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Based on some important biological meanings, we propose a class of HIV infection models incorporating both classical cell-free virus diffusion and direct cell-to-cell transmission. According to recent studies, the direct cell-to-cell transfer of HIV is a significantly more efficient mode of retroviral dissemination. In the first part of our analysis, we show that our model possesses non-negative solutions. Then, we derive sufficient conditions for the asymptotic stability of equilibriums. The analytical solutions are verified by simulation results. At the end of the paper, some important conclusions are given. [ABSTRACT FROM AUTHOR]

Abstract: It is well-known that the mathematical models provide very important information for the research of human immunodeficiency virus-type 1 and hepatitis C virus (HCV). However, the infection rate of almost all mathematical models is linear. The linearity shows the simple interaction between the T cells and the viral particles. In this paper, we consider the classical mathematical model with non-linear infection rate. The global dynamics of this model is rigorously established. We prove that, if the basic reproduction number , the HIV infection is cleared from the T-cells population; if , the HIV infection persists. Further, the existence of a non-trivial periodic solution is also studied by means of numerical simulation. [Copyright &y& Elsevier]

Abstract: Human T-cell lymphotropic virus I (HTLV-I) infection is linked to the development of adult T-cell leukemia/lymphoma (ATL), among many illness. The healthy CD4+ T cells infect HTLV-I through cell-to-cell contact with infected T-cells. The infected T cells can remain latent and harbor virus for several years before virus production occurs. Actively infected T cells can infect other T cells and can convert to ATL cells, whose growth is assumed to follow a classical logistic growth function. In this paper, we consider the classical mathematical model with saturation response of the infection rate. By stability analysis we obtained the condition for the infected T cells die out and the condition for HTLV-I infection becomes chronic. At the same time, we also obtained the condition for a unique endemic equilibrium is globally stable in the interior of the feasible region. [Copyright &y& Elsevier]