# Projecting the Impact of SARS-CoV-2 Variants and the Vaccination Program on the Fourth Wave of the COVID-19 Pandemic in South Korea

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Model Structure

#### 2.2. Disease Dynamics

#### 2.3. Vaccination

Notation | Description | Estimates | References |
---|---|---|---|

$1/{\gamma}_{E}$ | Incubation period (days) | 5.2 days | [18] |

$1/{\gamma}_{A}$ | Asymptomatic period (days) | 5.0 days | [16,20,21] |

$1/{\gamma}_{P}$ | Pre-symptomatic period (days) | 2.3 days | [14,16,19] |

$1/{\gamma}_{M}$ | Infectious period from onset of mild symptoms (days) | 3.2 days | [16,20] |

$1/{\gamma}_{S}$ | Infectious period from onset of severe symptoms (days) | 3.2 days | [16,20] |

$1-\sigma $ | Reduction of infection by variant strain due to cross immunity | 0.7 | [32] |

$\upsilon $ | Relative transmission potential of strain 2 compared to strain 1 | 2 | [10] |

${q}_{A}$ | Relative infectivity of asymptomatic individuals compared to the pre-symptomatic stage | 0.26 | [15] |

${q}_{M}$ | Relative infectivity of mildly symptomatic individuals compared to the pre-symptomatic stage, considering isolation | 0.22 | [14,17,33] |

${q}_{I}$ | Relative infectivity of severely symptomatic individuals compared to the pre-symptomatic stage, considering isolation | 0.44 | [14,17,33] |

${h}_{k}$ | Proportion of infections that are symptomatic | 0.29 for k = 1; 0.21 for k = 2; 0.27 for k = 3; 0.33 for k = 4; 0.40 for k = 5; 0.49 for k = 6; 0.63 for k = 7; 0.69 for k = 8 | [13] |

${\rho}_{k}$ | Proportion of symptomatic cases that exhibit mild symptoms | 0.90 for k = 1 and 2; 0.85 for k = 3, 4, and 5; 0.60 for k = 6 and 7; 0.20 for k = 8 | [34,35] |

${\eta}_{1,k}$ | Vaccine efficacy, after the first dose to before the second dose, against infection by strain 1 among the age group k | 0.53 for k = 1, 2, …, 6; 0.37 for k = 7 and 8 | [22,23,24,31] |

${\eta}_{2,k}$ | Vaccine efficacy, after the first dose to before the second dose, against infection by strain 2 among the age group k | 0.21 for k = 1, 2, …, 6; 0.14 for k = 7 and 8 | [10,29,36,37] |

${\delta}_{1,k}$ | Vaccine efficacy, after the first dose to before the second dose, against symptomatic disease by strain 1 among the age group k | 0.58 for k = 1, 2, …, 6; 0.41 for k = 7 and 8 | [22,23,24,31] |

${\delta}_{2,k}$ | Vaccine efficacy, after the first dose to before the second dose, against symptomatic disease by strain 2 among the age group k | 0.14 for k = 1, 2, …, 6; 0.10 for k = 7 and 8 | [10,29,36,37] |

${\alpha}_{1,k}$ | Vaccine efficacy, after the second dose, against infection by strain 1 among the age group k | 0.64 for k = 1, 2, …, 6; 0.37 for k = 7 and 8 | [38,39] |

${\alpha}_{2,k}$ | Vaccine efficacy, after the second dose, against infection by strain 2 among the age group k | 0.48 for k = 1, 2, …, 6; 0.33 for k = 7 and 8 | [8,9] |

${\chi}_{1,k}$ | Vaccine efficacy, after the second dose, against symptomatic disease by strain 1 among the age group k | 0.37 for k = 1, 2, …, 6; 0.26 for k = 7 and 8 | [22,23,24,31] |

${\chi}_{2,k}$ | Vaccine efficacy, after the second dose, against symptomatic disease by strain 2 among the age group k | 0.33 for k = 1, 2, …, 6; 0.23 for k = 7 and 8 | [8,9] |

#### 2.4. Model Implementation

**Table 2.**Cumulative percentage of people who have received a COVID-19 vaccine in South Korea by vaccination status and age group as of 5 July 2021 [25].

Partially Vaccinated (%) | Fully Vaccinated (%) | ||
---|---|---|---|

Total | 19.5 | 10.4 | |

Age group | 20–29 | 6.4 | 4.1 |

30–39 | 16.4 | 14.4 | |

40–49 | 9.0 | 4.7 | |

50–59 | 8.6 | 3.6 | |

60–69 | 79.9 | 3.3 | |

70 and above | 33.6 | 51.1 |

## 3. Results

_{e}= 1.2. For the base-case scenario without the emergence of a SARS-CoV-2 variant, the attack rate was projected to be 6.9% on day 150 without further vaccination.

#### 3.1. Attack Rates

_{e}= 1.3, the vaccination program would reduce the attack rate from 9.2% to 4.9%, averting 47% of symptomatic infections.

#### 3.2. Hospitalization and Deaths

## 4. Discussion

## 5. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Model diagram of COVID-19 transmission and vaccination with two co-circulating strains, denoted by n (n = 1 or 2). All individuals are stratified by age, although age indices have been omitted for clarity.

**Figure 2.**Impact of vaccination program against COVID-19 during the fourth wave in the absence of SARS-CoV-2 variant. (

**A**) Projected cumulative attack rates over 150 days with and without further vaccination. The shaded areas represent the simulation outputs with lower and higher reproductive ratios of the wild type with R

_{e}= 1.1 and 1.3, respectively. (

**B**) Overall and age-specific relative reduction of attack rates with vaccination, as compared to the outbreak scenario without further vaccination over 150 days.

**Figure 3.**Impact of vaccination program against COVID-19 during the fourth wave in the presence of SARS-CoV-2 variant. The shaded areas represent the simulation outputs with lower and higher reproductive ratios of the Delta variant with $\upsilon =1.8$ and $\upsilon =2.2$, respectively (

**A**) Projected cumulative attack rates over 150 days with and without further vaccination. (

**B**) Overall and age-specific relative reduction of attack rates with vaccination, as compared to the outbreak scenario without further vaccination over 150 days.

**Figure 4.**Projected total number of (

**A**) ICU hospitalizations and (

**B**) deaths per 10,000 persons over 150 days.

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**MDPI and ACS Style**

Shim, E. Projecting the Impact of SARS-CoV-2 Variants and the Vaccination Program on the Fourth Wave of the COVID-19 Pandemic in South Korea. *Int. J. Environ. Res. Public Health* **2021**, *18*, 7578.
https://doi.org/10.3390/ijerph18147578

**AMA Style**

Shim E. Projecting the Impact of SARS-CoV-2 Variants and the Vaccination Program on the Fourth Wave of the COVID-19 Pandemic in South Korea. *International Journal of Environmental Research and Public Health*. 2021; 18(14):7578.
https://doi.org/10.3390/ijerph18147578

**Chicago/Turabian Style**

Shim, Eunha. 2021. "Projecting the Impact of SARS-CoV-2 Variants and the Vaccination Program on the Fourth Wave of the COVID-19 Pandemic in South Korea" *International Journal of Environmental Research and Public Health* 18, no. 14: 7578.
https://doi.org/10.3390/ijerph18147578