Theoretical Analysis of SIRVVD Model to Provide Insight on the Target Rate of COVID-19/SARS-CoV-2 Vaccination in Japan

TL;DR

This paper provides a theoretical analysis of the SIRVVD model for COVID-19 vaccination, deriving an analytical expression for infection numbers and determining target vaccination rates to control the spread in Japan.

Contribution

It offers a novel analytical solution for the SIRVVD model and insights into optimal vaccination rates for different COVID-19 variants in Japan.

Findings

Derived an analytical expression for infection numbers in the SIRVVD model.

Identified target vaccination rates to reduce COVID-19 infections.

Compared vaccination strategies for different COVID-19 variants.

Abstract

The effectiveness of the first and second dose vaccinations are different for COVID-19; therefore, a susceptible-infected-recovered-vaccination1-vaccination2-death (SIRVVD) model that can represent the states of the first and second vaccination doses has been proposed. By the previous study, we can carry out simulating the spread of infectious disease considering the effects of the first and second doses of the vaccination based on the SIRVVD model. However, theoretical analysis of the SIRVVD Model is insufficient. Therefore, we obtained an analytical expression of the infectious number, by treating the numbers of susceptible persons and vaccinated persons as parameters. We used the solution to determine the target rate of the vaccination for decreasing the infection numbers of the COVID-19 Delta variant (B.1.617) in Japan. Further, we investigated the target vaccination rates for cases with strong or weak variants by comparison with the COVID-19 Delta variant (B.1.617). This study contributes to the mathematical development of the SIRVVD model and provides insight into the target rate of the vaccination to decrease the number of infections.