Abstract
HIV and HTLV-I are two retroviruses that infect the CD4(+) 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 CD4(+) 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.