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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]

Abstract: In this paper, a method of parameter estimation, based upon Hopfield neural networks, is applied to the identification of a model of the HIV/AIDS epidemic in Cuba. This estimation technique presents a number of features that make it especially suitable for the identification of such epidemic models. In particular, its remarkable ability to estimate time variant parameters allows us to outline the evolution of parameters, thus assessing the efficiency of health policies. A complementary aim is the validation of the model, which stems from basic concepts and reasoning in disease modelling rather than from specific physical laws, thus it is not supported by rigorous mathematical results. Indeed, the experimental results show a significant adjustment of simulated data to actual ones, which provides considerable support to model validity. A sequence of real data, corresponding to the HIV and AIDS affected populations in Cuba from 1986 to 2004, has been compared to both simulations of the epidemic model and used to test the estimation method. A detection threshold, which plays a similar role to the basic reproduction number, has been calculated to complement the information about the current situation of the epidemic and the possible evolution perspectives. The obtained results are plausible and coherent according to health experts. [Copyright &y& Elsevier]

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: In this paper, the Laplace Adomian Decomposition Method is implemented to give an approximate solution of nonlinear ordinary differential equation systems, such as a model for HIV infection of cells. The technique is described and illustrated with numerical example. Some plots are presented to show the reliability and simplicity of the methods. [ABSTRACT FROM AUTHOR]

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]

Abstract: In this paper, we propose and study models of long-term Human Immunodeficiency Virus (HIV-1) infection. Our aim is to identify model mechanisms that allow one to explain the trends observed in clinical measurements of the number of CD4+ T-cells and virus throughout the long-term HIV-1 infection, from the acute phase until the onset of AIDS. To achieve our goal, we apply some standard methods of modeling and analysis of dynamical systems. Among these methods, are model development and validation processes such as parameter estimation, as well as Painleve and bifurcation analysis. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a continuous time model for modelling the spread of HIV in a network of prisons. We give some sufficient conditions for the equilibrium points of the system to be stable. We also develop an efficient algorithm based on Newton’s method and the Sherman–Morrison–Woodbury formula for computing the equilibrium values of the infectives in each prison. [Copyright &y& Elsevier]