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 (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$I^-$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>I</mi> <mo>-</mo> </msup> </math></EquationSource> </InlineEquation>), infected with high immune protection (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$I^+$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>I</mi> <mo>+</mo> </msup> </math></EquationSource> </InlineEquation>), 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 <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\mathcal {R}_0$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> under global mixing. Simulations reveal sharp clearance–persistence transitions driven by inoculum size and immune trait, and an emergent <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$S\!\rightarrow \!I^-\!\rightarrow \!I^+\!\rightarrow \!R$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>S</mi> <mspace width="-0.166667em" /> <mo stretchy="false">→</mo> <mspace width="-0.166667em" /> <msup> <mi>I</mi> <mo>-</mo> </msup> <mspace width="-0.166667em" /> <mo stretchy="false">→</mo> <mspace width="-0.166667em" /> <msup> <mi>I</mi> <mo>+</mo> </msup> <mspace width="-0.166667em" /> <mo stretchy="false">→</mo> <mspace width="-0.166667em" /> <mi>R</mi> </mrow> </math></EquationSource> </InlineEquation> cascade. Under sharp thresholds and activation, chronic within-host equilibria can sustain infection even when <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$\mathcal {R}_0<1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> <mo><</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>, 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.

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

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2026年5月6日

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Cyrille Kenne,
Pascal Zongo

摘要

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 ( $I^-$ $I^{-}$ ), infected with high immune protection ( $I^+$ $I^{+}$ ), 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 $\mathcal {R}_0$ $R_{0}$ under global mixing. Simulations reveal sharp clearance–persistence transitions driven by inoculum size and immune trait, and an emergent $S\!\rightarrow \!I^-\!\rightarrow \!I^+\!\rightarrow \!R$ $S \to I^{-} \to I^{+} \to R$ cascade. Under sharp thresholds and activation, chronic within-host equilibria can sustain infection even when $\mathcal {R}_0<1$ $R_{0} < 1$ , 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.