Accurate quantification of uncertainty in epidemic parameter estimates and predictions using stochastic compartmental models

Abstract

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.

Use of daily Internet search query data improves real-time projections of influenza epidemics

“…We also note that the improvement associated with using daily-resolved data has been achieved using our calibration and prediction framework as in Zimmer et al [ 27 ] and in the previously described methods. We did not investigate whether similar improvements would be seen if other calibration and prediction approaches were used.…”

“…P is the observation probability mapping the state ν i to the observation y i incorporating any additional uncertainty in the data collection such as reporting errors. The observation probability P for the new cases y i is assumed to be normally distributed with a mean ν (I) i − ν (I) i −1 + R * i and variance 10 (as previously assumed in MSSa version in Zimmer et al [ 27 ]).…”

“…The calibration is carried out iteratively according to equation ( 2.5 ) as previously described [ 27 ]. Next, we make predictions for targets denoted by Z based on the posterior distribution of the parameters π and state estimates using the simulation model.…”

“…Specifically, we sample M ′ = 100 (as in [ 27 ]) parameter vectors θ (1) , …, θ ( M ′) from the parameter posterior π i and state vectors from the belief state. For each of these M ′ epidemic scenarios, we carry out simulations with a stochastic model P Sim resulting in M ′ target values Z (1) , …, Z ( M ′) .…”

Computational Strategies to Combat COVID-19: Useful Tools to Accelerate SARS-CoV-2 and Coronavirus Research

“…COPASI has been used to model various aspects of virology, including mechanisms of action [76][77][78][79], pharmaceutical interventions [80], virus life-cycle [81], vaccine design [82] and dynamics of epidemics [83][84][85].…”