From Trait-Structured Within-Host Dynamics to SIR Models: A Multiscale Framework With Re-Exposure

We present a threshold-based multiscale framework that links mechanistic within-host infection dynamics to a structured, SIR-like population model. Starting from a two-variable system for pathogen load and immune response that includes inoculum (Allee-like) thresholds and nonlinear immune activation, we derive mapping rules that classify continuous trajectories into four states: susceptible (S), infected with low immune protection ( $I^{-}$ ), infected with high immune protection ( $I^{+}$ ), and recovered (R). Here, "infected" refers to individuals with a detectable pathogen load. Unlike previous multiscale approaches, our framework integrates both scales into a single system: population compartments emerge by direct projection of within-host trajectories, avoiding ad hoc linking functions. We derive a next-generation operator for trait-structured re-exposure (local vs. global mixing) and an explicit expression for $R_0$ under global mixing. Simulations reveal sharp clearance-persistence transitions driven by inoculum size and immune trait, and an emergent $S\to I^{-}\to I^{+}\to R$ cascade. Under sharp thresholds and activation, chronic within-host equilibria can sustain infection even when $R_0<1$ , producing backward-bifurcation-like behavior at the population level. The framework provides a consistent route from immunological heterogeneity to epidemic indicators, with implications for identifying chronic reservoirs, interpreting dose-response data, and estimating control thresholds directly from within-host measurements.