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Abstract: In this paper, we introduce fractional-order into a model of HIV infection of CD4+ T-cells. We show that the model established in this paper possesses non-negative solutions, as desired in any population dynamics. We also carry out a detailed analysis on the stability of equilibrium. Numerical simulations are presented to illustrate the results. [Copyright &y& Elsevier]

The mass action infection law, the most frequently used transmission process in the theoretical studies of disease dynamics, has been challenged in various ways. Hill type infection rate is supposed to be a better alternative to mass action law. In the first phase of this paper, we study a basic HIV model with Hill type infection rate. In the second phase, we modify our basic model with intracellular delay τ that measures the time between the first effective contact between a virus and a healthy CD4 + T cell and the latter becomes productively infective. Mathematical results like well-posedness, permanence, local stability and global stability of both the delayed and non-delayed systems are studied. It is observed that the endemic equilibrium is locally and globally asymptotically stable if the virus replication factor is greater than a threshold value and unstable otherwise. In the latter case, the disease-free steady state occurs and is proved to be globally asymptotically stable. Our simulation results shed different insights on drug therapy when various perturbations are given to the system. It is shown that multi-blockers drug therapy is more appropriate in the treatment of HIV patients in comparison to any mono-blocker drug therapy. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the homotopy analysis method (HAM) is investigated to give an approximate solution of a model for HIV infection of CD4+ T-cells. This method allows for the solution of the governing differential equation to be calculated in the form of an infinite series with components which can be easily calculated. The HAM utilizes a simple method to adjust and control the convergence region of the infinite series solution by using an auxiliary parameter. The results obtained are presented, and six terms are sufficient to obtain an approximation solution that is very accurate. [Copyright &y& Elsevier]

Abstract: In this paper, a multi-step differential transform method (MsDTM) is performed to give approximate and analytical solutions of nonlinear fractional order ordinary differential equation systems such as a model for HIV infection of CD4+ T cells. The numerical solutions obtained from the proposed method indicate that the approach is easy to implement and accurate when applied to systems of fractional differential equations. Some figures are presented to show the reliability and simplicity of the methods. [Copyright &y& Elsevier]

Abstract: The capability of the HIV to persist latent inside CD4+ T-cells is currently regarded as a barrier to recovery from infection. On the other hand, immune activation, which is a normal immune reaction to pathogens, is now recognized as a key ingredient to sustaining the HIV caused infection. Further, it has been shown that activation of infected memory T-cells indirectly promotes apoptosis (programmed cell death) of bystander CD4+ and CD8+ T-cells. In this paper we use standard modeling techniques to develop a model compliant with the above mentioned mechanisms. Our farthest goal is to study how the long-term depletion of T-cells that characterizes HIV pathogenesis depends on these mechanisms. Consequently, we conduct parameter estimation, and apply standard results of sensitivity analysis and principal component analysis of the state variables with respect to the parameters. [ABSTRACT FROM AUTHOR]