Solutions of Some Mathematical Models by Homotopy Perturbation Method

Abstract

The main objective of this study is to apply homotopy perturbation method to solve some nonlinear dynamical models, especially the models which lead to predict and control the pandemic diseases or SIR (S = susceptible, I = infected and R = recovered). We solve two models by using homotopy perturbation method (HPM), one is the “population dynamics” and the second is “novel coronavirus (COVID-19)” with six compartments which consist on susceptible, exposed, asymptomatic infected, symptomatic infected and recovered people and the concentration of the COVID-19 in the environment, denoted by S(t), E(t), A(t), I(t), R(t) and B(t) respectively. We provide the convergence order of HPM and show the convergence order of a series solution. Moreover, we analyze the series solution of the model of novel coronavirus (COVID-19) by taking the different values of controlling parameter and showing them in graphs.