# A Modified Iterative Algorithm for Numerical Investigation of HIV Infection Dynamics
###### Abstract
In order to solve the HIV infection model, [PERSON] [23] introduced the Bessel collocation approach. [PERSON] [24] solved the model using the multi-step Laplace-Adomian decomposition method (MSLADM). [PERSON] [25] employed the homotopy perturbation method (HPM) on the determined system. [PERSON] et al. [26] recently used the modified variational iteration technique (MVIM) to get the approximate solutions of (1)-(3). [PERSON] et al. [27] used the homotopy analysis method (HAM) to resolve the variation of the noted model. To acquire the numeric solution of the HIV model, the stochastic global search approach known as genetic algorithm (GA) is combined with two local search optimizers known as interior point algorithm (IPA) and active set algorithm (ASA) in [28]. Very recently, [PERSON] and [PERSON] [29] used continuous Galerkin-Petrov (cGP) and the Legendre wavelet collocation method (LWCM) for the approximate solution to the selected mathematical model. For the general nonlinear problem, the new iterative method (NIM) has received a lot of attention since it requires no multiplier or polynomials for nonlinear terms of the problems. The NIM algorithm was developed by [PERSON] and [PERSON] [30] to solve stochastic and deterministic problems. Recently, [PERSON] et al. [31] used NIM to identify analytical and numerical solutions for linear and nonlinear multidimensional problems. The approximate solutions for second order nonlinear ordinary differential equations (ODEs) have been provided by [PERSON] et al. [32] using NIM. By using semi analytic NIM, the nonlinear problem of Jeffery-Hamel flow has been solved analytically and numerically by [PERSON] et al. [33]. [PERSON] et al. [34] have extended the applications of NIM to find the solutions of Klein-Gordon equations (KGEs), which have been applied in the modeling of spin wave, quantum field theory, kink dynamics, astrophysics, cosmology and classical mechanics. First, they reduced the level of calculation by using the Elzaki transform method and then solved the corresponding equations with the help of NIM. Recently, the technique has been applied widely to several dynamical systems (see [35; 36; 37; 38; 39]). The design of semi-analytical methods such as the Adomian decomposition, homotopy perturbation, variational iteration approaches and new iterative method (NIM) differ from each other. Although these methods provide some helpful solutions that are frequently represented in terms of polynomials and the region of convergences (ROCs) is relatively small in certain nonlinear problems such as the HIV infection model. Both perturbation techniques and non-perturbative approaches cannot provide a straightforward procedure for adjusting or controlling the convergence region and rate of a given approximation series [27]. So it is occasionally essential to improve them. Also, the recent results provided in the literature of [PERSON] and [PERSON] [21], used continuous Galerkin-Petrov (cGP) and the Legendre wavelet collocation method (LWCM) to match at least four decimal places with RK4, which is considered to be more accurate than all previous results published, so there could be the scope for further investigation to attain more accuracy. The goal of this research is to modify the new iterative method (NIM) by implementing the modified new iterative method (MNIM), i.e., the combination of Laplace transformation and NIM to solve the class of nonlinear HIV infection model and achieve higher accuracy than previous methods. The rest of the present study is presented as: the solution procedure of NIM and modified NIM are interpreted in Section 2. The applications of both NIM and MNIM for the considered HIV infection model are introduced in Section 3. The results and discussion of the present methods are illustrated in Section 4, and then the concluding remarks of the research has been given in Section 5.