Resolving Parameter Uncertainty in Outbreak Models Through Population-Level Serological Surveillance

Outbreak modeling faces a critical blind spot: the vast majority of infectious disease cases go undetected, yet epidemiological models frequently ignore this reality. During major outbreaks—from H1N1 to COVID-19—surveillance systems capture only a fraction of true infections, with detection rates often below 10%. When compartmental models treat these incomplete data as ground truth, they produce seemingly accurate fits while generating catastrophically wrong estimates of transmission rates, epidemic size, and intervention effectiveness. We reveal the mathematical foundations of this crisis through two distinct but related problems. First, ignoring case underdetection entirely yields parameter errors exceeding 1000%, even when model fits appear visually perfect. Second, when models explicitly account for underdetection by including case ascertainment ratios as unknown parameters, an infinite spectrum of epidemiologically distinct scenarios can fit the data equally well due to structural unidentifiability. Using rigorous structural identifiability analysis, we prove that transmission rates and detection ratios cannot be uniquely identified from detected case data alone. Strikingly, incorporating just a single population-level seroprevalence measurement transforms model reliability by breaking this mathematical degeneracy. Serological surveys directly measure cumulative population exposure, unlike case surveillance which captures only ongoing infections imperfectly. This integration reduces parameter uncertainty by orders of magnitude and enables accurate inference of transmission rates, peak timing, and final outbreak size. The approach remains robust under realistic noise conditions—with up to 40% measurement noise in observed case counts and 10% in seroprevalence data. Our findings expose a systematic vulnerability in pandemic preparedness while providing an actionable remedy, showing that population-level serosurvey costs are orders of magnitude smaller than the healthcare expenditures prevented through improved outbreak modeling. Our uncertainty quantification framework provides a systematic approach for assessing when surveillance data are adequate for epidemic inference, making serological surveillance integration both a mathematical necessity and a strategic investment in pandemic preparedness.