Threshold dynamics of an age-structured HIV model with virus-to-cell, cell-to-cell transmissions, and CTL immune response.

Both virus-to-cell and cell-to-cell transmission modes play a crucial role in the long-term dynamics of HIV infection. Additionally, the immune response - particularly the activity of cytotoxic T lymphocytes (CTLs) - can significantly influence the threshold conditions for viral persistence. By incorporating age-structured within-host virus dynamics and the immune response, we develop a dynamical model to explore the intricacies of HIV transmission and progression within a detailed mathematical framework. Specifically, by analyzing the characteristic equations, we establish the local stability of the feasible steady states. Using Lyapunov functionals and LaSalle's invariance principle, we demonstrate that the global threshold dynamics of the model can be described by the immune-inactivated and immune-activated reproduction rates. This study provides a more accurate representation of the complex interplay between HIV and the immune system, offering valuable insights for potential therapeutic strategies.