A Study on Herd Immunity of COVID-19 in South Korea: Using a Stochastic Economic-Epidemiological Model
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A Study on Herd Immunity of COVID‑19 in South Korea: Using a Stochastic Economic‑Epidemiological Model Hojeong Park1,2 · Songhee H. Kim3,4 Accepted: 30 June 2020 © Springer Nature B.V. 2020
Abstract Vaccination is an effective measure to control the diffusion of infectious disease such as COVID-19. This paper analyzes the basic reproduction number in South Korea which enables us to identify a necessary level of vaccine stockpile to achieve herd immunity. An susceptible-infected-susceptible model is adopted that allows a stochastic diffusion. The result shows that the basic reproduction number of South Korea is approximately 2 which is substantially lower than those of the other regions. The herd immunity calculated from economic-epidemiological model suggests that at least 62% of the susceptible population be vaccinated when COVID-19 vaccine becomes available. Keywords COVID-19 · Vaccination stockpile · SIS · Stochastic disease JEL Classification D81 · I18
1 Introduction Although COVID-19 virus is still ongoing in South Korea, the number of new infected cases has been substantially reduced since the mid April. The diffusion rate of the virus has been suppressed as a result of the various measures and efforts, e.g. the policy to keep social distancing among others. However, because the possibility of second or third wave of COVID-19 cannot be ruled out, it is necessary to study the level of herd immunity of COVID-19. This short paper attempts to examine the herd immunity of COVID-19 using an economic-epidemiological model. The model allows us to calculate the basic reproduction number, R0 , which is an essential indicator to understand the infective power of the virus. * Hojeong Park [email protected] 1
Department of Food and Resource Economics, Korea University, Seoul, Korea
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KU KIST Energy and Environment School, Korea University, Seoul, Korea
3
Department of Microbiology, College of Medicine, Yonsei University, Seoul, Korea
4
Institute of Immunology and Immunological Diseases, College of Medicine, Yonsei University, Seoul, Korea
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Vol.:(0123456789)
H. Park, S. H. Kim
The herd immunity calculated by means of R0 provides a useful information on the scale of vaccine stockpile, if there is any vaccine that will be available in the near future. In addition, the paper confirms the importance of the social distancing rule in curbing the spread of the virus. We start with an epidemiological model to analyze the herd immunity of COVID-19 in South Korea. The model to be presented in the paper is based on SIS (Susceptible-InfectedSusceptible) in which the population is distinguished into two compartments: susceptible S and infected I. An alternative compartment model is SIR (Susceptible-Infected-Recovered) that allows the full immunity once recovered from a disease. Which model is suitable for COVID-19 depends on whether the population can obtain immunity to the disease. As discussed in Bokharaie (2020), it is somewhat premature to say which is the suitable one for analyzing COVID-19. Neverthel
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