk are needed. The metrics often utilized by previous studies can be categorized into the following three types: ① infection-based metrics
[9],
[10]; ② contact-based metrics
[11],
[12],
[13]; and ③ network-based metrics
[11],
[14],
[15]. While these metrics have been chosen differently depending on the modeling method or research goals, it is not yet clear how to interpret the contrasting results of different metrics under the same conditions. Since different metrics can lead to different conclusions regarding the most effective NPI, it is difficult for facility managers to decide which metric to base their decision on, indicating the need to understand the circumstances under which discrepancies between different metrics occur.
In this paper, we aim to identify the pedestrian environment characteristics that bring about contrasting results across different metrics for transmission-risk assessment. To do so, we first generate data on various pedestrian environments through simulations. Based on the generated data, we then derive correlation coefficients between infection-based metrics and other metrics. Through this, we show the types of pedestrian environments that give rise to conflicting results between different metrics and discuss how to interpret such results. We compare the infection-based metric of infected ratio with four other metrics: the contact-based metric of exposure time and the three network-based metrics of degree centrality, betweenness centrality, and closeness centrality. The results of our work provide insights into applying various transmission-risk assessment metrics to analyze the effectiveness of NPIs and contribute to improving the pandemic response capabilities of policymakers and facility managers.
2. Literature review
2.1. NPIs to prevent the spread of infection
The most direct way to respond to a pandemic would be through pharmaceutical interventions such as vaccines and treatments. However, as in the case of COVID-19, when there are delays in developing pharmaceutical measures, NPIs are necessary to minimize the spread of infection
[16],
[17]. NPIs can be categorized into ① bottom-up measures that encourage personal hygiene measures (e.g., wearing masks and self-quarantining) and ② top-down measures established by the government and facility managers to induce social distancing
[18]. The goal of top-down measures is to minimize contact between people by changing pedestrian flows by means of spatial constraints (e.g., limiting the capacity of spaces) and temporal constraints (e.g., limiting break times in school). However, before the outbreak of COVID-19, relevant existing studies on this topic were mostly theoretical, and there were doubts about the effectiveness of various social-distancing-related NPIs due to the lack of relevant empirical evidence
[18]. Also, such NPIs can cause various forms of socio-economic damage, such as reduction of sales
[1], increases in unemployment rate
[2], social isolation
[19], and learning loss
[20]. Therefore, policies are needed that consider the trade-offs between reducing the spread of infection and causing socio-economic damage, and a method to analyze the effectiveness of NPIs in reducing transmission risks is necessary to support such policies.
In general, mathematical models such as compartmental models are often used to analyze the effectiveness of NPIs. Compartmental models can measure the entire process of people coming into contact with an infected individual and becoming infected themselves, based on the reproduction number (R0), which indicates how contagious a disease is
[21],
[22]. To assess the risk of COVID-19 transmission, existing studies have estimated the R0 value using data on the number of confirmed cases and people’s mobility; in addition, the effectiveness of an NPI has been evaluated by comparing the expected number of infected people before and after introducing the NPI
[21],
[23]. However, with compartmental models, it is difficult to conduct modeling at the individual level
[24],
[25] or to gather data that can explain the relationship between a disease and the movement of people indoors. As a result, compartmental models have mostly been used at either the community level or city level. Hence, a better approach that overcomes this limitation and can be used to analyze the effectiveness of NPIs at the facility level is needed.
