Highlights
- •Age-specific fractions immune to SARS-CoV-2 in Japan were examined.
- •Fractions immune to infection varied by age.
- •Vaccination contributed to a substantial decrease in the reproduction number.
ABSTRACT
Objectives
Methods
Results
Conclusion
Keywords
Introduction
- Haas EJ
- Angulo FJ
- McLaughlin JM
- Anis E
- Singer SR
- Khan F
- et al.
- Thompson MG
- Burgess JL
- Naleway AL
- Tyner HL
- Yoon SK
- Meece J
- et al.
- Haas EJ
- Angulo FJ
- McLaughlin JM
- Anis E
- Singer SR
- Khan F
- et al.
GISAID, 2022, https://www.gisaid.org (accessed 15 June 2022)
- Ferdinands JM
- Rao S
- Dixon BE
- Mitchell PK
- DeSilva MB
- Irving SA
- et al.
National Institute of Infectious Diseases, 2021. About new concerning variant of SARS-CoV-2 that may have different infectiousness, transmissibility, and antigenicity (9th report), https://www.niid.go.jp/niid/ja/2019-ncov/2484-idsc/10434-covid19-43.html. (accessed 15 June 2022)
Ministry of Health, Labour and Welfare, 2021a. The situation analysis on COVID-19 and response from MHLW, December 31, 2021. https://www.mhlw.go.jp/stf/newpage_23137.html (accessed 15 June 2022)
Materials and methods
Vaccine registry data
Statistical model
First doses allocated to healthcare workers
First doses administered to the general population, university students/staff, and company employees
2.2.2 Estimating the number of vaccinees with a reporting delay in the VRS
where is the number of people vaccinated on day and reported on day , and represents the true number of people vaccinated on day . We assumed that the proportion of vaccinees on day who were reported by day followed, which is a cumulative distribution function of the delay and has a gamma distribution. The gamma distribution parameters were estimated through the maximum likelihood method and assuming that followed a Poisson distribution:
where E(.) represents the expected number, represents the date on which the VRS dataset was obtained, is the dataset number (= 10 snapshots), and represents the population parameter governing the gamma distribution. To quantify the uncertainty of the parameters, a parametric bootstrap method was employed, resampling 1,000 sets of parameters using a Hessian matrix. The number of vaccinees, , was calculated, accounting for the estimated reporting delay.
2.2.3 Estimating the age-specific fraction of people who are susceptible to infection
where represents the cumulative number of people immune to infection at time in age group , and is the maximum vaccination effectiveness, which we assumed to be 0.8 against infection with the Delta variant (
where and are the number of documented infections among unvaccinated and vaccinated population, respectively at time (i.e., days elapsed since receiving the first dose), whereas and are the total number at risk during each fraction of follow-up period. was determined to be the median of each period at risk. We employed the bootstrapping method and derived 1,000 sample parameter sets from a Hessian matrix. It should be noted that this time-varying vaccine effectiveness since the first dose vaccination is based on the assumption that all of those who received the first dose vaccine would take the second dose on day 21 after the first dose. This assumption was deemed reasonable because the percentage of people who received the first dose but not second dose was only about 1% in Japan (
Prime Minister's Office of Japan, 2022. About COVID-19 vaccination 2022, https://www.kantei.go.jp/jp/headline/kansensho/vaccine.html. (accessed 15 June 2022)
where represents the fraction of people susceptible to infection in age group at time , and is the number of people in age group . The 95% CIs for were computed by two sets of samples: parameters for the gamma distribution, representing the reporting delay in the VRS, and the Weibull distribution, representing the time-dependent vaccine effectiveness. This study monitored the immune landscape near the end of the two-dose program; for simplicity, we did not account for waning immunity.
2.2.4 Next-generation matrix
where is the relative susceptibility to infection through an effective contact with a COVID-19 case in age group . is the contact rate between an infectee in age group and an infector in age group , obtained from a contact survey conducted in Japan (
where represents the number of newly infected COVID-19 cases in age group on day , and is the probability mass function of the generation time. We quantified the NGM during the period in which the Alpha variant was initially present in Japan, using the confirmed case data (representing the incidence of symptom onset on day ) and the serial interval (
where represents the expected number of cases derived from the right-hand side of Equation (8). Minimizing the negative logarithm of Equation (9), we obtained the unknown parameter , i.e., {}. The 95% CIs were calculated using parametric bootstrapping.
2.2.5 Time-dependent reproduction number
where represents the fraction of people who are susceptible to infection in age group at time estimated from Equation (6), and is the NGM as derived from the Alpha variant epidemic. We set June 6, 2021 as the starting point for applying Equation (10); this day was just before vaccinations shifted from focusing on older people to the younger age groups. The relative reduction of the reproduction number was explored using the dominant eigenvalue of the time-dependent NGM over time. We used the from the Alpha variant epidemic, but the monitoring was carried out during the period when the Delta variant was dominant. We therefore further assessed an impact of the replacement of Alpha by Delta, by adjusting the estimated largest eigenvalues on the basis of the relative transmissibility of the variants (
Results





Discussion
- Abu Jabal KA
- Ben-Amram H
- Beiruti K
- Batheesh Y
- Sussan C
- Zarka S
- et al.
Prime Minister's Office of Japan, 2022. About COVID-19 vaccination 2022, https://www.kantei.go.jp/jp/headline/kansensho/vaccine.html. (accessed 15 June 2022)
Ministry of Health, Labour and Welfare, 2021b. Advisory board for COVID-19 control, 50th. https://www.mhlw.go.jp/stf/seisakunitsuite/bunya/0000121431_00294.html (accessed 15 June 2022)
Conflict of interest
Funding sources
Ethical approval statement
Acknowledgments
Appendix. Supplementary materials
Supplementary material
Supplementary data 1: Openly shared Vaccination Record System (VRS) data from February 17, 2021, to October 17, 2021
Supplementary data 2: Age-dependent fraction susceptible from February 17, 2021, to October 17, 2021
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