Analysis and numerical solution of SEIR epidemic model of measles with non-integer time fractional derivatives by using Laplace Adomian Decomposition Method

SEIR epidemic model which represents the direct transmission of infectious disease are considered to control the measles disease for infected population. The Caputo fractional derivative operator of order alpha is an element of (0, 1] is employed to obtain the system of fractional differential equations of SEIR epidemic model. The stability analysis of fractional order model has been made and verify the non-negative unique solution of the scheme with in the domain. The Laplace Adomian Decomposition Method is applied to give an approximate solution of nonlinear system of purposed model at different values of alpha and comparative study between the new algorithm and differential transform method is presented in the case of integer-order derivatives. (C) 2018 Production and hosting by Elsevier B.V. on behalf of Ain Shams University.