A numerical approach for an epidemic SIR model via Morgan-Voyce series

Abstract

Abstract This study presents the problem of spreading a disease that is not fatal in a population by using the Morgan-voyce collocation method. The main aim of this paper is to find the exact solutions of the SIR model with vaccination. The problem may be modeled with a nonlinear system of ordinary differential equations, mathematically. The presented method reduces the problem into a nonlinear algebraic system of equations by using unknown coefficients Morgan-Voyce polynomials and expanding approximate solutions. The Morgan-Voyce Polynomials are used. These unknown coefficients are calculated via the collocation method and matrix operations derivations. Two examples are given to show the feasibility of the method. To calculate the solutions, MATLAB R2021a is used. Additionally, comparing our method to Homotopy perturbation method (HPM) and Laplace Adomian decomposition method (LADM) proves the accuracy of the solution. The method studied can be seen as effective from these comparisons. So, it is essential to find solutions for the governing model. The study will contribute to the literature since we also discuss the vaccination situation. The results of this study are valuable for controlling an epidemic.