We employed a behavioral COVID-19 transmission model calibrated to Omicron data in South Korea, covering the period from February 1 to May 31, 2022, as reported in a recent study⁸. The model examines how behavior changes among partially immune and nonimmune individuals influence disease spread, specifically by affecting care-seeking behaviors such as vaccination and testing rates. Below, we provide a brief description of the model and calibration method.

The transmission model

A compartmental model was used to represent the transmission dynamics of the disease. In the model, the total population is divided into two major groups depending on the immune status of the individuals: partially immune—individuals who are vaccinated or have recovered from infection and are assumed to be partially immune against infection and nonimmune, who are never vaccinated or exposed to the disease. People in each group are further grouped into compartments based on the natural history of diseases—susceptible (S1, S2), exposed (E1, E2), asymptomatic infection (A1, A2), symptomatic infection-undetected (I1, I2), symptomatic infection—detected (It1, It2), hospitalized (H), and recovered (R)-and vaccination status-vaccinated with a primary series vaccination (V1) and booster vaccination (V2). The model is based on several key assumptions: First, the initial distribution of the susceptible population (S1: naive 15%, S2: immune 85%) reflects observed data, where 85% of Koreans had received at least a primary COVID-19 vaccine dose by the starting time for model simulation (February 01, 2022)⁹. The model accounts for waning immunity by considering factors such as time since vaccination, vaccine type (primary vs. booster), and prior infection. Immunity declines over time (\(\phi\)), reducing the effectiveness of primary series vaccines from an initial level (\(\eta _1\)) to a lower level (\(\eta _2\)) after \(\phi\) time. Booster doses restore protection (\(\eta _4\)), whereas infection recovery provides immunity (\(\eta _3\)) comparable to or greater than that of vaccination alone after the average waning period. Second, individuals will seek testing only if they exhibit symptoms or if they are asymptomatic but believe they have been in contact with an infected person. Third, 80% of individuals who test positive and all hospital admissions comply with self-quarantine, reducing transmission. Self-isolation includes minimizing contact, mask-wearing, and hygiene, not just staying home. Studies reported quarantine adherence rates of 74–94% in South Korea, exceeding 85% before the Omicron wave^10,11. Fourth, reactivity to disease information varies by immune status: naïve individuals often exhibit stronger fear responses, whereas immune individuals perceive themselves as less vulnerable because they presume prior infection or protection. Importantly, the vaccination and testing rates are assumed to depend on two rates: the mandatory rate and the voluntary rate. The mandatory rate reflects baseline uptake among individuals or groups—such as older adults, teachers, and healthcare workers—for whom vaccination or testing is required or strongly recommended, thereby capturing inherent acceptance and compliance. This rate is assumed to remain unaffected by changes in the disease level within the population and is therefore represented as a constant. The voluntary rate is a rate for a portion of the population that voluntarily chooses to be vaccinated or tested depending on the information about the level of disease prevalence and severity. The voluntary rates are influenced by several factors, including information coverage, individuals’ responsiveness to information, the delay in information reaching the population, and information prioritization (among prevalence and severity) that differs between nonimmune and partially immune populations. The rate of change in the number of individuals within each compartment was determined by solving a system of ordinary differential equations describing the transitions of the state variables over time. A flowchart illustrating disease transmission, the governing system of ordinary differential equations, along with the formulations for vaccination and testing rates, is provided in Supplementary Fig. S1, Eqn. S1, Eqns. S3–S6 online.

Data

Parameter values in the model are determined through two approaches: (1) utilizing demographic and epidemiological data from Our World in Data⁹ and prior studies and (2) fitting the model to Korean COVID-19 data on vaccination, incidence, and mortality during the Omicron wave, covering the period from February 1, 2022, to May 31, 2022 (see Supplementary Fig. S2 online). A detailed description of the parameters, their values, and references is provided in Supplementary Table S1 online.

