Analysis of drug treatment of the fractional HIV infection model of CD4+ T-cells

Abstract

In this paper we consider fractional order model to HIV infection whose components are plasma densities of uninfected CD4+ T-cells, the infected such cells and the free virus. The main purpose of this work is to study the dynamic of fractional HIV infection of CD4+ T-cells with the impact of drug treatment. An iterative scheme based on the discretization of the domain and short memory principle is proposed to solve fractional HIV infection model numerically. The main reason for using this discretization technique is low computational cost and high accuracy compared to some other methods. Numerical results are presented graphically. Figures are used to show the behaviour of densities of uninfected and infected cells before and after the drug therapy. It is also shown that how the approximate solution varies from fractional order to integer order derivative. By listing CPU time in tabular form efficiency of the iterative scheme is shown. The proposed scheme is also effective in a long time period. The validation of results are shown by comparing results among the proposed technique, Runge Kutta Fourth order method, homotopy perturbation method, homotopy analysis method, Adam-Bashforth predictor-corrector method, Legendre wavelets operational matrix method and Laplace adomian-decomposition method.