We adapted a previously described model which estimated the age-varying susceptibility to the Delta variant [9] and updated the model with recent vaccine coverage data and waning of vaccine effectiveness against the Omicron infection.

Age-stratified daily COVID-19 incidence and vaccine uptake rates have been reported in public by the Ministry of Health and Welfare of South Korea through NIDSS and National Immunization Registry [7, 8, 10]. More refined vaccination data of doses and manufacturers were provided by Korea Disease Control and Prevention Agency (KDCA) and National Health Insurance Service (NHIS). Age-structured population data was obtained from the Statistics Korea [11].

Following our previous study, we built an age-structured compartmental model stratified into 5-year age bands [9]. Compartments in the model were stratified by infection states (i.e., susceptible [S], exposed [E], infectious and pre-symptomatic [Ipresym], infectious and symptomatic [Isym], infectious and asymptomatic [Iasym], or quarantined [Q]), age band, and the transition time to the next infection state (Additional file 1: eMethods). In South Korea, individuals diagnosed with COVID-19 are isolated immediately; thus, the confirmation date could be regarded as the date on which quarantine started.

The strength of this model is that we know the diagnostic delay distribution (symptom onset to Q), transmission onset distribution relative to the symptom onset (I given symptom onset), and latent period distribution (E to I), based on the robust contact tracing study in South Korea (Table 1) [12]. For those who had never developed any symptoms (Iasym), we assumed that their latent period distribution was the same as that of individuals who developed symptoms (Ipresym → Isym) and that their infectious period distribution was the same as the total infectiousness period distribution of symptomatic individuals as suggested [13]. With this backward inference method, the remaining unknown distribution was the transition time from S to E, which depends on the force of infection. To estimate the parameters in the force of infection, we used a Bayesian inference method with a carefully designed Markov chain Monte Carlo (MCMC) algorithm. In this MCMC algorithm, we inferred the exposure times conditional on that the force of infection for each age group i was known and then inferred the force of infection given that the exposure times were available. We repeated these two steps several times until the Markov chain converged.

According to Vynnycky and White [22], the force of infection λi is written as follows:

Here, βij is the rate at which susceptible individuals in the age group i and infectious individuals in the age group j come into effective contact per unit time, and Ιj is the number of infectious individuals in the age group j. We further divide βij into:

Here, qi is the probability that a contact between a susceptible individual in age group i and an infectious person leads to infection, ϕij is the number of contacts an individual in age group j makes with those in age group i per unit time, and ni is the number of individuals in age group i. Since we know the contact matrix for South Korea and the age-stratified incidence of COVID-19 at discrete time t, we could infer the λi (accordingly qi) of age group i [23]. To capture the changes of contact patterns as a result of social distancing measures, we considered school closure policies and reduced contact rates both at work and other places using Google mobility data (Fig. 1A, Additional file 1: Table S1 to S2) [24, 25]. Detailed Bayesian inference methods are available in Additional file 1: eMethods. All analyses were conducted using the Python statistical software version 3.6.13.

The age-specific susceptibility (qi) during the 5th wave (Omicron driven, from January 1 to January 31, 2022) were compared with those during the 4th (Delta driven, from June 27 to August 21, 2021) and 3rd (pre-Delta, from October 15 to December 22, 2020) waves in South Korea. Since we know the domestic composition of variants during the study period (Fig. 1C), we only take into account the Omicron infections during the 5th wave and the Delta infections during the 4th wave.

As vaccine uptake increased, individuals who were vaccinated have been excluded from the susceptible population in accordance with the vaccine effectiveness against the Delta and the Omicron variants. The waning of vaccine effectiveness was also considered [21]. In detail, age-specific vaccine coverage data by vaccine doses and manufacturers have been reported weekly by the Ministry of Health and Welfare of South Korea (Additional file 1: Table S3) [7]. We divided the weekly number of immunized individuals by 7 to get a daily number of immunized individuals for the corresponding week and removed them from the susceptible population 2 weeks after the vaccination, considering the time to achieve immunity against COVID-19.

There are uncertainties about these model parameters, including the age-specific contact patterns, the proportion of individuals who were infected and asymptomatic, and vaccine effectiveness. Therefore, we varied those values with sensitivity analyses. First, the number of contacts made in school was varied from 0.8-fold to 1.2-fold to the baseline, given that school-aged children have higher contact rates compared with other age groups and were likely to affect the result most. Second, considering the high asymptomatic infections with the Omicron variant, we increased the proportion of asymptomatic infections to 50% in all age groups [26]. At baseline, we adopted the prospective household cohort study reporting age-varying asymptomatic proportions (i.e., 52%, 50%, 45%, and 12% among individuals aged 0–4 years, 5–11 years, 12–17 years, and ≥18 years, respectively) [14]. For vaccine effectiveness, we adopted lower and upper bounds of the 95% confidence interval (CI) for sensitivity analyses as reported in another study [21].