As of February 26, 2022, South Korea had 2,831,283 confirmed COVID-19 cases and 7,895 deaths. Daily confirmed COVID-19 cases and deaths from April 1, 2020, to February 26, 2022, were obtained from the Korea Centers for Disease Control and Prevention (KCDC) and the CB provincial website (2, 14). The clinical and epidemiological characteristics of COVID-19 are heavily dependent on age; therefore, we incorporated age-specific features in our model, and age-specific cases were divided into eight groups, as shown in Table 1. The CB province comprises approximately 3% of the total Korean population, and COVID-19 cases in CB constituted approximately 2% of the total COVID-19 cases in South Korea. CB constitutes 7.4% of Korea; this implies that the population density per area is lower than the average in South Korea and, therefore, provides a rationale for the lower number of confirmed cases of COVID-19 in CB. However, the proportion of the elderly population (age > 50 years) in CB was higher than the overall proportion of the elderly population in South Korea (42 vs. 40%, respectively), whereas the proportion of younger age groups (age <30 years) was lower. Furthermore, the age-specific comorbidities in the CB province are presented in the last row of Table 1. Note that the population with comorbidities had at least one human immunodeficiency virus infection, tuberculosis, cancer, cardiovascular disease, chronic respiratory disease, chronic liver disease, diabetes, and chronic neurological disease (Table 1). The severity and case fatality rates are high in patients with comorbidities (15, 16).

Between January 2020 and January 2022, there were five large waves of COVID-19 in South Korea. Figure 1A compares the levels of NPI (social distancing) implemented by the Korean government in metropolitan and non-metropolitan areas. Note that a high level of social distancing was implemented at the end of November 2020 in metropolitan areas, and COVID-19 vaccination began on February 26, 2021. Figure 1B presents the weekly age-specific data of confirmed COVID-19 cases across eight age groups from April 1, 2020, to February 6, 2022. In Figure 1B, the top and bottom panels show the weekly number of COVID-19 cases in South Korea and the CB Province, respectively. In both panels, the weekly number of COVID-19 cases showed a similar age-specific temporal pattern. Lastly, Figure 1C shows the first, second, and third vaccination doses per week for each age group in Korea.

We developed an age-structured mathematical model to investigate the impact of age-specific vaccinations on COVID-19 transmission dynamics. The age-specific classes were composed of the following eight groups: 0−9, 10−19, 20−29, 30−39, 40−49, 50−59, 60−69, and 70−. The population was separated into eight compartments based on the epidemiological characteristics of each age group i. S_i(t) is susceptible, E_i(t) is exposed, A_i(t) is unconfirmed infectious, I_i(t) is confirmed infectious, Him(t) is quarantined or hospitalized with mild symptoms, His(t) is hospitalized with severe symptoms, R_i(t) is recovered, and D_i(t) is dead. Moreover, ViF(t) is the first dose vaccinated, ViS(t) is the second dose vaccinated, ViB(t) is the third dose (or booster) vaccinated, RiVF(t) is recovered and first-dose vaccinated, RiVS(t) is recovered and second-dose vaccinated, and we have the epidemiological status for vaccinated classes Xiv(t) at the same status as X_i(t) for X = E, A, I, H^m, H^s, R.

Furthermore, we divided the total population into groups under normal conditions and groups with comorbidities. Xin(t) and Xic(t) are populations with normal conditions and comorbidities of the same status as X_i(t) for X = S, E, A, I, H^m, H^s, V^F, V^S, V^B, E^v, A^v, I^v, H^mv, H^sv, respectively.

A schematic diagram of this model is shown in Figure 2. The model is presented as a system of ordinary differential equations, which are provided in Supplementary Section 1. The parameters used and the baseline values are shown in Supplementary Section 1. We computed the effective reproduction number, R_t, which involves the fraction of susceptible population and potentially infectious vaccinated population. It measures the average number of secondary cases per infectious individual at time t, which is obtained by calculating the spectral radius of the next-generation matrix. The details of the derivation of R_t of the model are provided in Supplementary Section 2.

In this subsection, we present four age-specific vaccination prioritization strategies. We have proposed four prioritization strategies, because there are critical age-specific characteristics, such as a higher activity level (aged 30–49 years) and a higher mortality rate (over 60 years and people with comorbidities). In addition, we considered a uniform vaccination strategy: all age groups to be vaccinated (over 20 years old) due to Korea's vaccination policy (only for people aged 19 years or older by October, 2021). These four strategies were applied to the primary dose and booster vaccination, except for the second dose vaccination. The second dose of vaccination was implemented after ψ days, the mean period between the first and the second dose of vaccination, as recommended by the Korean government.