2.2. Pedestrian simulations for analyzing the effectiveness of NPIs
Pedestrian simulations are utilized in various fields to study methods for providing a safe and convenient pedestrian environment in indoor spaces
[26]. More recently, as responding to infectious diseases is increasingly being recognized as part of facility-management procedures since the outbreak of COVID-19, multiple studies have applied pedestrian simulation to analyze the transmission risk of infectious diseases in indoor spaces
[6],
[27],
[28]. In particular, agent-based models (ABMs)—one of the most well-known methodologies for simulating pedestrian movement—have been widely used in various research fields as a tool to support decision-making processes by evaluating various strategies
[29]. An ABM enables analysis at the individual level, as the heterogeneity of each agent can be reflected in the model. In addition, it can include spatial information, which enables the generation of indoor pedestrian flow data through simulation. These features allow ABMs to overcome the limitations of compartmental models for facility-level analysis, which explains their wide adoption for assessing transmission risks in indoor spaces and evaluating strategies for managing such risks. Existing studies have analyzed the risk-reducing effects of interventions such as spatial constraints (e.g., redesigning shared spaces)
[28],
[30], temporal constraints (e.g., changing business hours)
[25], and behavioral inducements (e.g., social distancing)
[31],
[32] for different types of facilities (e.g., education facilities, transportation facilities, and multi-use facilities).
In order to conduct simulation-based policy analysis, metrics for evaluating transmission risks are needed. Prior works have proposed various metrics that take into account different research goals, characteristics of different models, and so forth, and have carried out modeling to calculate the metrics. As mentioned earlier, these metrics can be largely divided into contact-based metrics
[25], infection-based metrics
[9],
[33], and network-based metrics
[14],
[34]. The most well-known metric for pedestrian simulation is the contact-based metric, which refers to the amount of contact between agents. Since transmission occurs through contact between people, most prior works have used the amount of contact as the metric for analyzing the effectiveness of NPIs
[35],
[36]. Works that use infection-based metrics (e.g., the number of infected individuals through person-to-person contact) integrate pedestrian dynamics with compartmental models or computational fluid dynamics (CFD) models
[18],
[19]. More recently, Gunaratne et al.
[11] used a network-based metric (a centrality metric from network theory) to analyze the effectiveness of NPIs. Their study created a contact network by combining information about contacts between people induced from pedestrian simulation, which was then used to analyze transmission risks. This approach allowed a contact network—which is often utilized at the macro level to analyze the impact of social network structures on transmission risks—to be applied at the facility level.
However, questions remain as to how to interpret the conflicting results produced by different metrics under the same conditions. Indeed, it has been shown that the effects of an intervention for the same network differ depending on the type of centrality
[16], and that contact-based metrics and network-based metrics (e.g., degree centrality) correlate differently with intervention intensity
[11]. These findings highlight the need for further research on the applicability of and application methods for each metric in analyzing transmission risks. In this work, we analyze the correlation between metrics in various simulation environments to show what types of situations give rise to conflicting results across metrics and discuss how to interpret the results.
The rest of this paper is organized as follows: In Section 3, we discuss the concept, advantages, and limitations of each metric. In Section 4, we describe the simulation model used to conduct our experiments and our experiment design. Lastly, in 5 Discussion, 6 Conclusions, based on our experiment results, we discuss how to choose and utilize various transmission-risk metrics to analyze the effectiveness of NPIs.
2.3. Metrics for assessing transmission risk
2.3.1. Infection-based metric: Infected ratio
Infection-based metrics such as the
infected ratio use the number of infected people in a simulated environment to assess the transmission risk. The value of the metric can be derived by observing the number of people becoming infected after the simulation. The simulation process is as follows: ① A certain proportion of people in the model are set as infected; and ② when contact occurs between an infected person and a non-infected person and certain conditions are satisfied, the infection is transmitted. Prior works have modeled transmission such that the state of a non-infected agent is changed to an infected state with a probability equal to the transmission rate when the agent comes into contact with an infected agent
[37],
[38]. This simple modeling method intuitively describes the process of infection transmission. However, it is important to note that this approach requires a significant number of simulations to be run, which can be computationally intensive.
2.3.2. Contact-based metric: Exposure time
A contact-based metric determines that an environment has a high transmission risk if agents are within a specific distance. The metric can be derived by calculating the amount of time exposed to the risk. Prior works have measured the amount of time exposed to a risk based on health authorities’ recommended distancing standards of 2 m
[7],
[25].
