On the solution of the Human Immunodeficiency Virus (HIV) infection model using spectral collocation method

Abstract

In this research work, we study the Human Immunodeficiency Virus (HIV) infection on helper T cells governed by a mathematical model consisting of a system of three first-order nonlinear differential equations. The objective of the analysis is to present an approximate mathematical solution to the model that gives the count of the numbers of uninfected and infected helper T cells and the number of free virus particles present at a given instant of time. The system of nonlinear ODEs is converted into a system of nonlinear algebraic equations using spectral collocation method with three different basis functions such as Chebyshev, Legendre and Jacobi polynomials. Some factors such as the production of helper T cells and infection of these cells play a vital role in infected and uninfected cell counts. Detailed error analysis is done to compare our results with the existing methods. It is shown that the spectral collocation method is a very reliable, efficient and robust method of solution compared to many other solution procedures available in the literature. All these results are presented in the form of tables and figures.