COVID-19 Vaccine Rollout Plans Should Consider Spatial Distribution of Age-Specific Population

In the early phases of COVID-19 vaccine distribution, most countries adopted age-based rollout plans due to vaccine shortages. The plans, however, might overlook different spatial distributions of each age group. In this study, we first examine separate spatial accessibility to vaccine sites varying by different age groups, transportation modes, and times to find differences in spatial patterns of accessibility scores based on the enhanced two-step floating catchment area method. We also investigate spatial inequality in measured accessibility through the Gini coefficient. Finally, we scrutinize to what extent spatial accessibility to vaccine sites is overestimated or underestimated by different age groups. Results showed that there is spatial disparity in accessibility scores between the total population and multiple age-stratified groups. We also found that transportation modes play a significant role in determining spatial patterns of accessibility to vaccine locations, whereas time was not a major factor making differences in spatial accessibility patterns. Our findings suggest that vaccine rollout plans should incorporate age-specific population distribution to maximize accessibility and minimize spatial disparity.

In the early phases of COVID-19 vaccine distribution, most countries adopted age-based rollout plans due to vaccine shortages.The plans, however, might overlook different spatial distributions of each age group.In this study, we first examine separate spatial accessibility to vaccine sites varying by different age groups, transportation modes, and times to find differences in spatial patterns of accessibility scores based on the enhanced two-step floating catchment area method.We also investigate spatial inequality in measured accessibility through the Gini coefficient.Finally, we scrutinize to what extent spatial accessibility to vaccine sites is overestimated or underestimated by different age groups.Results showed that there is spatial disparity in accessibility scores between the total population and multiple age-stratified groups.We also found that transportation modes play a significant role in determining spatial patterns of accessibility to vaccine locations, whereas time was not a major factor making differences in spatial accessibility patterns.Our findings suggest that vaccine rollout plans should incorporate age-specific population distribution to maximize accessibility and minimize spatial disparity.Key Words: COVID-19, enhanced two-step floating catchment area method, GIS, spatial accessibility, vaccine rollout.
S ince the first case on 20 January 2021, the novel coronavirus (COVID-19) had infected 971,018 people and resulted in 6,858 deaths in South Korea as of 3 February 2022 (Johns Hopkins Coronavirus Resource Center 2022).COVID-19 is transmitted through both direct (i.e., droplet and human-tohuman transmission) and indirect contact (i.e., contaminated objects and airborne contagion; Lotfi, Hamblin, and Rezaei 2020).The primary symptoms of the virus at onset of illness are fever, cough, shortness of breath, and fatigue (Docherty et al. 2020;Huang et al. 2020).After recovery, a high proportion of individuals still experiences fatigue, dyspnea, joint pain, and chest pain (Carf ı, Bernabei, and Landi 2020).In the absence of vaccines in 2020, the Korean government implemented various nonpharmaceutical interventions such as social distancing, extensive diagnostic testing, intensive contact tracing, and the distribution of personal protective measures to minimize the local transmission and flatten the epidemic curve (Min et al. 2020).
The first vaccine was developed by Pfizer and BioNTech on 9 November 2020.After about a month, the U.S. Food and Drug Administration (FDA) granted an emergency use authorization for the vaccine.On 23 August 2021, the agency granted full approval to the vaccine for people sixteen years and older.On 22 September, the FDA approved a third dose as a booster shot for people sixty-fiveyears and older.By the end of February 2021, a total of 256 COVID-19 vaccine candidates were in development, with seventy-four in clinical trials and 182 in preclinical studies (Li et al. 2021).With the rapid development of the COVID-19 vaccines, many countries began a massive vaccination campaign.As of 3 February 2022, about 61.3 percent of the world's population had received at least one dose of a COVID-19 vaccine, more than 10.18 billion doses had been administered globally, and 17.75 million were administered every day (ourworldindata 2022).