Exposure time has the advantage of not being computationally intensive, since it is independent from infection modeling and is only determined by the movement of pedestrians. Therefore, it is more suited for analyzing the effectiveness of NPIs for large buildings, as it can avoid the limitations of infection-based metrics
[38],
[39],
[40],
[41].
2.3.3. Network-based metric: Centrality
Network-based metrics are used to analyze the impact of social network structures on transmission. They are grounded in the concept of centrality, a metric in network theory that evaluates the significance of nodes. Centrality enables the identification of key nodes that exert influence across the entire network
[42] and has been widely employed to assess epidemic risks. Our study employs several widely used types of centrality:
degree centrality [11],
[43],
betweenness centrality [44], and
closeness centrality [45].
Table 1 provides a comprehensive overview of the definitions and calculation methods for each centrality type.
The process of deriving a network-based metric is as follows: First, construct a contact network in which each individual is represented as a node in the network, contacts between each individual are represented by links between the nodes, and the amount of contact between individuals is the weight of the links. Then, compute the centralities of all nodes of the contact network. A node with a high centrality indicates that, if the node is an infected person, that node has a high possibility of transmitting infection to others. The more nodes have high centrality, the more vulnerable the contact network is to infection. To calculate the risk of the network, the average centrality value of the nodes with high centrality is used. Centrality is calculated differently depending on how the importance of a node is determined. Detailed definitions and calculation methods for each metric will be elaborated in Section 3.1.3.
3. Experiments
3.1. Simulation model development
We developed an agent-based simulation model to perform a comparative analysis of transmission-risk metrics. For this study, we used the Pedestrian Library feature of the AnyLogic software, along with the layout of building 35 at Seoul National University. This building encompasses 10 lecture rooms, five communal areas including bathrooms, and open corridor spaces. Within the building, student movements are dictated by their lecture schedules and behavioral rules, which served as inputs for our simulation model. At the end of the simulation, we obtained values for an infection-based metric (infected ratio), a contact-based metric (exposure time,
M2), and network-based metrics (degree centrality, betweenness centrality, and closeness centrality). To compare changes in the transmission-risk metric according to different scenarios, two assumptions were made. The first concerns the movement of students in indoor spaces: Students move according to their class schedules, staying in classrooms during lectures and moving to the next classroom during breaks. During this time, they may also use other spaces such as restrooms. The second assumption pertains to the method of disease transmission. Infection transmission occurs with a probability equivalent to the infection transmission rate when an infected person and another occupant are in contact for more than 30 s (
Fig. 1). Each assumption and simulation process is described in the following sections.
3.1.1. Model inputs
To simulate the movement of students in a university building environment, the model requires two inputs: lecture timetables and lecture room allocations. Lecture timetables contain information about which lectures the students will attend at what time, and lecture room allocations refer to which room in the building each lecture will take place in. Using these two inputs, students decide their next destinations within the simulation environment. Therefore, we can generate different pedestrian routes for the same lecture timetable by changing the lecture room allocation. In our study, by conducting multiple simulations with different lecture room allocations, we can collect a significant amount of data on specific pedestrian environments, enabling a correlation analysis between different metrics.
3.1.2. Agents’ behavior rules
In our model, students follow their timetable and move to the next lecture room during break time. Some students, however, opt to move to a designated rest area based on a specific probability and subsequently proceed to the next lecture room. In this study, this probability is referred to as the “free activity rate.” The resting place is chosen randomly from among five predefined locations. By controlling this variable, we can control the degree of freedom of the pedestrian environments. To implement this, we created a state machine chart using AnyLogic’s Pedestrian Library, as shown in
Fig. 2.
3.1.3. Model outputs
The simulation model is designed to derive three types of metrics: infection-based, contact-based, and network-based metrics. Infection-based metrics are derived using the proportion of infected agents after simulation (i.e., the infected ratio). According to the model, when an infected agent is in contact with other agents for longer than a set period, transmission occurs at the probability of the infection transmission rate. The simulation in this study starts with just one of the students being infected. When an infected person and a non-infected person come into contact within a 2-m radius, transmission occurs based on the probability of the infection transmission rate. For example, if the infection transmission rate is 0.1, a transmission event occurs 1 in 10 times when an infected person and a non-infected person come into contact within 2 m. Harweg et al.
