  Compartmental models are widely adopted to describe and predict the spreading
of infectious diseases. The unknown parameters of such models need to be
estimated from the data. Furthermore, when some of the model variables are not
empirically accessible, as in the case of asymptomatic carriers of COVID-19,
they have to be obtained as an outcome of the model. Here, we introduce a
framework to quantify how the uncertainty in the data impacts the determination
of the parameters and the evolution of the unmeasured variables of a given
model. We illustrate how the method is able to characterize different regimes
of identifiability, even in models with few compartments. Finally, we discuss
how the lack of identifiability in a realistic model for COVID-19 may prevent
reliable forecasting of the epidemic dynamics.