COVID-19 vaccination was started in South Korea on 26 February 2021.Due to an initially limited supply of COVID-19 vaccine doses, the Korea Disease Control and Prevention Agency (KDCA) developed a COVID-19 vaccine national rollout for COVID-19 control and prevention.In the first phase, the COVID-19 vaccines were offered to health-care workers (e.g., field epidemiologists, emergency medical service workers) and elderly patients in long-term-care facilities and welfare facilities.In the second phase, vaccines were given to those age sixty-five and older, employees and patients in medical institutes or home-based longterm-care facilities for elderly, and those with disabilities.In the third phase, vaccines were offered to people with chronic disease, adults between nineteen and sixty-four years old, police, soldiers, firefighters, educators, and child-care workers.The last phase includes all remaining people who did not meet the qualifications of the first three phases.
Unlike other countries, South Korea's vaccine rollout plan used more detailed age groups within each phase.More important, all age groups were mutually exclusive in all phases of the vaccine rollout plan.People in South Korea had only one designated vaccine phase.Those who missed a vaccine during the designated vaccine phase had to wait until the last phase.For example, if a person over sixty-five did not receive a vaccine during the second phase, he or she could not get a vaccine in other following phases.Because of this age-specific vaccine phase rule, spatial distributions of age-specific populations were especially important in South Korea's vaccine rollout plan.
The vaccination plans for most countries have only been made based on the variables that are highly related to the risk of infections or deaths such as age (e.g., over sixty-five) and occupation (e.g., health-care workers), which does not take into consideration the locations of vaccination sites (Jung 2021).Importantly, measuring spatial accessibility to vaccine locations could help identify less or more accessible communities to the sites, helping stakeholders to allocate additional resources to more vulnerable areas (Luo and Wang 2003;Park and Goldberg 2021).For this reason, spatial accessibility has been widely employed in various public services, such as hospitals (Cheng et al. 2020;Zhao, Li, and Liu 2020;Kim, Ghorbanzadeh, et al. 2021), food outlets (Hu et al. 2020;Kang and Lee 2022), and shelters (Zhu et al. 2018;Kim, Jung, et al. 2021;Su, Chen, and Cheng 2021).
Multiple studies have already examined the spatial accessibility to COVID-19 vaccination sites, showing that rural and medically vulnerable populations have limited access to vaccination sites (Vasudevan et al. 2020;Rader et al. 2022;Kim et al. 2022).Most of the previous studies, however, have only focused on total census residence population, not considering age-specific population distributions, time, and transportation.These factors could be responsible for the spatially and temporally varied accessibility to COVID-19 vaccine sites.The agedependent spatial access to COVID-19 vaccine sites needs to be measured in considering age-based vaccine rollout campaigns (Glover, Heathcote, and Krueger 2022).For example, people over age sixty-five receive the vaccine at the early stage of campaigns and other age groups get the vaccine afterward.Thus, at early stages of a vaccine deployment plan, more vaccination sites are needed near the areas with a high percentage of older people, whereas in the later phases, more sites are needed near the areas with a high percentage of younger people.Furthermore, the locations of vaccination sites could also be time-dependent.People are more likely to be in schools, workplaces, or other locations (e.g., grocery stores, parks, etc.) during the day, whereas people are likely to be at home at night.Ideally, more sites are needed near residential areas at night and near nonresidential areas during the day.Ignoring age-and time-dependent characteristics could underestimate or overestimate actual accessibility to vaccine sites.
Multiple challenges exist to efficiently supply and disseminate vaccines to people: ensuring sufficient vaccine and supply chain capacity, preparing effective vaccine deployment and allocation plans, safely and securely transporting and delivering vaccines, and encouraging vaccination (Forman et al. 2021).In this study, we focus on effective vaccine allocation, which aligns with guidelines on vaccine distribution and protection of the rights and interests of groups (e.g., World Health Organization and National Academies of Sciences; Shi et al. 2021).We first separately measure accessibility to vaccines sites by age (over fifteen, fifteen to forty-nine, fifty to fifty-nine, sixty to sixty-four, sixty-five to sixtynine, over seventy), times (daytime or nighttime), and transportation modes (driving and walking).We then investigate spatial inequality in the measured spatial accessibility with the Gini coefficients.Finally, we look at to what extent spatial accessibility to COVID-19 vaccine locations is underestimated or overestimated regarding different age groups, which are highly associated with vaccine rollout plans.Through our study, we sought to provide a better understanding of the impacts of age-specific distribution, times, and transportation modes on dynamic interactions of vaccine supply and demand to maximize accessibility and to alleviate the inequality of accessibility to vaccine sites.

