Uncovering identifiability of epidemiological models: basic reproduction number and complementary data streams

Mathematical models of infectious disease dynamics are routinely fitted to surveillance data to estimate epidemiological parameters and inform public health decisions. Such data are typically discrete and noisy, but before attempting estimation, it is essential to ask whether the model structure itself permits unique parameter identification at least under perfect (continuous, noise-free) observations. This mathematical property of a model with respect to observation(s), known as structural identifiability, serves as a necessary precondition for reliable inference, since a model that fails this test cannot yield unique parameter estimates even from perfect data. In this study, we systematically investigate structural identifiability in various classes of compartmental epidemic models and establish two main findings. First, we present and deploy a methodology for assessing structural identifiability of epidemiological quantities of interest and demonstrate that the basic reproduction number exhibits identifiability across diverse model structures--including models with multiple transmission pathways and host-vector dynamics--even when individual parameters are not uniquely identifiable. These findings challenge the assumption that complete model identifiability is necessary for reliable epidemiological inference and suggest reformulating the central question from "is the model identifiable?" to "are the quantities that matter for the decision-making identifiable?" Second, we prove that incorporating minimal complementary data, as little as a single time-point measurement from an additional state variable, can make otherwise nonidentifiable models globally identifiable. This result has direct implications for surveillance design: rather than putting limited resources into frequent monitoring of multiple data streams or relying on external parameter estimates that may be uncertain or context-dependent, public health systems can strategically prioritize collecting high-quality complementary measurements.