It was assumed that when the vaccination rate of the priority group reached 80%, vaccination was switched to the uniform vaccination strategy. Vaccination was stopped when the vaccinated population reached 80% of the total Korean population. At the beginning of the vaccination, Korea's policies were limited to 19 years or older; however, in October 2021, vaccination was extended to individuals older than 12 years. Therefore, for the first and second dose vaccination, people above 20 years of age were vaccinated before October 2021. The current vaccination data in Korea, according to which about 60% of those aged between 12 and 18 years were vaccinated, is reflected for the population ViFn, ViFc, ViSn, and ViSc. Currently, in Korea, the booster vaccination is implemented for aged 20s or older; hence, the booster shot is applied to people above 20 years of age. Then, the results are compared to the case when people above 10 years of age are vaccinated.

In this subsection, we estimate the age-specific transmission probability β_i for each age group i per contact by fitting the age-specific confirmed case data in the CB. The contact matrix involving home, school, workplace, and other factors for each age group in Korea (17) was used and adjusted using the population in CB (18). The contact matrices M^L, M^M, and M^H, for low, moderate, and high NPI levels, respectively, were constructed by the linear combination of location-specific matrices of home, school, workplace, and others and by multiplying the weights given in Table 2 based on the level of NPI implementation. The contact matrices are presented in Supplementary Section 3. The mobility of the vaccinated population was assumed to be higher than that of the unvaccinated population. Therefore, for the contact matrix of the vaccinated group, we used M^L for all NPI levels. The transmission probability βiv of those vaccinated but without antibody in age group i per contact was assumed to be the same as that for β_i.

Furthermore, we estimated the age-specific transmission probability under various NPI levels, as shown in Figure 1A. For the first and second dose vaccinations, {_{βi}i = 1, ..., 8} values were obtained under three different NPI levels: low, moderate, and high. For the booster shot, {_βi}i values were estimated based on the data from November 1 to December 5, 2021. This is due to the step-by-step recovery for the first major reorganization of the quarantine rules. The estimated {_βi}i values are presented in Table 2. Details of the age-specific estimation results are provided in Supplementary Section 4. We also carried out sensitivity analyses on parameters related to vaccination: β_i, βiv, ρ, ρ^v, τ₁, τ₂, ν₀, and 1/ψ (see Supplementary Section 7).

In this subsection, we investigate the impacts of age-specific vaccination prioritization for the primary and second doses from March 11, 2021 [14 days, duration for antibodies to be detectible (19), after the first vaccination began which is on February 26, 2021] to 6 months thereafter. The initial conditions were determined by reflecting the confirmed case data in CB, Korea at the start date of the simulation. Figure 3 shows the impact of the four age-specific vaccination prioritization strategies on daily confirmed cases and deaths. In Figure 3A, weekly age-specific confirmed COVID-19 cases of CB (circled) are compared with the model outputs under moderate and high NPI levels. The confirmed case data was most similar to the simulation results with a moderate NPI among the low, moderate, and high NPI scenarios (see the solid curves in Figure 3A). Indeed, according to Figure 1A, the level of NPI implemented in the CB region during that period was moderate.

The panels in Figures 3B–D show the time series of confirmed cases; cumulative confirmed cases; cumulative deaths; and the hospitalized population with severe symptoms at the low, moderate, and high NPI implementation levels, respectively. The number of confirmed cases was lowest when the 30−49 years age group was vaccinated first for all the NPI levels; however, the cumulative death was lowest when the comorbidity group was vaccinated first for all the NPI levels. When the comorbidity group was vaccinated first, both of the number of deaths and the number of confirmed cases were lower than when those over 60 were vaccinated first. Therefore, it can be said that it is an effective policy to inoculate the comorbidity group first in order to reduce the number of deaths and the patients with severe symptoms.

Epidemic outputs under the four age-specific vaccination prioritizations are summarized in Supplementary Tables 2–6. The number of confirmed cases decreased the most under Strategy 1 (30−49 years old) combined with a moderate NPI level. This implies that age-specific vaccination strategies with appropriate NPI policies are needed to maximize the benefits. In addition, we calculated the average R_t for 60 days under the vaccination priority scenarios in Supplementary Table 3. R_t decreased the most under Strategy 1 (30−49 years old). This is consistent with the results that the reduction in the number of confirmed cases.

Finally, we present the effects of the daily vaccination doses. Table 3 shows the number of cumulative confirmed cases and deaths under different NPI levels, daily dose of vaccination, and vaccination priority policies. Supplementary Table 2 shows percentage reduction of the estimated confirmed cases and deaths for each case. It can bee seen that at the Mod NPI level, the number of confirmed cases and the number of deaths due to vaccination were significantly reduced than at the low and high NPI levels. Therefore, if appropriate level of NPI policies such as social distancing are implemented, vaccine effectiveness can be increased. In all cases, the number of confirmed cases was the lowest when the 30−49 year olds were vaccinated first. When the daily dose is high (ν₀ = 10, 000, 15, 000), that is, when the vaccine supply is sufficient, priority should be given to the comorbidity group to reduce the number of deaths. On the other hand, when a moderate or high NPI level with relatively small vaccination doses (ν₀ = 5, 000, 7, 500), was implemented, the cumulative death was the lowest when the 30−49 year olds were first vaccinated. Moreover, when ν is small, the change in the number of cumulative confirmed cases and deaths according to the vaccination strategy is large. Therefore, it is important to apply an effective vaccination strategy when the vaccine supply is limited.

