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.
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