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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]

The "shock and kill" strategy is being widely explored to purge Human Immunodeficiency Virus (HIV) latent reservoirs. Romidepsin, a kind of latency-reversing agents (LRAs), has been shown to induce HIV RNA transcription. However, several clinical trials testing this drug have resulted in limited effect in reducing the HIV latent reservoirs. To understand the mechanisms underlying such limited effect, we develop a multi-scale model that incorporates pharmacokinetics and considers the toxicity of romidepsin to T cells in this paper. By fitting the model to the viral load data from plasma of six patients received romidepsin, we find that the model with T cell toxicity of romidepsin can well explain the clinical data. The dynamics of latently infected cells during romidepsin administration are explored using the best-fit parameter values. The results show that latently infected cells decrease very slowly and remain very stable overall in four of the six participants under the assumption of T cell toxicity of romidepsin. This implies that the ineffectiveness of romidepsin on latent reservoirs can be explained by its toxicity to T cells. In the remaining two participants, however, latently infected cells are quite stable without T cell toxicity of LRAs. It is found that the estimated activation rate of latently infected cells by romidepsin and the estimated elimination rate of romidepsin on immune cells for these two patients are very different from those for the other four patients. Thus we speculate that the heterogeneous response to romidepsin across participants may also be a determining factor of the effectiveness of romidepsin. These results may have significant implications in the search for the control of HIV infection. • An HIV model is proposed to understand the cause of ineffectiveness of romidepsin in the "shock and kill" strategy. • The model has a good fit to patients' data when T cell toxicity of romidepsin is considered. • The toxicity of romidepsin to T cell may contribute to the ineffectiveness of "shock and kill" strategy concerning romidepsin. [ABSTRACT FROM AUTHOR]

Mathematical modeling of biological systems is an interesting research topic that attracted the attention of many researchers. One of the main goals in this area is the design of mathematical models that more accurately illustrate the characteristics of the real-world phenomena. Among the existing research projects, modeling of immune systems has given a growing attention due to its natural capabilities in identifying and destroying abnormal cells. The main objective of this paper is to investigate the pathological behavior of HIV-infection using a new model in fractional calculus. The proposed model is examined through three different operators of fractional derivatives. An efficient numerical method is also presented to solve these fractional models effectively. In fact, we believe that the new models presented on the basis of these three operators show various asymptomatic behaviors that do not appear during the modeling with the integer-order derivatives. Therefore, the fractional calculus provides more precise models of biological systems that help us to make more realistic judgments about their complex dynamics. Finally, simulations results are provided to confirm the theoretical analysis. [ABSTRACT FROM AUTHOR]

In this paper, we formulate the intricate process of Human Immunodeficiency Virus (HIV) infection in a mathematical model. In the formulation of the model, the density of CD 4 + T-cells is categorized into healthy and infected classes while the density of free HIV viruses in the human host's blood is considered a separate class. It is reported that when HIV enters a human's body, it infects a large amount of CD 4 + T-cells and unbalance the supply of new cells from the thymus. Therefore, we incorporate variable source term relying on the viral load for the supply of new cells instead of using a fixed value for the supply of these cells. We implement a continuous Galerkin Petrov time discretization scheme, particularly cGP(2)-scheme to visualize the dynamical behavior of the mentioned model and a detailed description of the effects of different physical parameters of interest are depicts graphically and discuss that how the level of healthy, infected CD 4 + T-cells and free HIV particles varies concerning the emerging parameters in the model. In the proposed cGP(2)-method, two unknowns terms can be found by solving a 2 × 2 block system. This method is accurate of order 3 in the whole time interval and shows even superconvergence of order 4 in the discrete-time points. Furthermore, determine the solution of the model utilizing the fourth-order Runge-Kutta (RK4)-method and find out the absolute errors between the solutions obtained from both approaches. Finally, the validity and reliability of the proposed scheme are verified by comparing the numerical and graphical results with the RK-4 method. We examine the accuracy of the cGP(2)-sheme and observe that it produces more accurate results at relatively larger step sizes as in comparison to RK-4 scheme. Correspondence between the findings of cGP(2)-method and RK4-method reveal that the new technique is a promising tool for obtaining approximate solutions to the nonlinear systems of real-world problems. [ABSTRACT FROM AUTHOR]

Human immunodeficiency virus (HIV) dynamics represent a complicated variant of the text-book case of non-linear dynamics: predator–prey interaction. The interaction can be described as naturally reproducing T-cells (prey) hunted and killed by virus (predator). Virus reproduce and increase in number as a consequence of successful predation; this is countered by the production of T-cells and the reaction of the immune system. Multi-drug anti-HIV therapy attempts to alter the natural dynamics of the predator–prey interaction by decreasing the reproductive capability of the virus and hence predation. These dynamics are further complicated by varying compliance to treatment and insurgence of resistance to treatment. When following the temporal progression of viral load in plasma during therapy one observes a short-term (1–12 weeks) decrease in viral load. In the long-term (more than 12 weeks from the beginning of therapy) the reduction in viral load is either sustained, or it is followed by a rebound, oscillations and a new (generally lower than at the beginning of therapy) viral load level. Biomathematicians have investigated these dynamics by means of simulations. However the estimation of the parameters associated with the dynamics from real data has been mostly limited to the case of simplified, in particular linearized, models. Linearized model can only describe the short-term changes of viral load during therapy and can only predict (apparent) suppression. In this paper we put forward relatively simple models to characterize long-term virus dynamics which can incorporate different factors associated with resurgence: (Fl) the intrinsic non-linear HIV-1 dynamics, (F2) drug exposure and in particular compliance to treatment, and (F3) insurgence of resistant HIV-1 strains. The main goal is to obtain models which are mathematically identifiable given only measurements of viral load, while retaining the most crucial features of HIV dynamics. For the purpose of illustration we demonstrate an application of the models using real AIDS clinical trial data involving patients treated with a combination of anti-retroviral agents using a model which incorporates compliance data. [Copyright &y& Elsevier]