ABSTRACT
The world’s largest vaccination program to control COVID-19, which began in India on 16 January 2021 with a goal of first immunizing 300 million people. As of 17 August 2021, more than 55 million people have been vaccinated in India. In this chapter, a fractional order compartmental model is constructed to study the effect of vaccination on the spread of coronavirus disease 2019 (COVID-19). In this compartmental model, the infected class is divided into two subclasses to study special characteristics of vaccination on moderately and severely infected classes separately. In particular, it includes an original approach that estimates the transmission rate of the disease over the ratio of partially and fully vaccinated populations, which provides the effect of the vaccination on transmission of the COVID-19. The chapter includes the study of a particular case of the outbreak in Indian states. The reported data for the disease spread and the rate of partial and complete vaccination in the Indian states are used to identify the model parameters. The stability of the model is proved using mathematical theory. The simulated results of the model show a graphical design of the estimations given by the model. We also study the behaviour of the transmission rate when the whole population is fully vaccinated and the output is plotted on a map using QGIS 52software. Moreover, the behaviour of the model for different fractional orders is also analysed in the model.
