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ABSTRACT. In this paper, an algorithm based on He’s variational iteration method (shortly, VIM) is developed to approximate the solution of a non-linear mathematical model of HIV dynamics. Using a system of ordinary differential equations, the model describes the viral dynamics of HIV-1. Some plots of the solution are depicted and used to investigate the influence of certain key parameters on the spread of the disease. The results shows that the VIM has the advantages of being more concise for numerical purposes. Furthermore, this work opens a new direction of research whereby He’s VIM applications might offer more insight into the modeling of dynamical systems in life sciences.Mathematics Subject Classification (2010): 35R99, 49M27.

Keywords: Iteration method, HIV-1 dynamics, mathematical epidemiology, ODE models.