Study of Fractional Order SEIR Epidemic Model and Effect of Vaccination on the Spread of COVID-19.

ABSTRACT

In this manuscript, a fractional order SEIR model with vaccination has been proposed. The positivity and boundedness of the solutions have been verified. The stability analysis of the model shows that the system is locally as well as globally asymptotically stable at disease-free equilibrium point E 0 when R 0 < 1 and at epidemic equilibrium E 1 when R 0 > 1 . It has been found that introduction of the vaccination parameter η reduces the reproduction number R 0 . The parameters are identified using real-time data from COVID-19 cases in India. To numerically solve the SEIR model with vaccination, the Adam-Bashforth-Moulton technique is used. We employed MATLAB Software (Version 2018a) for graphical presentations and numerical simulations.. It has been observed that the SEIR model with fractional order derivatives of the dynamical variables is much more effective in studying the effect of vaccination than the integral model.