Contact-adjusted immunity levels against COVID-19 in South Korea

June Young Chun¹, Hwichang Jeong² Yongdai Kim²

1 Department of Internal Medicine, National Cancer Center, Goyang, South Korea / june.y.chun@gmail.com

2 Department of Statistics, Seoul National University, Seoul, South Korea

Main Concept:

Following the general concept of previous study: June Young Chun, Wan Beom Park, Nam Joong Kim, Eun Hwa Choi, Sebastian Funk, Myoung-don Oh (2019). Estimating contact-adjusted immunity levels against measles in South Korea and prospects for maintaining elimination status.

Detailed Method: Contact-adjusted immunity r' is given by

r'=1−R/R₀

where R/R₀ is the ratio of the effective reproduction number R to the basic reproduction number R₀. In an age-structured population, the basic reproduction number is related to the contact matrix via

R₀=ρ(K)

where ρ denotes the spectral radius and K is a next generation matrix(NGM) with elements

k_ij=q_iϕ_ijN_i/N_j

where q_i is the probability that a contact between a susceptible in age group i and an infectious person leads to infection, ϕ_ij is the number of contacts that an individual in age group i makes with that in age group j, and N_i is the size of age group i. The effective reproduction number R is obtained in the same way, except that the matrix K is multiplied with a vector of susceptibility to yield an effective matrix K'

k'_ij=k_ij(1−r_i)

where r_i is the proportion immune in age group i.

Here, we included both vaccinated and infected individuals in age group i as immune (r_i ). We could only include population who received one dose of COVID-19 vaccine, and assume 86% of vaccine efficacy for Astrazeneca vaccine, 89.7% efficacy for Pfizer vaccine, and 66.9% efficacy for Janssen vaccine according to the KDCA report. For those who have been infected by COVID-19, we regard they acquired 100% of immunity.

We tried to capture the changes of contact patterns as a result of social distancing measures, and much detailed method could be found in the manuscript “COVID-19 Vaccine Prioritisation in Japan and South Korea” (doi: https://doi.org/10.1101/2021.04.16.21255649).

Conclusion:

The contact adjusted immunity against COVID-19 by June 21th, 2021 under the social distancing level 2 is 14.1% (12.5% under the social distancing level 1).

※ The optimal distribution of COVID-19 vaccines under the limited resources could be found in the study below. COVID-19 Vaccine Prioritisation in Japan and South Korea doi: https://doi.org/10.1101/2021.04.16.21255649