Application of Homotopy Perturbation Method for SIR Model with Vital Dynamics and Constant Population

Abstract

In this work, we have studied Susceptible-Infected-Recovered (SIR) model with vital dynamics and constant population, which is used as a mathematical models in many physically significant fields of applied science. The Homotopy Perturbation Method (HPM) and Runge-Kutta method (RK) have been used for solving the SIR model with vital dynamics and constant population. The convergence of HPM has been studied. Also, we have tested the HPM on solving different implementations which are show the efficiency and accuracy of the method. The approximated solutions of HPM for the tested problems are agree well with the numerical solutions of Runge-Kutta method.

Analytical Solution of the Transmission Dynamics of Diarrhea using Homotopy Perturbation Method

“…Let 𝑁 represent the total population of a given region, then the total population at a given time 𝑡 is given as: 𝑁 = 𝑆(𝑡) + 𝑉(𝑡) + 𝐸(𝑡) + 𝐼(𝑡) + 𝑅(𝑡) (11) where…”

“…The results obtained when compared with the Adomian Decomposition Method (ADM) results for the same governing differential equations demonstrated that although the outcomes were identical, HPM and VIM were significantly simpler, more convenient, and more effective than ADM. Ayoade [10] applied Homotopy Perturbation Method to a SIR mumps model and the theoretical results confirmed the ability and appropriateness of the HPM in solving epidemic models. [11] implemented the Homotopy Perturbation approach on the SIR model with vital dynamics which resulted in an approximate solution that was effective and highly precise. Also, in the analysis of the Homotopy Perturbation approach and its application to the solution of infectious disease models (HIV/AIDS), it was discovered that the Homotopy Perturbation Method provides a series solution that is mostly convergent for both linear and nonlinear differential equations, after obtaining a convergent series solution of the HIV/AIDS model with four compartments.…”