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In this paper, we formulate a within‐host dynamics model for HIV/HTLV‐I co‐infection under the influence of cytotoxic T lymphocytes (CTLs). The model incorporates silent HIV‐infected CD4+T cells and silent HTLV‐infected CD4+T cells. The model includes two routes of HIV transmission, virus to cell (VTC) and cell to cell (CTC). It also incorporates two modes of HTLV‐I transmission, horizontal transmission via direct CTC contact and vertical transmission through mitotic division of Tax‐expressing HTLV‐infected cells. The model takes into account five types of distributed‐time delays. We analyze the model by proving the nonnegativity and boundedness of the solutions, calculating all possible equilibria, deriving a set of key threshold parameters, and proving the global stability of all equilibria. The global asymptotic stability of all equilibria is established by utilizing Lyapunov function and LaSalle's invariance principle. We present numerical simulations to justify the applicability and effectiveness of the theoretical results. In addition, we discuss the effect of HTLV‐I infection on the HIV dynamics and vice versa. [ABSTRACT FROM AUTHOR]

In this paper, applying both Lyapunov function techniques and monotone iterative techniques,we establish new sufficient conditions under which the infected equilibrium of an HIV pathogenesis model with cure rate is globally asymptotically stable. By giving an explicit expression for eventual lower bound of the concentration of susceptible CD4C T cells, we establish an affirmative partial answer to the numerical simulations investigated in the recent paper [Liu, Wang, Hu and Ma, Global stability of an HIV pathogenesis model with cure rate, Nonlinear Analysis RWA (2011) 12: 2947-2961]. Our monotone iterative techniques are applicable for the small and large growth rate in logistic functions for the proliferation rate of healthy and infected CD4+ T cells. [ABSTRACT FROM AUTHOR]