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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: We develop and analyze a model for the interactions of T-cells, antigen presenting cells (APCs), and HIV-1. Our model consists of five components: APCs, resting helper T-cells, activated uninfected helper T-cells, activated and infected helper T-cells, and the free virus. We emphasize the impact of APCs during HIV infection and the cell-to-cell contact manner in the transference of HIV-1 in vivo. The existence and stability of the uninfected steady state and those of the infected steady states are discussed. The uniform persistence of the system is also obtained. As a novel approach, multiple exposures of HIV-1 are illustrated and discussed in the paper. Through numerical stimulations, we check the sensitivity of APCs and helper T-cells in impacting the infection outcome and obtain some relevant results. We also give the lowest infectioe dose for certain individuals. [Copyright &y& Elsevier]