An inverse problem of determining the fractional order in a fractional SVIRS epidemic model based on the asymptotic solution

In this paper we propose a fractional SVIRS epidemic model by directly choosing the survival probability distribution as a power-law decay function in the non-Markovian process, where the model incorporates with the Riemann–Liouville fractional derivative and the coefficients depending upon the order of the derivative. The asymptotic solution of the fractional epidemic model is obtained by using the Laplace Adomian decomposition method (L-ADM), and numerical simulations are performed to reveal the impact of the order of the derivative on the fractional dynamic system. An inverse problem of determining the order of the fractional derivative by one data of the recovered people is transformed to a nonlinear equation with the aid of the asymptotic solution, and a uniqueness of the inverse problem is proved by monotonicity of the nonlinear function on the order.