In this subsection, we investigate the impact of age-specific booster vaccination prioritization during the second period. As reported in recent studies, vaccination efficacy is decreasing due to the reduction in neutralizing antibodies (20) or the prevalence of the Omicron variant (21). Hence, we investigated the impact of the reduction in vaccine efficacy of the second dose (τ₂), priority vaccination policy, and rollout speed for booster shots.

Figure 4A presents model outputs of daily confirmed cases (left) and cumulative death (right) according to the priority vaccination strategies with daily confirmed data where black and red circles represent the number of confirmed cases in CB before and after the Omicron is dominant in Korea (January 24th, 2021). The confirmed case increases rapidly after the Omicron variant becomes dominant. According to (20), the vaccination efficacy against infection is reduced to about 0.4 after 5 months of vaccination. Therefore, we assume that the vaccine efficiency is further reduced.

Figure 4A shows the effects of the priority vaccination policies (30−49, 60+, Comorb., 20+) under τ₂ = 0.4, and daily third vaccine dose (ν^B = 10, 000). When those aged 30–49 years were vaccinated first, the number of confirmed cases and deaths decreased the most. The infection prevention rate decreases significantly while the death prevention rate does not decrease significantly (20), so prioritizing the high-activity group rather than the high-risk group seems to be effective in decreasing both confirmed cases and deaths.

Figures 4B,C shows the cumulative confirmed cases (left) and cumulative deaths (right) for 180 days in the variation of second vaccination efficacy (τ₂) and daily third vaccine doses (ν^B) for (Figure 4C) the priority vaccination strategies policies (30−49, 60+, Comorb., 20+) and (Figure 4D) for those aged 30−49 years. In Figure 4B, priority vaccination on 30−49 years groups and on 60+ years group are the most and the least effective strategies reducing cumulative cases and deaths in almost all cases. Figure 4C shows that as the second vaccination efficacy is smaller, the cumulative cases and deaths decrease more when the daily third vaccine doses increase. Therefore, it is necessary to accelerate the third vaccination as the efficacy of the second vaccination decreases.

In Korea, the first and second vaccinations are currently administered to teenagers, but booster shot vaccinations are not implemented in this subpopulation. We also studied the effects of booster shot inoculation on teenagers. Figures 4C,D show the difference in the number of confirmed cases when those aged 20 or older and those aged 10 or older were vaccinated according to the variation in second vaccination efficacy (Figure 4C) and the rollout speed of third vaccination (Figure 4D). For all cases, the cumulative confirmed cases were smaller when 10 years of age and over were vaccinated. It was shown that when the second vaccination efficacy was lower (Figure 4C) and the daily third vaccine dose was greater (Figure 4D), vaccination of teenagers reduced the number of confirmed cases. Currently, Korea's secondary vaccine efficiency is decreasing owing to the prevalence of Omicron, and the vaccine supply is sufficient. Therefore, it is recommended for teenagers to be vaccinated with a booster shot.

In this subsection, we illustrate the impact of the mitigation of NPI levels combined with age-specific vaccination for the primary and second doses (before booster shots). As the vaccination rate increased rapidly, the government planned to relax the NPI policy, and recently, the number of confirmed COVID-19 cases has increased significantly. Hence, we performed simulations of NPI relaxation from moderate to low NPI levels. We compared the effectiveness of the NPI-level mitigation policy for a population of individuals older than 10 and 20 years.

Figure 5A shows the time series of the number of new confirmed cases when the NPI level is mitigated based on the given secondary vaccination rates when the vaccination is implemented on those aged 20 years and older (top panels) and on those aged 10 years and older (bottom panels). The increase in the cumulative confirmed cases under the mitigation of NPI level when the vaccination is implemented on individuals aged 20 years and older (in red curves) and 10 years and older (in blue curves) are compared in Figure 5B.

It has been shown that too early NPI-level mitigation with low vaccination coverage could bring about another COVID-19 outbreak wave. Figure 5 shows that the increase in the confirmed cases was lower when those aged 10 years and older were vaccinated than when those aged 20 years and older were vaccinated, and the difference in the confirmed cases was greater when the vaccination coverage was low. Therefore, to mitigate NPIs effectively, it is necessary to vaccinate various groups of the population, not only to consider the vaccination rate.