Delayed immune responses and heterogeneous exposure shape within-host viral dynamics

In this paper, we present a delayed within-host viral dynamics model that integrates nonlinear immune responses and heterogeneous exposure. The model combines logistic viral replication, delayed immune-mediated clearance, and time-dependent external forcing. We introduce a 4 × 4 factorial framework that systematically couples four canonical immune response architectures (linear, Michaelis-Menten, Hill-type, and switch-like) with four representative exposure profiles (constant, periodic, event-driven, and adaptive), yielding sixteen distinct dynamical scenarios. A rigorous theoretical analysis established positivity, boundedness, equilibrium structure, and delay-induced Hopf bifurcations. Extensive numerical simulations quantified transient amplification, timing, clearance efficiency, oscillatory behavior, and long-term persistence using a comprehensive set of nine quantitative metrics. The results reveal robust dynamical hierarchies governed by immune sensitivity and exposure intermittence rather than maximal clearance capacity. In particular, ultrasensitive immune responses amplified early overshoots and cumulative burden, whereas impulsive or adaptive exposure substantially reduced persistence and accelerated post-peak decay. These findings revealed fundamental trade-offs between early transient control and long-term viral persistence in delayed immune feedback systems.