J Korean Med Sci.  2022 Jul;37(26):e209. 10.3346/jkms.2022.37.e209.

Multi-Faceted Analysis of COVID-19 Epidemic in Korea Considering Omicron Variant: Mathematical Modeling-Based Study

  • 1Department of Mathematics, Konkuk University, Seoul, Korea
  • 2Institute of Mathematics, University of the Philippines Diliman, Quezon City, Philippines
  • 3Division of Infectious Disease, Department of Internal Medicine, Kangnam Sacred Heart Hospital, Hallym University College of Medicine, Seoul, Korea
  • 4Division of Public Health Emergency Response Research, Korea Disease Control and Prevention Agency, Cheongju, Korea


The most recent variant of concern, omicron (B.1.1.529), has caused numerous cases worldwide including the Republic of Korea due to its fast transmission and reduced vaccine effectiveness.
A mathematical model considering age-structure, vaccine, antiviral drugs, and influx of the omicron variant was developed. We estimated transmission rates among age groups using maximum likelihood estimation for the age-structured model. The impact of non-pharmaceutical interventions (NPIs; in community and border), quantified by a parameter μ in the force of infection, and vaccination were examined through a multi-faceted analysis. A theory-based endemic equilibrium study was performed to find the manageable number of cases according to omicron- and healthcare-related factors.
By fitting the model to the available data, the estimated values of μ ranged from 0.31 to 0.73, representing the intensity of NPIs such as social distancing level. If μ < 0.55 and 300,000 booster shots were administered daily from February 3, 2022, the number of severe cases was forecasted to exceed the severe bed capacity. Moreover, the number of daily cases is reduced as the timing of screening measures is delayed. If screening measure was intensified as early as November 24, 2021 and the number of overseas entrant cases was contained to 1 case per 10 days, simulations showed that the daily incidence by February 3, 2022 could have been reduced by 87%. Furthermore, we found that the incidence number in mid-December 2021 exceeded the theory-driven manageable number of daily cases.
NPIs, vaccination, and antiviral drugs influence the spread of omicron and number of severe cases in the Republic of Korea. Intensive and early screening measures during the emergence of a new variant is key in controlling the epidemic size. Using the endemic equilibrium of the model, a formula for the manageable daily cases depending on the severity rate and average length of hospital stay was derived so that the number of severe cases does not surpass the severe bed capacity.


COVID-19; Mathematical Modeling; Omicron Variant; Nonpharmaceutical Interventions; Endemic; Vaccination


  • Fig. 1 Flow diagrams of the mathematical model of coronavirus disease 2019 in Korea. (A) Epidemiological flow diagram, where Xi represents a vaccine- or waning-related status of a host in compartment X and age group i. Note that X can be u, w, v1, v2, wv, b, or wb and each follows this epidemiological flow. (B) Flow diagram describing vaccination, including booster, and waning of immunity after vaccination or infection, which constitute the IN flow to and OUT flow from each Xi in (A). The time-dependent parameters νi(t) and νib(t) are the number of primary and booster doses administered per day and are obtained from data. The blue line in the bottom graph shows that the values used for vaccine effectiveness against severe infection are the same across all vaccinated individuals but the vaccine effectiveness against infection (red curve) peaks after completing the primary dose and after getting a booster shot.

  • Fig. 2 The transmission rate matrix among age groups using maximum likelihood estimation.

  • Fig. 3 Estimation results of the qualification of NPIs. (A) Daily incidence, NPIs-related reduction factor, and reproductive number. Dark solid curve is the model simulation and red boxes are data. Pale blue solid lines indicate NPIs-related reduction factor and dashed curve is the effective reproductive number. The magenta curve is the proportion of omicron variant among new cases. (B) Cumulative incidence. (C) Administered severe patients. Red dashed curve indicates the severe patient capacity of Korea. (D) Proportion of incidence by age on two different periods. The blue bar is from August 1 to December 31, 2021, and the red bar is from January 1 to February 3, 2022. The green boxes indicate data.NPI = non-pharmaceutical intervention.

  • Fig. 4 Forecast results considering different intensity of NPIs and vaccine hesitancy. (A) Daily incidence. (B) Administered severe patient. Colors of model simulation curves indicate the value of NPIs related factor (µ). The solid and dashed curves correspond to maximum daily booster shot administration set to 300,000 and 100,000, respectively. Blue dotted line in (B) is the expected severe patient capacity assuming that the increasing trend continues (25.42 per day, based on historical data), while the red dotted line indicates a constant trend. Red boxes are the data points.NPI = non-pharmaceutical intervention.

  • Fig. 5 Examination of screening measure. Colored area indicates the range of daily incidence in log-scaled simulation as the number and date of daily overseas entrant case is varied.

  • Fig. 6 Theory-driven manageable number of daily incidence considering endemic equilibrium. (A) Color-scaled result considering varying length of hospital stay and severe rate, with fixed severe patient capacity to 2,800. Blue square indicates the severe rate of Korea in mid-February 2022. (B) Color-scaled result considering varying severe patient capacity and severe rate, with fixed length of hospital stay as 7 days. (C) Real daily incidence data and theory-driven manageable number of daily incidence using real data.


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