Parameter non-identifiability limits ecological inference from historical plague mortality records
Historical plague mortality records provide unusually detailed temporal records of epidemic dynamics. However, the ecological processes underlying those dynamics are rarely observed. This creates a fundamental challenge for inference into ecological mechanisms, as multiple combinations of unobserved ecological parameters and initial conditions may produce similar mortality trajectories. We investigated this problem by examining the geometry of parameter compensation for models of the Barcelona plague outbreak of 1490. We fit a mechanistic rat-flea-human transmission model to daily human mortality data under three values of flea search efficiency, then characterized the resulting joint posterior distributions. We then used a phenomenological model in which human infection was driven by a time-varying external force of infection, allowing us to separate parameter dependencies arising from deterministic structure. The mechanistic model reproduced the broad temporal structure of the observed epidemic, but exhibited strong linear and nonlinear dependencies among transmission parameters and initial rat and flea conditions. Similar dependencies persisted in the phenomenological model, despite its substantially reduced complexity. However, fixing the timing of the external hazard substantially reduced these dependencies. These results demonstrate that detailed mortality records can constrain the temporal pattern of an epidemic without uniquely identifying the mechanisms that generated it. Rather than simply adding additional mortality records, improving mechanistic inference from historical epidemics may require recovering independent observations of upstream ecological processes, such as timing of rodent or flea dynamics as well as environmental drivers. Mechanistic models can therefore serve not only to reconstruct historical epidemics but also to identify which missing observations would most improve inference.