Method
Study Area and Data Seoul experienced a shortage of vaccines due to the limited supply of vaccines at the early stages of vaccination.Although people living in Seoul might not need to take a long trip to vaccine locations because of the large number of vaccine sites throughout the city (Figure 1), inequality in spatial accessibility to the vaccine sites could still exist.Various factors such as distance from the vaccine sites, nearby population size, neighboring land use, and transportation generate spatial disparity in accessibility to vaccine sites.Such spatial disparity created competition for vaccination among people.In addition, unlike other countries, South Korea's vaccine rollout plan was mutually exclusive in terms of age.Because each age group had only one period when they were eligible to receive a vaccine, South Korea provides a good testbed for investigating different accessibility by age.
In this study, we used three data sets to measure the different spatial accessibility of separate age groups (i.e., over fifteen, fifteen to forty-nine, fifty to fifty-nine, sixty to sixty-four, sixty-five to sixtynine, over seventy), times (i.e., day and night), and transportation modes (i.e., driving and walking) in Seoul, South Korea: (1) vaccine location, (2) population, and (3) road network.The Seoul COVID-19 data portal provides a vaccine location data set with address, hospital name, and visiting hours (https:// www.seoul.go.kr/coronaV/coronaStatus.do).People can obtain information on when and where to receive vaccines using the portal.As of 26 July 2021, there were 2,634 vaccine sites in Seoul.For the road network, we carried out geocoding for each vaccine site using OSMnx (Boeing 2017), a Python library, to allow us to download, visualize, and analyze the road network.
We also obtained population data from the Seoul Data Portal (see https://data.seoul.go.kr/), which provides the number of hourly estimated floating (daytime) and residence population (nighttime) at a finer scale geographical unit, called the K-unit.The K-unit is the finest geographical unit in South Korea (Statistics Korea 2021).In general, the Kunit, 1.1 km 2 on average, is exptected to contain 300 to 1,000 people, but some K-units have more people due to the high population density (15,865/km 2 ) of Seoul, with a total population of 9.6 million people in 2020.To measure the floating (9 a.m.-6 p.m.) and residence population (12 a.m.-5 a.m.), we used the maximum value of population counts, which provides a more rigorous spatial access measure than others, during January and February 2021, excluding weekends.As shown in Figure 2, there was a difference in spatial patterns between floating and residence total population.Daytime total population shows several highly populated areas in central and southeast Seoul where the central business district is located, whereas few populated areas were found in the nighttime total population.No large differences were found in north and southwest Seoul, where residential areas are located.This difference in spatial distribution supports the importance of people's time-dependent movements.More details on agespecific population distributions can be found in Figure S.1 in the Supplemental Material.

An Enhanced Two-Step Floating Catchment Area Method
This study used an enhanced two-step floating catchment area (E2SFCA) method for measuring spatial accessibility to vaccine sites.The method developed by Luo and Qi (2009) is an extended version of the two-step floating catchment area (2SFCA) method devised by Luo and Wang (2003).The 2SFCA method was initially created to The 2SFCA method implements two steps, as the name implies, to account for service demand and supply.In the first step, the population within a threshold of a service location is counted, and then the provider-to-population ratio is calculated by dividing the capacity of the service (i.e., service supply) by the number of populations within the catchment area (i.e., service demand).In the next step, the ratios of service locations within the catchment area of a given demand location are summed up.As a relative measure, a larger value of the 2SFCA method denotes better accessibility compared to other regions.
As one of the extensions of the conventional 2SFCA method, E2SFCA was developed to overcome a limitation of the 2SFCA method that assumes the same level of access to service locations within the catchment area by employing a distance decay function between service supply and demand (Luo and Qi 2009).The E2SFCA method also follows two steps as in 2SFCA: where P k is the population of a k's zone within the catchment j, S j is a hospital distributing a vaccine at location j, d kj is the travel time between demand location k and supply location j, and D r is the rth travel time zone (here, r is from 1 to 3) within the catchment area.W r is the distance weight for the rth travel time zone derived from the Gaussian function that is 1, 0.68, and 0.22 for W 1 , W 2 , and W 3 , respectively.The travel time zones and the distance weights can be modified if the data about travel behavior surveys are available.In detail, the travel time can be defined based on distance between the hospital and visitor's home locations.The weights can also be specified based on the proportions of the counts of time spent for the visitors to the hospitals.