[46] estimated the relationship between contact time and infection rate through simulation. For our experiments, we used the range of contact time and infection rate used in their study.
Contact-based and network-based metrics can be derived from the contact matrix obtained from the simulation results. The contact matrix shows the amount of contact time between each agent, where each value is the amount of contact time between two agents within the distance of 2 m. For example, if the value of the
ith row and
jth column is 20, it means that agent
i and agent
j were within 2 m for 20 s during the simulation. By summing the values of each element in the contact matrix, we can derive the exposure time, which is a contact-based metric that shows the transmission risk. Also, since the contact matrix corresponds to the network model in network theory
[11], we can derive the value of centrality of each agent from the contact matrix. Individuals with high centrality possess significant influence within the overall social network, indicating a greater likelihood of becoming so-called “super spreaders.” Therefore, in this study, we utilize the average centrality values of the top 10% of agents as metrics to assess the transmission risk in contact networks. This approach takes into account the substantial impact of super spreaders on the propagation of infections. The centrality measures employed include degree centrality, betweenness centrality, and closeness centrality, which are among the most critical metrics. The meaning of centrality varies slightly depending on its type. High degree centrality indicates many direct contacts, while high betweenness centrality signifies that an individual plays the role of a bridge between different groups. Closeness centrality reflects the extent to which an individual can transmit infectious diseases to many people in the group through secondary and tertiary contacts.
Table 1 summarizes the types of metrics and equations that can be obtained using our simulation model.
3.2. Experimental design
We evaluate the applicability of each metric by deriving and comparing their values via performing simulations using the simulation model introduced in the previous section. This study generates data for a variety of scenarios through simulation and calculates several transmission-risk metrics for each scenario. It then evaluates which metric most accurately represents the actual transmission risk. As previously described, each scenario can be depicted as a contact network and is influenced by the infection transmission rate and pedestrian flow. Accordingly, in this study, the infection transmission rate, free activity rate, and zoning are set as environmental variables to represent the infection transmission rate and pedestrian flow.
The infection transmission rate indicates the likelihood of transmitting the infection to others when the contact duration exceeds a specific period. We conducted experiments with values ranging from 0.01 to 0.30, referencing the infection transmission rates of diseases such as Middle East respiratory syndrome (MERS) and COVID-19
[47],
[48]. The free activity rate denotes the proportion of students who visit other spaces instead of going directly to the classroom during breaks, representing the degree of movement restriction among occupants in indoor spaces during a pandemic. The final variable pertains to whether occupants are zoned within indoor spaces. In this research, zoning is facilitated through class schedules. Students in the same zone attend the same lectures, creating an environment where encountering students from other zones is less likely. Instituting movement restrictions
[13] and zoning are key strategies for mitigating transmission risk, which is why they were selected as environmental variables for this study.
Table 2 displays the three environmental variables described above and their respective ranges.
This study conducts a sensitivity analysis on three environmental variables to observe changes in the accuracy of transmission-risk metrics according to disease and pedestrian flow characteristics. The indicator’s accuracy is assessed using the correlation coefficient with the infection ratio. We conducted experiments across 60 distinct combinations of environmental variables (
Table 2). For each combination, 50 simulations were carried out with varied lecture room allocations to determine the correlation between the infected ratio and other metrics.
Fig. 3 illustrates the complete experimental process. More specifically,
Fig. 3(a) depicts the method of calculating each metric for a single case. To ascertain the infected ratio, the number of simulations conducted matches the number of agents.
Fig. 3(b) illustrates the accumulation of data for correlation analysis by replicating the procedure shown in
Fig. 3(a). To generate 50 unique cases, random modifications were made to lecture room allocations and schedules. Altering the lecture room allocations while maintaining the same timetable and varied pedestrian trajectories enabled the generation of a diverse set of cases. Subsequently, as shown in
Fig. 3(c), Pearson correlation coefficients between various metrics were derived from these 50 outcomes. The processes in
Figs. 3 (a)–(c) were repeated for each environmental variable to analyze how correlations between different metrics varied with different types of infectious diseases and pedestrian flow characteristics.
