Stud. Univ. Babe¸ s-Bolyai Math. Volume LVI, Number 1 March 2011, pp. 165–178 Simulated results for deterministic model of HIV dynamics Marwan Taiseer Alquran, Kamel Al-Khaled and Ameen Alawneh 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 epidemi- ology, ODE models. 1. Introduction Mathematical modeling of many biological or physical systems leads to non- linear ordinary differential equations. An effective method is required to ana- lyze the mathematical model which provides solutions conforming to physical reality. Therefore, we must be able to solve nonlinear ordinary differential equations. Common analytic procedures linearize the system or assume that nonlinearities are relatively insignificant. Such procedures change the actual problem to make it tractable by the conventional methods. In short, the physical problem is transformed to a purely mathematical one, for which the solution is readily available. This changes, sometimes seriously, the solution, which means that the problem being solved is no longer a proper represen- tation of the physical problem whose solution is desired. However, in spite of the extensive development in the mathematical and statistical techniques