In general, S j denotes the capacity of services (e.g., the number of beds, the number of physicians, the size of parks).This article focuses on the availability of the vaccine site, and S j refers to one (Kang and Lee 2022).Thus, R j is the hospital-to-population ratio at location j.
where A i is the accessibility score at location i to hospitals distributing vaccines, R j is the hospital-topopulation ratio at location j within the catchment area from location i, d ij is the travel time between i and j, and W r is the same distance decay function used in Step 1.Here, when the data about travel behavior surveys are available, as mentioned earlier, d ij and W r can also be applied.

Study Design
The South Korean government started a vaccine rollout campaign with the elderly population ages seventy to seventy-four, followed by those in their sixties, those in their fifties, and the remaining age groups.Because each age group has a different spatial distribution and population size, we measure the spatial accessibility to vaccine locations to understand if there are any accessibility disparities among different age groups using the E2SFCA method.
In this analysis, we also calculate separate spatial accessibility by time (daytime or nighttime) and transportation mode (walking and driving).As the Seoul Data Portal does not provide detailed population data, we use the proxy age group, as follows: (1) seventy and older, (2) sixty-five to sixty-nine, (3) sixty to sixty-four, (4) fifty to fifty-nine, and (5) fifteen to forty-nine.As we described in the introduction, everyone had a designated vaccination period based on their age.People who missed the vaccine during the designated period could not be vaccinated in other phases until the last phase was over.
Relatedly, the vaccine competition among different age groups did not happen in South Korea.
The catchment area in this study was determined as fifteen minutes and was divided into three zones with zero to five minutes (W 1 ), five to ten minutes (W 2 ), and ten to fifteen minutes (W 3 ) for different distance weights.Although most of the previous 2SFCA studies have used a thirty-minute catchment area, especially in U.S. settings, we applied a fifteenminute threshold because road networks are densely developed and hospitals are highly concentrated in Seoul.With these thresholds, we constructed three convex hulls for supply and demand locations using OSMnx and networkX packages in Python.
To calculate the accessibility score with 2SFCA, we first counted the total number of people within the convex hulls (i.e., service demand) from a given hospital (i.e., service supply).We then calculated the provider-to-population ratio by dividing the capacity of the service (i.e., service supply) by the population that falls within the convex hulls (i.e., service demand).In this process, we assumed that all service capacities are the same by applying the same weight (i.e., one).Next, we calculated accessibility scores by summing all the ratios within the convex hulls of a given population location.Finally, the extracted accessibility scores were normalized with Equation 3 because the score is highly dependent on the denominator (population size) in Equation 1.For example, those over seventy years old are more likely to have higher accessibility scores than other age groups because it is the smallest population size.Using the normalized accessibility scores, it helps to compare the accessibility scores with ease.Here, we additionally conducted a one-way analysis of variance (ANOVA) and Tukey post-hoc analysis to see if there are any significant differences in the normalized spatial accessibility scores between age groups.
where i denotes a single K-unit, and max(ACC) and min(ACC) denote the maximum and minimum value of accessibility score among all K-units.
With the normalized accessibility scores, we measured the spatial inequality in the spatial accessibility to vaccine locations for each age group using Gini coefficients.Gini coefficients range from zero to one, with zero referring to perfect equality in spatial access to vaccine locations, which means spatial accessibility scores for all K-units are the same.On the other hand, one indicates perfect inequality in spatial accessibility measures, suggesting that spatial accessibility to the vaccine sites at some regions is greater (or smaller) than other regions.