4. Results analysis
Here, we analyze the correlations between different metrics for transmission-risk assessment in simulation model environments. We show how the correlation between metrics changes as the infection transmission rate—a characteristic of an infectious disease—changes and as the free activity rate and grouping level—characteristics of pedestrian flow—change.
4.1. Correlation changes according to changes in infection transmission rate
We analyze how the correlation between the infected ratio (an infection-based metric) and other metrics changes as the infection transmission rate changes.
Fig. 4 shows the changes in correlation for four different experiment environments.
Fig. 4 includes 20 scenarios. Among them, exposure time, degree centrality, and closeness centrality demonstrated
p values below 0.05. However, for betweenness centrality, 14 scenarios had
p values above 0.05. Consequently, while the correlation coefficients between these three indicators and the infected ratio are statistically significant, betweenness centrality does not show a correlation with the infected ratio.
In all four environments, we can see that the correlations between the infected ratio and the other metrics increase as the infection transmission rate increases, except for betweenness centrality. However, the trends are different for different types of centralities. For degree centrality and closeness centrality, their correlation with the infected ratio tends to increase with the infection transmission rate, although the degree of correlation varies for different experiment environments. However, for betweenness centrality, its correlation with the infection transmission rate varies depending on the experiment environment. In an environment where pedestrians move in an orderly manner, it shows a weak positive correlation with the infection transmission rate, while the degree of correlation decreases as the orderliness in the pedestrian movement decreases. The distinct trend exhibited by betweenness centrality—as opposed to other centralities—can be explained as follows: Typically, centrality metrics are designed to yield higher values with an increase in the number of contacts. However, betweenness centrality stands out from other centralities in its ability to achieve high values based on the network structure, even with a lower number of contacts. This difference is the reason for the unique pattern of betweenness centrality illustrated in
Fig. 4. As a result, betweenness centrality demonstrates a considerably lower correlation with the infection ratio compared with the other indicators. This finding implies that betweenness centrality might not be a suitable metric for assessing contagion risk in indoor environments.
4.2. Correlation changes according to changes in pedestrian flow
We also observed how the correlation between different metrics changed for different pedestrian flow characteristics (i.e., free activity rate and zoning).
Fig. 5 illustrates how the correlation coefficients of exposure time, degree centrality, betweenness centrality, and closeness centrality with the infection ratio vary with changes in free activity rate and zoning. We can see that the greater the value of free activity ratio and zoning, the higher the randomness of pedestrian flow. For exposure time and degree centrality, as the free activity rate increases, their correlation coefficients with the infected ratio decrease. The correlation coefficients decrease further in an environment with non-zoning. When the free activity rate is 0, the correlation coefficients with the infected ratio are 0.85 and 0.76 respectively; when the free activity rate is 0.5, the coefficients decrease significantly to 0.291 and 0.259, respectively, indicating a weak positive correlation.
On the other hand, for closeness centrality, the pedestrian flow characteristics have relatively little effect on its correlation with the metrics (
Fig. 5(c)). In a high-randomness environment (i.e., a free activity rate of 0.5 and non-zoning), its correlation coefficient with the infected ratio is over 0.5, which is higher than the correlation coefficient of exposure time. This finding indicates that metrics with the characteristics of a contact network, compared with the amount of contact, may have a stronger correlation with the total number of infected people.
Finally, for betweenness centrality, in most environments, it is difficult to conclude that it has correlation at all, or else it shows a negative correlation. It is only in an environment where the randomness is low (i.e., a free activity rate of zero and zoning) that the Pearson correlation coefficient rises above 0.4, although it is still small compared with those of the other metrics. These results illustrate that the between centrality metric is only effective in an environment where pedestrians move in groups or follow a fixed route.
