A Computational Study of HIV Infection Model using Galerkin and Wavelet
Collocation Method
Abstract
In this work we implement two numerical schemes namely continuous
Galerkin-Petrov (cGP(2)) and Legendre Wavelet Collocation Method (LWCM)
for the approximate solution of the mathematical model which describes
the behavior of CD4+ T-cells, infected CD4+T-cells and free HIV virus
particles after HIV infection. The present study discuss and analyse the
effect of constant and different variable source terms (depending on the
viral load) used for the supply of new CD4+ T-cells from thymus on the
dynamics of CD4+ T-cells, infected CD4+ T-cells and free HIV virus.
Furthermore, the model is also solve using fourth order Runge Kutta
(RK4) method. Finally, the validity and reliability of the proposed
schemes are verified by comparing the numerical and graphical results
with the results of RK4-method. Comparison of the numerical and
graphical results of cGP(2) and LWCM with RK4-method confirmed that
cGP(2) and LWCM performs excellent accuracy. The present study
highlights the accuracy and efficiency of the proposed schemes with the
other traditional schemes such as the Laplace Adomian Decomposition
Method (LADM), Variational Iteration Method (VIM), Homotopy Analysis
Method (HAM), Homotopy Perturbation Method (HPM), Genetic Algorithm
(GA), Interior Point Algorithm (IPA), Active Set Algorithm (ASA),
Multistep Laplace Adomian Decomposition Method (MSLADM) etc.