Search

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, a fractional order differential system for modeling human T-cell lymphotropic virus I (HTLV-I) infection of CD4+ T-cells is studied and its approximate solution is presented using a multi-step generalized differential transform method. The method is only a simple modification of the generalized differential transform method, in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding systems. The solutions obtained are also presented graphically. [Copyright &y& Elsevier]

Abstract: In this paper, a mathematical model for HILV-I infection of CD4+ T-cells is investigated. The force of infection is assumed be of a function in general form, and the resulting incidence term contains, as special cases, the bilinear and the saturation incidences. The model can be seen as an extension of the model [Wang et al. Mathematical analysis of the global dynamics of a model for HTLV-I infection and ATL progression, Math. Biosci. 179 (2002) 207-217; Song, Li, Global stability and periodic solution of a model for HTLV-I infection and ATL progression, Appl. Math. Comput. 180(1) (2006) 401-410]. Mathematical analysis establishes that the global dynamics of T-cells infection is completely determined by a basic reproduction number . If , the infection-free equilibrium is globally stable; if , the unique infected equilibrium is globally stable in the interior of the feasible region. [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]

Abstract: The T-cell antigen-activated signaling pathway is a highly regulated intracellular biochemical system that is crucial for initiating an appropriate adaptive immune response. To improve the understanding of the complex regulatory mechanisms controlling the early events in T-cell signaling, a detailed mathematical model was developed that utilizes ordinary differential equations to describe chemical reactions of the signaling pathway. The model parameter values were constrained by experimental data on the activation of a specific signaling intermediate and indicated an initial rapid cascade of phosphorylation events followed by a comparatively slow signal downregulation. Nonlinear analysis of the model suggested that thresholding and bistability occur as a result of the embedded positive and negative feedback loops within the model. These nonlinear system properties may enhance the T-cell receptor specificity and provide sub-threshold noise filtering with switch-like behavior to ensure proper cell response. Additional analysis using a reduced second-order model led to further understanding of the observed system behavior. Moreover, the interactions between the positive and negative feedback loops enabled the model to exhibit, among a variety of other feasible dynamics, a sustained oscillation that corresponds to a stable limit cycle in the two-dimensional phase plane. Quantitative analysis in this paper has helped identify potential regulatory mechanisms in the early T-cell signaling events. This integrated approach provides a framework to quantify and discover the ensemble of interconnected T-cell antigen-activated signaling pathways from limited experimental data. [Copyright &y& Elsevier]

Abstract: There is a fundamental difference in complexity between signaling initiated by ligands on the surface of one cell binding to receptors on the surface of another cell and ligands in solution binding to these receptors. The fact that two cells must approach each other and form a number of intercellular bonds of different types, all within the restricted geometry of the intercellular contact region, introduces the possibility of complex spatio-temporal dynamics of surface receptors that is not present otherwise. Mathematical modelling of these dynamics is in its early stages. However, useful tools have emerged. The purpose of this paper is to describe some of these mathematical tools, indicating their strengths and shortcomings, and suggest some directions for future theoretical studies. [Copyright &y& Elsevier]