The findings demonstrate that, although degree, closeness, and betweenness centralities are all network-based metrics, they exhibit varying correlation coefficients with the infected ratio. More specifically, the correlation between degree centrality and closeness centrality consistently exceeds 0.72 across all cases. Conversely, betweenness centrality shows either a weak correlation or no significant correlation with the other types of centralities. Notably, in controlled pedestrian environments characterized by zoning and a zero free activity rate, betweenness centrality exhibits a notable correlation with closeness centrality (R = 0.69).
5. Discussion
In this paper, we conducted correlation analyses based on data collected in a simulated environment to compare and analyze five different metrics for evaluating transmission risks in facilities through simulation. We derived the correlation coefficients between contact-based metrics (
exposure time) and network-based metrics (
degree,
betweenness, and
closeness) based on the infection-based metric of
infected ratio. Infection-based metrics have been widely used as a risk-assessment metric, as the number of infected people can be obtained through simulation. However, as mentioned in the literature review, the results vary depending on which agent in the simulation is set as the initially infected individual, such that many simulations are required to obtain reasonable results.
Fig. 6 shows how, in our experimental environment, the value of the infected ratio changes depending on who (among the 50 individuals) is set as the initially infected individual. We can see that the range is wide, from 4% to 72%. This finding confirms prior works that point out the shortcomings of infection-based metrics
[11],
[39]. Since multiple simulations are required to improve the reliability of the results of experiments that use infection-based metrics, a higher computation time is required compared with other metrics, which becomes a critical issue as the model size increases
[11]. Considering that the target facilities to evaluate the effectiveness of NPIs are usually indoor spaces where a large number of people gather, this issue must be critically considered when evaluating transmission risks using simulation.
If other metrics exist that are strongly correlated with infection-based metrics, those metrics could be used as an alternative to overcome the issues of infection-based metrics. Our results (
Fig. 4) indicate that as the infection transmission rate increases, the correlations among infection metrics (such as exposure time, closeness centrality, etc.) increase. The reason for this observation is that the exposure time quantifies the extent of contact with the transmission risk, and a higher infection transmission rate increases the likelihood of a contact leading to infection. Similarly, the centrality metric, which reflects the structural characteristics of a contact network, demonstrates a trend akin to that of the exposure time, as it is based on data regarding contacts at risk of infection. This suggests that the lower the transmission rate, the more difficult it becomes to replace the infected ratio with other metrics. Indeed, as shown in
Table 3[47],
[48], the infection transmission rates vary by disease. For diseases with high transmissibility (e.g., COVID-19 and measles), network-based metrics and contact-based metrics may provide a more pertinent approach for transmission-risk assessment. Conversely, in the case of less infectious diseases (e.g., MERS and severe acute respiratory syndrome (SARS)), despite computational time considerations, calculating the infection ratio could be a valuable method. Consequently, our findings suggest a potential validity of the exposure time metric that has been commonly employed in recent COVID-19 studies, although further research in this area is warranted to confirm these observations.
In addition to the type of infectious disease, the characteristics of pedestrian flow can change the correlation between different metrics. In particular, the results shown in
Fig. 6 demonstrate that there is a meaningful difference in the correlation coefficients between exposure time and infected ratio, as well as between closeness centrality and infected ratio, depending on how randomly pedestrians move in the indoor space. In congested pedestrian environments, the correlation between the actual number of infections and the exposure time diminishes, while closeness centrality shows a higher correlation with the actual number of infections. This finding suggests that the appropriate indicators can vary, depending on the indoor environment. Among the studies that evaluated the effects of NPIs at the building level, only one study
[11] utilized multiple metrics, including centrality. For a more scientific and in-depth analysis of policy effects, there is a need for future research that utilizes multiple metrics together. This result highlights the need for facility managers to consider pedestrian flow characteristics for different facilities when deciding which metric to use to compare different NPIs. Our results show that the lower the randomness of pedestrian activity, the higher the correlation between exposure time and infected ratio. This finding indicates that a contact-based metric is more appropriate in environments such as schools, where pedestrian activities are relatively simple and pedestrians tend to move in groups. On the other hand, in environments such as shopping malls, where the randomness of the pedestrian flow is high, the closeness centrality metric would be more reliable among the network-based metrics. This finding confirms prior works that showed that the structure of a network has an impact on the total transmission of infection.
