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HIV and HTLV-I are two retroviruses that infect the CD 4 + T cells. HIV causes acquired immunodeficiency syndrome, while HTLV-I is the causative agent for adult T-cell leukemia and HTLV-I-associated myelopathy/tropical spastic paraparesis. It is not surprising that a mono-infected patient with one of these viruses can be exposure to co-infect with the other virus since they share the same way of transmissions between individuals, through direct contact with certain contaminated body fluids. Mathematical modeling and analysis of HIV and HTLV-I mono-infections have received considerable attention during the last decades. However, the dynamics of HIV/HTLV-I co-infection has not been formulated. In the present paper, we formulate a new HIV/HTLV-I co-infection model with cytotoxic T lymphocytes (CTLs) immune response. The model describes the interaction between susceptible CD 4 + T cells, HIV-infected cells, Tax-expressing HTLV-infected cells, free HIV particles, HIV-specific CTLs and HTLV-specific CTLs. The HIV can spread by virus-to-cell and cell-to-cell transmissions, while the HTLV-I can only spread via cell-to-cell transmission. The well-posedness of the model is established by showing that the solutions of the model are nonnegative and bounded. We derive the threshold parameters which govern the existence and stability of all equilibria of the model. We prove the global asymptotic stability of all equilibria by utilizing Lyapunov function and applying Lyapunov–LaSalle asymptotic stability theorem. We present numerical simulations to illustrate the effectiveness of our main results. In addition, we discuss the effect of HTLV-I infection on the HIV-infected patients and vice versa. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model is formulated to investigate the dynamics of HIV infection. The model incorporates two routes of infection (namely cell-to-cell transmission and virus-to-cell infection), two types of adaptive immune responses (i.e., cellular and antibody immune response) and two intracellular delays (viz., the eclipse phase and virus production period). By constructing Lyapunov functionals, we show that the global dynamics of the model can be explicitly determined by five reproduction numbers. Using the uncertainty and sensitivity analyses, we obtain the mean values and standard deviation of the five reproduction numbers and find that the reproduction numbers are most sensitive to the death rate of infected cells, viral clearance rate and immune parameters. We further compare four related HIV models and show that cell-to-cell transmission, immune responses and time delays can substantially affect the dynamical behavior of the system. Specifically, cell-to-cell transmission increases the concentration of infected cells. Inclusion of cytotoxic T lymphocyte and virus production delay can significantly reduce the viral load and infected cell concentration, and generate a higher level of uninfected CD4+ T cells. The analytical and numerical results may help to improve the understanding of HIV dynamics. [ABSTRACT FROM AUTHOR]