Closed-Form Solutions for Kermack–McKendrick Dynamical System

Abstract

This work offers a (semi-analytical) solution for a second-order nonlinear differential equation associated to the dynamical Kermack–McKendrick system. The approximate closed-form solutions are obtained by means of the Optimal Homotopy Asymptotic Method (OHAM) using only one iteration. These solutions represent the ε-approximate OHAM solutions. The advantages of this analytical procedure are reflected by comparison between the analytical solutions, numerical results, and corresponding iterative solutions (via a known iterative method). The obtained results are in a good agreement with the exact parametric solutions and corresponding numerical results, and they highlight that our procedure is effective, accurate, and useful for implementation in applications.