Resolving parameter uncertainty in SIR models through population-level serological surveillance: A synthetic study

Epidemic models face a critical challenge: surveillance systems capture only a fraction of infections (often <10%). We reveal two fundamental problems. First, when models ignore underdetection entirely-treating detected cases as complete-parameter errors exceed 1000% despite visually reasonable fits. Second, when models explicitly account for underdetection by including case detection ratios as unknown parameters, structural identifiability analysis proves transmission rates and detection ratios become mathematically confounded-rendering infinite epidemiologically distinct scenarios equally plausible from case data alone. Integrating even a single population-level seroprevalence measurement resolves both problems by independently constraining cumulative exposure. Through Bayesian inference on synthetic SIR data, we demonstrate that this approach reduces parameter uncertainty by orders of magnitude, enabling accurate inference of transmission dynamics, peak timing, and outbreak size under realistic noise. Our framework establishes serological surveillance integration as both a mathematical necessity and a strategic investment for pandemic preparedness.