Next, we compared the magnitude of disparities in spatial accessibility among multiple age groups by summing up the differences between the total population accessibility score (i.e., over fifteen) and each age group accessibility score (i.e., fifteen to fortynine, fifty to fifty-nine, sixty to sixty-four, sixty-five to sixty-nine, seventy and older; Equation 4).For example, if a K-unit has an accessibility score of 0.2 for the total population group, and 0.1 for fifteen to forty-nine age group, 0.3 for fifty to fifty-nine, 0.4 for sixty to sixty-four, 0.5 for sixty-five to sixty-nine, and 0.6 for over seventy.We summed up the accessibility score differences between the total population group (over fifty) and the different age groups: fifteen to forty-nine (0.2 -0.1 ¼ 0.1), fifty to fiftynine (0.2 -0.3 ¼ À0.1), sixty to sixty-four (0.2 -0.4 ¼ À0.2), sixty-five to sixty-nine (0.2 -0.5 ¼ À0.3), and over seventy (0.2 -0.6 ¼ À0.4).Total accessibility difference from the total population group is À0.9 (0.1 À 0.1 À 0.2 À 0.3 À 0.4 ¼ À0.9) in this example.A positive number means age-specific accessibility scores are lower than the total population group accessibility score, suggesting the total population group accessibility overestimated the actual accessibility score.On the other hand, a negative number means age-specific accessibility scores are higher than the total population group accessibility score, indicating the total population group accessibility underestimated an actual accessibility score.Here, please note that we only compared normalized accessibility scores between the total population and multiple age groups, not between the different age groups.In addition, we only summed up the relative differences between the total population group accessibility score and the multiple agestratified accessibility scores at the K-unit level.Thus, the values we calculated should not be understood as absolute accessibility.
where i denotes a single K-unit, and j denotes age groups (i.e., fifteen to forty-nine, fifty to fifty-nine, sixty to sixty-four, sixty-five to sixty-nine, seventy and older).

Results
In this study, we tried to understand three questions: (1) to what extent spatial accessibility to vaccine cites changes by ages (fifteen to forty-nine, fifty to fifty-nine, sixty to sixty-four, sixty-five to sixty-nine, seventy and older), times (daytime or nighttime), and transportation modes (driving and walking); (2) whether there is spatial inequality in the measured spatial accessibility; and ( 3) to what extent spatial accessibility to vaccine sites is overestimated or underestimated by different age groups.
Table 1 summarizes the normalized spatial accessibility measures by age, time, and transportation mode.Overall, we observed higher accessibility from those over seventy, residence population, and walking mode.In detail, accessibility tended to increase with the increase in age.The age group over seventy had the highest accessibility, followed by those sixty to sixty-four, sixty-five to sixty-nine, fifty to fifty-nine, and fifteen to forty-nine.We also found higher accessibility from the walking mode than the driving mode.In addition, the residence population showed slightly higher accessibility than the floating population.Separate maps for the normalized spatial accessibility scores by age, time, and transportation are presented in Figures S.3 through S.6.For a better understanding of the accessibility measures, the unnormalized accessibility scores are provided in Table S.1 in the Supplemental Materials.
Then, we conducted a one-way ANOVA to see if there are any significant differences in the normalized spatial accessibility scores between age groups.Results show that there are significant differences in the normalized spatial accessibility scores for all scenarios: floating population by driving, F(5, 114912) ¼ 509.3, p < 0.001; floating population by walking, F(5, 114912) ¼ 46.12, p < 0.001; residence population by driving, F(5, 114912) ¼ 479, p < 0.001; and residence population by walking, F(5, 114912) ¼ 30.79, p < 0.001, among age groups.The results from the Tukey post-hoc analysis also confirmed that most of the normalized accessibility scores of various age groups are significantly different from each other (Tables S.2-S.5).
Next, we used the Gini coefficient to measure the degree of accessibility disparity (Table 2).The coefficient ranges from zero to one, with one indicating perfect inequality and zero representing perfect equality.Higher values close to one mean that accessibility to vaccine sites in some regions is greater than in other regions, whereas lower values close to zero mean all regions have the same level of accessibility.We observed the highest inequality from those between ages fifteen and forty-nine and the lowest inequality from those over age seventy.We also found that the walking mode had lower inequalities than the driving mode.Moreover, the floating population showed slightly higher inequalities than the residence population, but the difference was very small.
