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The second wave of COVID-19 is an unprecedented condition in India and began in mid February 2021. Individuals who were already suffering from other comorbidities were found with lung infection, and hence, the number of disease induced deaths were rising faster during the second wave in relation to the first wave. This paper has proposed a mathematical model with fractional order derivatives by correlating the model based number of infectives with the real number of infectives in India. For the system of fractional differential equations, a disease-free state has been computed and proved to be locally asymptotically stable with certain restrictions. The mathematical model has been numerically simulated using the predictor-corrector method to highlight the role played by fractional order in controlling the disease spread. Numerical simulations signify the fact that a vital role has been played by fractional order model over integer order model in determining the transmission of COVID-19. It can be visualized that the increment rate in the infectives is lower by taking into consideration the memory effect due to a previous exposure to COVID-19. [ABSTRACT FROM AUTHOR]

A non-linear SEIR mathematical model for coronavirus disease in India has been proposed, by incorporating the saturated incidence rate on the occurrence of new infections. In the model, the threshold quantity known as the reproduction number is evaluated which determines the stability of disease-free equilibrium and the endemic equilibrium points. The disease-free equilibrium point becomes globally asymptotically stable when the corresponding reproduction number is less than unity, whereas, if it is greater than unity then the endemic equilibrium point comes into existence, which is locally asymptotically stable under certain restrictions on the parameters value in the model. The impact of various parameters on the threshold quantity is signified by the sensitivity analysis. Numerical results imply that by implementing and strictly following the prevention measures a rapid reduction in the reproduction number for COVID-19 can be observed, through which the coronavirus disease can be controlled. [ABSTRACT FROM AUTHOR]