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Human immunodeficiency virus (HIV) infection may cause death by damaging some of the patient's vital organs through weakening the body's immune system, including CD 4 + T cells. In the meantime, mathematical models can be useful in dealing with this deadly virus by providing effective strategies based on the examination of different infection states. The major aim pursued in this paper is to present a computational algorithm for solving nonlinear systems of ordinary and partial differential equations resulting from the HIV infection models of CD 4 + T cells. The offered method is developed according to the use of local radial basis functions (LRBFs) as shape functions in the discrete collocation scheme. The new technique approximates the solution by a small set of nodes instead of all points located in the domain where the HIV mathematical model is given. Thus the presented method uses less computing volume compared to the globally supported radial basis functions, and as a result, its algorithm can be quickly run on a computer with relatively low memory. The computational efficiency of the scheme is studied by several test examples. [ABSTRACT FROM AUTHOR]

This paper proposes and analyzes an adaptive immunity HIV infection model. The model describes the interaction between healthy CD 4 + T cells, silent (latent) infected cells, active infected cells, free HIV particles, Cytotoxic T lymphocytes (CTLs) and antibodies. The healthy CD 4 + T cells can be infected when they are contacted by one of the following: (i) free HIV particles, and this is known as virus-to-cell (VTC) transmission (ii) silent infected cells, and we call this mode of infection as silent HIV-infected cell-to-cell (CTC) transmission, and (iii) active infected cells, and we call this mechanism active HIV-infected CTC transmission. The incidence rates of the healthy CD 4 + T cells with free HIV particles, silent infected cells, and active infected cells are given by general functions. Moreover, the production/proliferation and removal/death rates of all compartments are represented by general functions. The model is an improvement of the existing HIV infection models which have neglected the incidence between the silent infected cells and healthy CD 4 + T cells. We first show that the model is well-posed. Then, we show that the model has five equilibria and their existence are governed by five threshold parameters. Under a set of conditions on the general functions and the threshold parameters, we have proven the global asymptotic stability of all equilibria by using Lyapunov's method. We have illustrated the theoretical results via numerical simulations. We have studied the effect of CTC transmission on the dynamical behavior of the system. We have shown that inclusion of CTC transmission decreases the concentration of the healthy CD4 + T cells and increases the concentrations of the infected cells and free HIV particles. [ABSTRACT FROM AUTHOR]