Signal-memory immune regulation as a reduced-order surrogate for within-host viral dynamics

Target–infected–virus (TIV) models typically represent infected-cell removal as instantaneous and state-dependent, implying memoryless exponential loss. Immune regulation is incorporated either implicitly within this effective rate or explicitly through additional immune compartments. Yet biological immune responses are often delayed, heterogeneous, and shaped by how infection evolves over time rather than by burden alone. Here we introduce a memory-dependent immune feedback framework in which net regulation integrates the history of the infection signal \(\dot{I}(t)\) through a causal memory kernel. Under the assumed power-law response kernel, this formulation yields a Caputo fractional-derivative term in the infected-cell dynamics. In the examples examined here, the reduced-order model describes differences in peak timing and late-phase behavior without introducing explicit immune states. Within the stated fixed-target linearization, the model yields a uniquely defined invasion growth rate with continuous rate modulation and supports examination of viral-load quasi-steady-state approximations in the presence of memory-dependent feedback. Applied to human SARS-CoV-2 challenge data, the framework captures transition-associated dynamics and, in selected cases, improves information-theoretic performance relative to basic and immune-explicit TIV-QSSA formulations. Together, these results support memory-dependent immune feedback as a phenomenological reduced-order representation connecting basic viral dynamics and immune-explicit models.