Dynamical Behavior of Fractional Order SVIR Epidemic Model

In this Paper, we proposed a fractional order SVIR epidemic model is incorporated to investigate its dynamical behavior in random environments. S, V, I, R are known as variables and these variables represent the number of susceptible, vaccinated, infected and recovered cells from viruses in the body. The Caputo fractional derivative operator of order α \in (0,1] is employed to obtain the system of fractional differential equations. The basic reproductive number is derived for a general viral production rate which determines the local stability of the infection free equilibrium. The stability and sensitivity analysis of fractional order has been made and verify the non-negative unique solution. The solution of the time fractional model has been procured by employing Laplace Adomian decomposition method (LADM) and the accuracy of the scheme is presented by convergence analysis. Finally numerical solutions are also established to investigate the influence of system parameter on the spread of disease and which show the effect of fractional parameter on our obtained solution.