Asymptotic Solution to the Fsair Epidemic Model and Unique Identification of the Fractional Order

This article deals with the asymptotic solution to the fractional-order SAIR (FSAIR) epidemic model and identification of the order of the fractional derivative by using an observation of the recovered group at a given time. A unique solution to the forward problem is proved to be global and nonnegative under suitable conditions on the model parameters. The asymptotic solution is derived by the Laplace-Adomian decomposition method (L-ADM) and is shown to converge to the exact solution of the forward problem through an analysis of the Gamma function and Adomian polynomials. Furthermore, the computability of the asymptotic solution is illustrated by numerical analysis, through which the inverse order problem is transformed into an algebraic equation, and uniqueness of the inverse problem is obtained from the monotonicity of the nonlinear function of the order.