Stability of a delay-distributed HIV infection model with silent infected cell-to-cell spread and CTL-mediated immunity

Abstract

In this paper, we formulate a mathematical model to investigate a within-host HIV dynamics under the effect of cytotoxic T lymphocytes immune response. The model incorporates two modes of transmission, virus-to-cell (VTC) and cell-to-cell (CTC). The CTC infection is due to the contact of healthy CD $$4^{+}$$ T cells with (i) silent HIV-infected cells, and (ii) active HIV-infected cells. The model integrates three types of distributed time delays. We show that the model is well posed and it has three equilibria. The existence and stability of equilibria are governed by two threshold parameters. We prove the global asymptotic stability of all equilibria by utilizing Lyapunov function and LaSalle’s invariance principle. We have presented numerical simulations to illustrate the theoretical results. We have studied the effects of CTC transmission and time delays on the dynamical behavior of the system. We have shown that inclusion of time delay can significantly increase the concentration of healthy CD4 $$^{+}$$ T cells and reduce the concentrations of infected cells and free HIV particles. While the inclusion of CTC transmission decreases the concentration of healthy CD4 $$^{+}$$ T cells and increases the concentrations of infected cells and free HIV particles.