SOLUTION OF THE HIV INFECTION MODEL WITH FULL LOGISTIC PROLIFERATION AND VARIABLE SOURCE TERM USING GALERKIN SCHEME
Journal: Matrix Science Mathematic (MSMK)
Author: Attaullah, Rashid Jan, A. Jabeen
This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
The present study is related to the numerical solution of the human immunodeficiency virus (HIV) infection model with full logistic proliferation and variable source term (depending on the viral load) used for the supply of new CD4+ T-cells from thymus instead of using simple logistic proliferation and constant source term. In simple logistic proliferation term only the healthy or infected CD4+ T-cells proliferation are considered while in full logistic proliferation term both the proliferation of healthy and infected are considered. Consequently, the variable source term is used for the supply of new healthy CD4+ T-cells from thymus, which is a decreasing function depending on the concentration of viral load. Continuous Galerkin-Petrov method, in particular cGP(2)-method has been invoked for finding the approximate solution of the model. For cGP(2)-method, we have two unknowns on each time interval which have to be calculated by solving 2 × 2 block system. This method is an accurate of order three in the whole time interval and shows the convergence of order four in the discrete time points. We examined the impact of various clinical parameters and study the existence of the infected state. Additionally, the Runge Kutta method of order four briefly RK4-method has also been used to verify and strengthen the results obtained by cGP(2)-method. Obtained results are displayed both graphically and in tabular form. The results obtained in this study confirm the idea that the cGP(2)-method is a powerful technique which can be applied to a large class of linear and nonlinear problems arising in different fields of science and engineering.