Figure 3 shows which areas were underestimated or overestimated regarding spatial accessibility after considering age-specific population distributions.Here, underestimated (overestimated) regions refer to the places where accessibility using total population is much lower (higher) than that with age-stratified populations.With the driving population (Figure 3A and 3C), we found that spatial accessibility was highly underestimated in central Seoul, but it became overestimated as it moved out of the city center.We observed a different spatial pattern with the walking population, however (Figure 3B and  3D).The southwestern part of Seoul was underestimated, whereas the northeastern part of Seoul was overestimated.We also found that accessibility for the daytime population (Figure 3A and 3B) was more extensively and strongly underestimated than that for the nighttime population (Figure 3C

Discussion
There are findings that need to be highlighted.First, we observed discrepancies in spatial accessibility scores between the total age group (fifteen and older) and multiple age-stratified groups.The discrepancies were most evident near central and northeast Seoul.We suspect that this discrepancy would result mostly from the population distribution.We observed more people in central areas during the daytime and more people in residential areas (i.e., northeast Seoul) during the night.Older adults tend to live in northeast Seoul, whereas younger adults tend to live in southwest Seoul.This finding underscores the importance of considering age-stratified population distributions for maximizing accessibility to vaccination sites for all people.We showed that the spatial accessibility measures based on the total population would be overestimated or underestimated when the age-stratified population distribution was not considered.Given that spatial accessibility measures help policymakers to place additional resources, the accessibility mismatches between all age groups and age-stratified age groups could result in inefficient and disproportionate resource allocations.Namely, the regions with the overestimated and underestimated accessibility scores, respectively, might and might not indeed need more vaccine capacity than the expected number of vaccines calculated based on the total population when age-specific spatial distributions are considered.Even though no previous studies have investigated the impact of different age groups on accessibility to vaccine sites, multiple studies support the importance of spatial distribution of different age groups when assessing accessibility (Ryan et al. 2016;Wood and Horner 2019).These studies showed each age group has a different level of accessibility.Our result highly recommends that agestratified distribution should be included in vaccine rollout plans.We also found that transportation modes play a significant role in determining spatial accessibility to vaccine locations.People can travel longer via driving than those who travel via walking during a given amount of time, which subsequently affects the catchment areas.This means that larger catchment areas that cover broader service suppliers and many vaccine sites nearby further improve accessibility.It also highlights the importance of transportation modes (e.g., Duffy, Newing, and G orska 2021).Multiple accessibility studies on COVID-19 have looked at multiple transportation modes to cover various subpopulation groups using different transportation modes (e.g., Tao et al. 2020).We showed that accessibility of the total age group by walking tended to be overestimated compared to accessibility by driving.For example, northeast Seoul, with a larger population size, significantly overestimated accessibility.A larger population of older adults in these regions might increase disparities between the total population accessibility and age-stratified population accessibility.
Interestingly, we were not able to observe large differences in spatial accessibility patterns between floating (daytime) and residence (nighttime) populations.We suspect this small difference came from the standardization process, which smooths magnitudes and only leaves variations of regional accessibility scores.In addition, the difference in the number of maximum populations between daytime and nighttime might not be enough to create different spatial patterns.Unlike time-sensitive health issues such as strokes (Rauch et al. 2021), daytime and nighttime population distribution does not seem that important for COVID-19 vaccination accessibility.We still observed marginal differences in commercial and residential areas, however, which could be highly associated with the number of vaccine sites.In South Korea, anyone who is eligible to receive the vaccine can get the shot without an appointment at any vaccine site where it is available.Thus, many people often visit vaccine sites close to their workplaces during the daytime and near their homes during the night after checking vaccine availability.Even though the impact of time is relatively minor compared to transportation modes, we think floating and residence population-based accessibility also needs to be considered for commercial and residential areas.
Finally, we separately found noticeable spatial inequality of spatial accessibility among different transportation modes and multiple age-stratified groups.Our results especially revealed that driving mode tends to further increase spatial inequality compared to walking mode.In addition, those between fifteen and forty-nine years old had a worse spatial equality than other age groups.Relatedly, people over age seventy had better spatial equality than other age groups.Our results indicate that people's behavior and travel mode choice should be considered to alleviate spatial disparity when developing vaccine rollout plans, distributing additional vaccines, and selecting new vaccine sites.
