Functional form linking within-host viral load to transmission at the population scale

Determine the explicit functional dependence of the between-host transmission coefficient β_j(t) on the within-host viral load V(δt_j) for infectious diseases, so that multiscale models can couple within-host dynamics to population-level transmission without assuming an arbitrary form (e.g., linear). Precisely, characterize β_j(t) = f(V(δt_j)) by identifying and validating the function f that maps individual viral load trajectories to transmission rates over calendar time.

Background

In the proposed multiscale framework, the authors couple a deterministic within-host model to a stochastic population-level model by making the per-individual transmission coefficient β_j(t) depend on that individual’s viral load V at infection age δt_j. For implementation and illustration, they assume a linear relationship β_j(t) = l·V(δt_j).

However, they explicitly note that while empirical evidence indicates a link between viral load and transmission, the precise functional relationship is not established. Establishing this function would strengthen mechanistic coupling across scales and improve realism and predictive power of multiscale infectious disease models.

References

Although a variety of experimental observations indicate that population-level disease transmission is often associated with the infectious agent's within-host pathogen load, the specific functional form between these quantities is still uncertain .

— Accurate stochastic simulation algorithm for multiscale models of infectious diseases  (2406.05058 - Yin et al., 2024) in Subsubsection “Model coupling” (Methods, Section 2.1.3)

Because several different choices of linking function all produced qualitatively SEIR-like curves, it remains unclear if different choice of within-host dynamics and linking functions can cascade into population-level trajectories different than those produced by a standard SEIR-like model.

— A multi-scale immuno-epidemiological behavioral model for influenza-like illness: connecting scales through symptom scores  (2610.00862 - Pant et al., 1 Oct 2026) in Discussion, final paragraph

Multi-scale models are typically fitted to within-host data (e.g., viral load) and population-level disease data (e.g., case counts), but whether observing additional novel data sources, even sparsely sampled , (e.g., symptom-severity and corresponding behavioral survey data) could help identify the appropriate linking function remains an important open problem.

— A multi-scale immuno-epidemiological behavioral model for influenza-like illness: connecting scales through symptom scores  (2610.00862 - Pant et al., 1 Oct 2026) in Discussion, final paragraph