Global stability of HIV/HTLV co-infection model with CTL-mediated immunity

Abstract

<p style='text-indent:20px;'>Mathematical modeling of human immunodeficiency virus (HIV) and human T-lymphotropic virus type Ⅰ (HTLV-I) mono-infections has received considerable attention during the last decades. These two viruses share the same way of transmission between individuals; through direct contact with certain contaminated body fluids. Therefore, a person can be co-infected with both viruses. In the present paper, we construct and analyze a new HIV/HTLV-I co-infection model under the effect of Cytotoxic T lymphocytes (CTLs) immune response. The model describes the interaction between susceptible CD<inline-formula><tex-math id="M1">\begin{document}$ 4^{+} $\end{document}</tex-math></inline-formula>T cells, silent HIV-infected cells, active HIV-infected cells, silent HTLV-infected cells, Tax-expressing (active) HTLV-infected cells, free HIV particles, HIV-specific CTLs and HTLV-specific CTLs. The HIV can spread by two routes of transmission, virus-to-cell (VTC) and cell-to-cell (CTC). Both active and silent HIV-infected cells can infect the susceptible CD<inline-formula><tex-math id="M2">\begin{document}$ 4^{+} $\end{document}</tex-math></inline-formula>T cells by CTC mechanism. On the other side, HTLV-I has only one mode of transmission via direct cell-to-cell contact. The well-posedness of the model is established by showing that the solutions of the model are nonnegative and bounded. We calculate all possible equilibria and define the key threshold parameters which govern the existence and stability of all equilibria of the model. We explore the global asymptotic stability of all equilibria by utilizing Lyapunov function and LaSalle's invariance principle. We have discussed the influence of CTL immune response on the co-infection dynamics. We have presented numerical simulations to justify the applicability and effectiveness of the theoretical results. In addition, we evaluate the effect of HTLV-I infection on the HIV dynamics and vice versa.</p>