  Recent outbreaks of monkeypox and Ebola, and worrying waves of COVID-19,
influenza and respiratory syncytial virus, have all led to a sharp increase in
the use of epidemiological models to estimate key epidemiological parameters.
The feasibility of this estimation task is known as the practical
identifiability (PI) problem. Here, we investigate the PI of eight commonly
reported statistics of the classic Susceptible-Infectious-Recovered model using
a new measure that shows how much a researcher can expect to learn in a
model-based Bayesian analysis of prevalence data. Our findings show that the
basic reproductive number and final outbreak size are often poorly identified,
with learning exceeding that of individual model parameters only in the early
stages of an outbreak. The peak intensity, peak timing, and initial growth rate
are better identified, being in expectation over 20 times more probable having
seen the data by the time the underlying outbreak peaks. We then test PI for a
variety of true parameter combinations, and find that PI is especially
problematic in slow-growing or less-severe outbreaks. These results add to the
growing body of literature questioning the reliability of inferences from
epidemiological models when limited data are available.
