Analytical Solution of the Mathematical Model of Dengue Fever by the Laplace-Adomian Decomposition Method

Abstract

This paper presents and rigorously analyzes a deterministic mathematical model of the Dengue virus in apopulation, incorporating a nonlinear incidence function. The model considers five compartments: susceptible (S h), symptomatic infection (Ih), asymptomatic infection (IhA), recovered (Rh), and partial immunity(S hk). The female mosquito population is divided into two compartments: susceptible (S ν)and infected (Iν).An algorithm is provided to calculate a series-type solution to the problem using the Laplace Adomian Decomposition technique. The convergence of this technique is also analyzed. Approximations of the solutionsfor various compartments are calculated using a few terms. The reliability and simplicity of the method areillustrated with numerical examples and plots. The Laplace Adomian Decomposition algorithm is shown toyield very accurate approximate solutions using only a few iterations. Fourth-order Runge-Kutta solutionsare also compared with the solutions obtained by the Laplace decomposition scheme.