While we use the infected ratio as the ground truth in this study, as explained in the literature review, the infected ratio can vary depending on how the process of becoming infected is modeled. Therefore, our results and analysis are limited to infectious disease modeling methods. Another limitation to consider is that the indoor population density affects the social network, suggesting that variations in the number of individuals or the architecture of the building could lead to different outcomes. This is especially relevant for the correlation between the infected ratio and centrality metrics, which might be influenced by changes in the number of individuals or the building’s architecture. Therefore, additional research is needed to test the impact of population density and building type by altering the layout of the building and adjusting the number of agents in the model. Despite these limitations, this study provides quantitative evidence supporting the assumptions made in previous research. Many earlier studies have used exposure time as a metric of transmission risk. These types of studies assume that closer contact within 2 m will result in higher infection rates. Our findings demonstrate a strong correlation between infection rate and exposure time, thereby validating these assumptions.
Our work also holds significance in that we have demonstrated that no single metric exists that is universally applicable for assessing transmission risks, and that various factors such as research goals, type of infectious disease, and characteristics of pedestrian flow must be considered. In addition, our work provides the basis for a comparative analysis method for selecting metrics in consideration of such factors. Our simulation model not only derives various metrics but can also parameterize different pedestrian flow characteristics in setting up experimental environments. In this way, the validity and reliability of metrics for assessing transmission risks in indoor spaces can be tested, enabling a reasonable comparative analysis of the effectiveness of various NPIs.
6. Conclusions
In this paper, we conducted a correlation analysis between different transmission-risk metrics for different pedestrian environments and types of infectious diseases, based on data generated through simulations. By doing so, we identified an environment where conflicting results arise for five different types of metrics. We found that closeness centrality has a higher correlation coefficient with infection-based metrics than contact-based metrics when the randomness of pedestrian trajectories in an indoor space is low. In the same pedestrian environment, we observed a higher likelihood of discrepancies between infection-based metrics and other metrics for infectious diseases with lower transmission rates. These findings emphasize that the most effective NPIs identified in simulations can vary depending on the chosen metric. Consequently, facility managers should avoid relying solely on a single metric to evaluate NPIs. Instead, they should consider both the type of facility and the nature of the infectious disease when selecting the most appropriate metric. These indicators are valuable for assessing policy effectiveness and identifying risk areas within indoor spaces.
Since we modeled the pedestrian flows in university facilities, the results of our experiment are limited to university facilities. Also, since pedestrian characteristics other than the degree of freedom and zoning can give rise to conflicting results across different metrics, further research on more diverse pedestrian characteristics and facility types is needed. Therefore, future studies should explore a broader range of facilities and diverse conditions to enhance the comprehensiveness of our findings. Specifically, integrating concepts such as spatial stratified heterogeneity (SSH) will enable a deeper exploration of spatial characteristics, contributing to the current understanding of disease spread. The simulation model developed in this study can be used as a tool for such future research.
This study also contributes to improving the reliability of pedestrian-simulation-based methods in calculating transmission risks, which provides a scientific basis for facility managers and researchers analyzing the effectiveness of NPIs. This scientific basis allows for an accurate evaluation of NPI effects, thus preventing excessive restrictions on facilities during a pandemic. As a result, it minimizes the socio-economic damage caused by pandemic responses and contributes to faster recovery in the post-pandemic stage.
Acknowledgments
This research was supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science and ICT (MSIT), Republic of Korea (1711185759).
Compliance with ethics guidelines
Inseok Yoon, Changbum Ahn, Seungjun Ahn, Bogyeong Lee, Jongjik Lee, and Moonseo Park declare that they have no conflicts of interest or financial conflicts to disclose.
Data availability statement
Some data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
Some data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request
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