Parameter non-identifiability limits ecological inference from historical plague mortality records

Historical plague mortality records offer an unusually detailed timeline of epidemic progression, yet the ecological factors driving these trends remain largely unobserved. This presents a significant hurdle for understanding the underlying mechanisms, as various combinations of hidden ecological parameters and starting conditions can generate comparable mortality patterns.

To explore this issue, scientists examined the Barcelona plague outbreak of 1490, utilizing a rat-flea-human transmission model to analyze daily human mortality data under three different flea search efficiency levels. The researchers then employed a phenomenological model that incorporated a time-varying external force of infection, enabling them to distinguish parameter dependencies stemming from deterministic elements.

While the mechanistic model managed to mirror the overall temporal structure of the observed epidemic, it displayed considerable linear and nonlinear dependencies among transmission parameters and initial rat and flea conditions. Similar interdependencies continued to exist in the phenomenological model, despite its markedly simplified structure.

However, by fixing the timing of the external hazard, these dependencies were substantially reduced. The findings underscore that comprehensive mortality data can constrain the timeline of an epidemic without definitively pinpointing the mechanisms that initiated it. Instead of merely amassing more mortality records, enhancing mechanistic insights from historical outbreaks may necessitate uncovering independent observations of upstream ecological processes, such as the timing of rodent or flea dynamics as well as environmental influences.

In essence, mechanistic models not only facilitate the reconstruction of past epidemics but also aid in identifying which missing observations would most effectively improve inference.