Due to the severity of COVID-19, vaccination campaigns have been or are underway in most parts of the world. In the current circumstances, it is obligatory to examine the response of vaccination on transmission of the SARS-CoV-2 virus when there are many vaccines available. Considering the importance of vaccination, a dynamic model has been proposed to provide an insight in the same direction. A mathematical model has been developed where six population compartments viz. susceptible, infected, vaccinated, home-isolated, hospitalized and recovered population are considered. Moreover, two novel parameters are included in the model to ascertain the effectiveness and speed of the vaccination campaign. Reproduction number and local stability of both the disease-free and endemic equilibrium points are studied to examine the nature of population dynamics. Graphical results for the community stage of COVID-19 infection are simulated and compared with real data to ascertain the validity of our model. The data is then studied to understand the impact of vaccination. These numerical results evidently demonstrate that home isolation and hospitalization should continue for the infected people until the transmission of the virus from person to person reduces sufficiently after completely vaccinating every nation. This model also recommends that all type of prevention measures should still be taken to avoid any type of critical situation due to infection and also reduce the death rate.
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