Theoretical Analysis of the SIRVVD Model for Insights Into the Target Rate of COVID-19/SARS-CoV-2 Vaccination in Japan

The effectiveness of the first dose of vaccination for COVID-19 is different from that of the second dose; therefore, in several studies, various mathematical models that can represent the states of the first and second vaccination doses have been developed. Using the results of these studies and considering the effects of the first and second vaccination doses, we can simulate the spread of infectious diseases. The susceptible-infected-recovered-vaccination1-vaccination2-death (SIRVVD) model is one of the proposed mathematical models; however, it has not been sufficiently theoretically analyzed. Therefore, we obtained an analytical expression for the number of infected persons by considering the numbers of susceptible and vaccinated persons as parameters. We used the solution to determine the target vaccination rate for decreasing the infection numbers of the COVID-19 Delta variant (B.1.617) in Japan. Furthermore, we investigated the target vaccination rates for cases with strong or weak variants by comparing with the COVID-19 Delta variant (B.1.617). This study contributes to the mathematical development of the SIRVVD model and provides insights into the target vaccination rate for decreasing the number of infections.