There are at least two practical implications of the study results.We showed that accessibility based solely on the total population is more likely to underestimate or overestimate age-specific accessibility.We think operating mobile vaccination sites following age-dependent vaccine phases could substantially improve accessibility and decrease spatial disparity.This increased accessibility could subsequently increase vaccination rates.Many papers have pointed out that low accessibility to vaccine sites is strongly associated with low vaccination rates (Rozenfeld et al. 2020;Cochran et al. 2021).We also showed that transportation mode is a major factor in determining accessibility to vaccine sites.We recommend that local governments provide more transportation options to areas with poor walking accessibility.Previous studies have also highlighted the importance of transportation modes for improving accessibility and decreasing disparities (Brown et al. 2019;Gates et al. 2019).
This study has several limitations.First, our method is theoretically assessed with several model assumptions (e.g., travel time) due to limited empirical data availability (e.g., visitor data).Thus, our results might not perfectly reflect reality, and could be different from the results derived from empirical data.Nonetheless, this method has been employed by many researchers as a commonly used tool for evaluating accessibility (e.g., Zhu et al. 2018).The ways of incorporating the travel survey into the E2SFCA method were explained earlier.In this regard, our apparent next step is to carry out a survey about transportation mode of vaccine visitors and travel time to vaccine sites.By considering the proportion of the number of people who take a specific transportation mode, we are able to incorporate the transportation mode into the E2SFCA method (Mao and Nekorchuk 2013).Including such information in the model would help estimate more realistic spatial accessibility (Park et al. 2022).
Second, this study did not consider traffic conditions due to the absence of data.Driving distance during the day could be shorter than the distance at night because of traffic.In addition, commercial areas would have more traffic than residential areas.Unlike other time-sensitive topics such as strokes, however, distance differences due to traffic conditions would not have a major influence on our results.
Third, this study does not include capacity and operating hours of vaccine sites, due to data availability.In addition, each vaccine site had different operating days and hours.In this study, we assumed that all sites had the same capacity and operating hours because we were unable to consider all these differences in our analysis due to data unavailability.We believe capacity and operating hours might not play a significant role in determining accessibility to vaccine sites, however, because vaccination in South Korea was mostly based on appointments rather than walk-ins.

Conclusion
To control COVID-19, many countries made efforts to increase the number of vaccinated people.Specifically, countries developed vaccine rollout strategies based on age due to the limited number of vaccine doses available at the early stage of vaccination.Researchers have paid much attention to measuring spatial accessibility to COVID-19-related health-care services (e.g., ventilators, ICU beds) to find the optimal locations for vaccine sites that can maximize accessibility for all people to vaccine sites.These studies, however, ignored the different geographic distributions of various age group populations.As most vaccination plans are based on age groups, measuring spatial accessibility without consideration of age-specific population distributions could results in less accurate estimates.To address this issue, our study measured age-specific accessibility to vaccine sites and identified areas with overestimated and underestimated accessibility compared to the total population's accessibility.
Our results found that the accessibility to COVID-19 vaccine sites was spatially unequal due to the uneven geographic distributions of the sites and various age-specific population groups.In particular, we found that some areas had worse or better accessibility when age-specific accessibility was considered.These findings suggest that vaccine sites were not well distributed regionally.In addition, the age-specific populations should be considered in developing future vaccine rollout plans to better reflect reality.Our approach would help health-care policymakers allocate vaccines or other related resources more efficiently for highly contagious infectious disease, such as the current COVID-19 and other potential pandemics.

Figure 1
Figure 1 Vaccine sites and road networks in Seoul, South Korea.
and 3D).The details of the population distribution are provided in Figure S.2.

Figure 3
Figure 3 The level of underestimation or overestimation of accessibility: (A) floating population by driving, (B) floating population by walking, (C) residence population by driving, (D) residence population by walking.

Table 1
Normalized accessibility measures by age, time, and transportation modes

Table 2
Gini coefficient for each age group