Stochastic transmission dynamic models are needed to quantify the uncertainty in estimates and predictions during outbreaks of infectious diseases. We previously developed a calibration method for stochastic epidemic compartmental models, called Multiple Shooting for Stochastic Systems (MSS), and demonstrated its competitive performance against a number of existing state-of-the-art calibration methods. The existing MSS method, however, lacks a mechanism against filter degeneracy, a phenomenon that results in parameter posterior distributions that are weighted heavily around a single value. As such, when filter degeneracy occurs, the posterior distributions of parameter estimates will not yield reliable credible or prediction intervals for parameter estimates and predictions. In this work, we extend the MSS method by evaluating and incorporating two resampling techniques to detect and resolve filter degeneracy. Using simulation experiments, we demonstrate that an extended MSS method produces credible and prediction intervals with desired coverage in estimating key epidemic parameters (e.g. mean duration of infectiousness and R0) and short- and long-term predictions (e.g. one and three-week forecasts, timing and number of cases at the epidemic peak, and final epidemic size). Applying the extended MSS approach to a humidity-based stochastic compartmental influenza model, we were able to accurately predict influenza-like illness activity reported by U.S. Centers for Disease Control and Prevention from 10 regions as well as city-level influenza activity using real-time, city-specific Google search query data from 119 U.S. cities between 2003 and 2014.
On the Bernstein-v. Mises Approximation of Posterior Distributions
