  Measles presents a unique and imminent challenge for epidemiologists and
public health officials: the disease is highly contagious, yet vaccination
rates are declining precipitously in many localities. Consequently, the risk of
a measles outbreak continues to rise. To improve preparedness, we study
historical measles data both pre- and post-vaccine, and design new methodology
to forecast measles counts with uncertainty quantification. We propose to model
the disease counts as an integer-valued functional time series: measles counts
are a function of time-of-year and time-ordered by year. The counts are modeled
using a negative-binomial distribution conditional on a real-valued latent
process, which accounts for the overdispersion observed in the data. The latent
process is decomposed using an unknown basis expansion, which is learned from
the data, with dynamic basis coefficients. The resulting framework provides
enhanced capability to model complex seasonality, which varies dynamically from
year-to-year, and offers improved multi-month ahead point forecasts and
substantially tighter forecast intervals (with correct coverage) compared to
existing forecasting models. Importantly, the fully Bayesian approach provides
well-calibrated and precise uncertainty quantification for epi-relevent
features, such as the future value and time of the peak measles count in a
given year. An R package is available online.
