Applying Laplace Adomian decomposition method (LADM) for solving a model of Covid-19

Abstract

In this study, we apply the Laplace Adomian decomposition method (LADM) for the mathematical model of Covid-19. The mathematical model includes a system of nonlinear ordinary differential equations. Therefore, the model cannot be solved analytically but only by approximation. The application of LADM approximates the solution profiles of the dynamical variables of the Covid-19 model by an analytical power series. The conventional way to calculate the expressions of the approximation solutions is complicated both in terms of mathematical calculations and in terms of computer run time. In this paper, we propose a new algorithm for implementing the LADM method combined with the singularly perturbed vector field (SPVF) method. The new algorithm we offer is significantly reducing the running time of both the computer and the mathematical calculations. We compared the results obtained from the LADM to the numerical simulations. Some plots are presented to show the reliability and simplicity of the new algorithm.