A dual-delay model for complex dynamics of HIV latency reactivation

This paper introduces a novel class of delayed virus-to-cell HIV models incorporating general incidence and Logistic growth, with the objective of elucidating the complex reactivation dynamics of latently infected cells. Analytical results demonstrate that the HIV infection is cleared from the T-cells population when the basic reproduction number R 0 ≤ 1; if R 0 > 1, the criteria for local and global asymptotic stability of the endemic equilibrium are established under the condition that the death rate d of target T-cells is greater than or equal to the intrinsic mitosis rate r. Conversely, when d is less than r, the system is shown to exhibit rich dynamical behaviors. Furthermore, the characteristic equation at endemic equilibrium with the coefficients depend on two time delays is analyzed. Hopf bifurcation criteria are derived for both the general case, where both delays vary simultaneously as bifurcation parameters, and the special case involving only a single delay. The analyses reveal that stability switches can be induced, while chaotic phenomena emerge only when the delays become sufficiently large. Theoretical findings are validated through numerical simulations, which further indicate that a higher latency reactivation rate contributes to more effective control of HIV transmission. In contrast, a prolonged latent infection delay is ultimately predicted to precipitate a rapid viral load rebound.