Impact of Latent Reservoirs, Latent Infection Delays, and Treatments on HIV Dynamics

A within-host HIV dynamics model incorporating latent reservoirs, distributed time delays, and a B-cell-mediated humoral immune response is developed and analyzed mathematically. The model includes five compartments: uninfected CD4+ T cells, latently infected cells, actively infected cells, free virions, and B cells. Four distinct distributed delays are introduced to account for the periods between viral entry and the emergence of latently or actively infected cells, reactivation of latently infected cells, and intracellular virion production. For the non-delayed system, the basic reproduction number R0 is derived using the next-generation matrix method. Using Lyapunov functions and LaSalle’s Invariance Principle, a sharp threshold dynamic is proven: the infection-free equilibrium is globally asymptotically stable (GAS) when R0≤1, whereas a unique endemic equilibrium is GAS when R0>1. For the full distributed-delay system, a delay-dependent reproduction number R0d is defined. The global asymptotic stability of the infection-free equilibrium is established for R0d≤1, and the global asymptotic stability of the endemic equilibrium is established for R0d>1, using suitably constructed Lyapunov functionals that account for the delay history. Numerical simulations validate the analytical threshold behavior. A sensitivity analysis of R0d identifies the most influential parameters for potential intervention. A treatment-dependent reproduction number is derived, and the critical drug efficacy required for viral eradication is determined. The intracellular production delay is shown to act as a critical threshold for infection clearance.