Solving a non-linear model of HIV infection for CD4+T cells by combining Laplace transformation and Homotopy analysis method

TL;DR

This paper introduces a novel analytical approach combining Laplace transform and homotopy analysis to approximate solutions for a nonlinear HIV infection model involving CD4+ T cells, demonstrating its convergence and accuracy.

Contribution

It develops a new hybrid method (HATM) that enhances the traditional homotopy analysis method with Laplace transform for solving nonlinear HIV models.

Findings

The method converges for various iteration counts.

Residual errors decrease with more iterations.

H-curves illustrate the convergence regions.

Abstract

The aim of this paper is to find the approximate solution of HIV infection model of CD4+T cells. For this reason, the homotopy analysis transform method (HATM) is applied. The presented method is combination of traditional homotopy analysis method (HAM) and the Laplace transformation. The convergence of presented method is discussed by preparing a theorem which shows the capabilities of method. The numerical results are shown for different values of iterations. Also, the regions of convergence are demonstrated by plotting several h-curves. Furthermore in order to show the efficiency and accuracy of method, the residual error for different iterations are presented.