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The authors formulate and analyze a mechanistic ordinary differential equation (ODE) framework capturing within-host HIV dynamics across CD4$^+$ T cells, latent and productive infections, virions, and cytotoxic immune effectors under dual-action antiretroviral therapy (ART). Quantifying these within-host interactions is critical for analytically predicting treatment failure, latent reservoir persistence, and the boundary conditions governing viral rebound. The analysis derives the basic reproduction number ($R_0$) and explicit treatment-dependent suppression thresholds, proving that while ART facilitates CD4$^+$ T-cell recovery, latent reservoirs persist and decaying or periodic drug efficacy forces sustained viral oscillations.
Latent HIV reservoirs remain stubbornly persistent even under dual-action therapy, with analytical suppression thresholds revealing exactly when waning drug efficacy tips the system into sustained viral rebound and oscillatory escape.
We develop and analyse a mechanistic ODE model of within-host HIV dynamics that includes uninfected CD4$^+$ T cells, latently and productively infected cells, free virions, and cytotoxic immune effectors. Antiretroviral therapy is described by two time-dependent efficacy functions that separately reduce new infections and virion production. We show that solutions remain non-negative and bounded, identify the infection-free and endemic equilibria, and derive the basic reproduction number together with the local stability condition for the infection-free state. We also obtain treatment-dependent suppression thresholds and an analytical estimate of when this threshold is crossed as treatment efficacy declines. Numerical simulations consider untreated infection, ART initiation, periodic variation in efficacy, and progressive loss of treatment effect. Without therapy, the model approaches a state of persistent infection. ART reduces viral load and promotes recovery of the CD4$^+$ T-cell population, while the latent reservoir persists under the parameter set considered. Periodic changes in treatment efficacy produce sustained forced oscillations. These results connect the analytical threshold conditions with the treatment-dependent dynamics of the model and provide a basis for future calibration, sensitivity analysis, uncertainty quantification, and extensions informed by clinical data.