Cost

We accounted for direct costs associated with vaccination, testing and treatment. The vaccination (testing) cost is obtained by multiplying the average per person cost of vaccination (test) and the total number of vaccinated (tested) individuals. The vaccination and testing costs encompass the average per-person cost of vaccines (or test kits), procedural expenses, and logistics. South Korea’s COVID-19 control strategy combined rapid antigen tests (RATs) and RT-PCR assays, with RATs widely used for home based screening due to their low cost and fast turnaround, and RT-PCR for confirmatory testing^12,13,14. However, it was difficult to ascertain the exact distribution between PCR and RAT use, and given the possibility of duplicate testing across modalities, we assumed RAT to be the primary diagnostic practice during the peak of the Omicron wave. Treatment costs cover both inpatient and outpatient care. We assume that 20% of detected cases are managed as outpatients. The inpatient costs are calculated as the product of the average daily hospital cost per patient, the mean length of stay ( 10 days), and the cumulative number of hospitalised cases. The outpatient costs are the average cost per visit multiplied by the total number of outpatient visits. Testing costs in this study were estimated using South Korean currency and converted to U.S. dollars at the 2024 exchange rate, while other costs were drawn from published literature based on South Korean data. All costs are therefore reported in U.S. dollars. The costs for vaccination, testing, and treatment are detailed in Table 1. Additionally, the table includes descriptions and values for certain epidemiological and behavior-related parameters, which are pertinent to the sensitivity analysis.

Scenarios

To evaluate the impact of voluntary compliance, we analyzed two scenarios: (1) care-seeking driven solely by mandatory policies, where individuals do not perceive COVID-19 as a threat and therefore vaccinate or test only if required (i.e., individuals’ behavior no longer responds to disease burden); and (2) care-seeking influenced by both mandatory policies and voluntary decisions, where individuals adjust their vaccination or testing behavior in response to population-level prevalence. Comparing these scenarios highlights the incremental effect of voluntary care seeking compliance on incidence, healthcare demand, and health system costs, compared to the mandatory components alone. The economic evaluation adopts a healthcare system perspective, including direct medical costs of testing, vaccination, and treatment. Outcomes include averted cumulative incidence, averted total cost, and ICER to measure the effect of voluntary care-seeking strategies relative to a mandatory-only strategy. We assessed the distribution of the population in the care cascade between the two scenarios–mandatory policies and voluntary decisions—and its consequences to costs related to vaccination, testing, and treatment (Fig. 1).

Sensitivity analysis

We conducted several sensitivity analyses related to voluntary care-seeking behavior. First, we examined how changes in voluntary compliance—through varying information coverage, reactivity, and prioritization of prevalence versus severity—affected cumulative incidence and total costs. In this framework, information coverage reflects government-driven efforts, while reactivity and prioritization represent patient-driven responses (Fig. 2). Second, we explored the possibility that immune individuals may respond differently to vaccination and testing. Our hypothesis was that immunized individuals might be less inclined to seek additional vaccination but more likely to seek testing if they suspect infection. We considered three scenarios for clarity: (i) reactivity only to voluntary testing (vaccination = 0, testing = 10); (ii) reactivity only to voluntary vaccination (vaccination = 10, testing = 0); and (iii) reactivity to both voluntary testing and vaccination (vaccination = 10, testing = 10) (Fig. 3 and Table 2).

Finally, we also performed one-way sensitivity analyses with a comprehensive list of parameters and a probabilistic sensitivity analysis (PSA) to capture the combined impact of parameter uncertainty on model outcomes. Key epidemiological, behavioral, and cost parameters-including vaccine efficacy (\(\eta _1, \eta _2, \eta _3, \eta _4\)), quarantine proportion (\(\delta\)), symptomatic proportion (\(\tau\)), reduced infection rate for asymptomatic class (\(\psi\)), transmission rates (\(\beta _1, \beta _2\)), behavioral parameters (\(k, \theta , \alpha _1, \alpha _2\)), and unit costs for vaccination, testing, hospitalization, and outpatient care—were simultaneously varied around baseline estimates (some estimated through model fitting and others drawn from the literature) with parameter distributions specified such that their 95% confidence intervals approximated \(\pm 10\%\) the baseline value, see Table 1. For each of 1000 Monte Carlo simulations, parameter values were sampled from their respective distributions, the model was solved under four scenarios (only mandatory vaccination and testing (reference scenario) and three voluntary vaccination and testing scenarios—response to only voluntary vaccination, response to only voluntary testing and response to both), and ICERs were calculated relative to the reference scenario. PSA results were summarized using mean values and 95% uncertainty intervals for each outcome per scenario (Table 2), and a cost-effectiveness plane was generated to illustrate the joint distribution of incremental costs and effects (Fig. 4, panel a). In addition, cost-effectiveness acceptability curves (CEACs) were constructed to assess the probability that each strategy is cost-effective across a range of willingness-to-pay thresholds (Fig. 4, panel b).