question: COVID-19 pandemic is one of the major disasters that humanity has ever faced. In this paper, we try to model the effect of vaccination in controlling the pandemic, particularly in context to the third wave which is predicted to hit globally. Here, we have modified the susceptible-exposed-infected-recovered-dead model by introducing a vaccination term. One of our main assumptions is that the infection rate (β(t)) is oscillatory. This oscillatory nature has been discussed earlier in literature with reference to the seasonality of epidemics. However, in our case, we invoke this nature of the infection rate (β(t)) to model the cyclical behavior of the COVID-19 pandemic within a short period. This study focuses on a minimalistic approach where we have logically deduced that the infection rate (β(t)) and the vaccination rate (λ) are the most important parameters while the other parameters can be assumed to be constants throughout the simulation. Finally, we have studied the rich interplay between the infection rate (β(t)) and the vaccination rate (λ) on the infectious cases of COVID-19 and made some robust conclusions regarding the global behavior of this pandemic in near future. © 2022 World Scientific Publishing Company.