A LIKELIHOOD APPROACH FOR EPIDEMIC PARAMETER ESTIMATION AND PREDICTION USING STOCHASTIC COMPARTMENTAL MODELS

Purpose:

During the period of initial emergence of novel pathogens, the accurate estimation of key epidemic parameters (such as expected number of secondary cases) is challenging because observed metrics (e.g. the number of pathogen-associated hospitalizations) only partially reflect the true state of the epidemic. Stochastic transmission dynamic models are especially useful for guiding decisions during the emergence of novel pathogens given the importance of chance events and the fluctuations in observations when the number of infectious individuals is small. Our goal is to develop and evaluate a method for real-time calibration of stochastic compartmental models using observed, but likely imperfect, epidemic data.

Method:

We develop a calibration method, called Multiple Shooting for Stochastic systems (MSS), that seeks to maximize the likelihood of the epidemic observations. MSS applies a linear noise approximation to describe the size of the fluctuations, and uses each new surveillance observation to update the belief about the true epidemic state. Using simulated novel viral pathogen outbreaks (Figure A), we evaluate our method's performance throughout epidemics of various magnitudes and host population sizes. In this analysis, we assume that the weekly number of new diagnosed cases is available and serves as an imperfect proxy of disease incidence. We further compare the performance of MSS to that of three state-of-the-art and commonly used benchmark methods; Method A: a likelihood approximation with an assumption of independent Poisson observations; Method B: a particle filter method; and Method C: an ensemble Kalman filter method. We use Wilcoxon Signed-Rank test to evaluate the hypothesis that the median of relative errors for MSS is smaller than that of the benchmark methods.

Results:

Our results (Figure B-D) show that MSS produces accurate estimates of basic reproductive number R₀, effective R₀, and the unobserved number of infectious individuals throughout epidemics. MSS also allows for accurate prediction of the number and timing of future cases and the overall attack rate (Figures E-F). The p-values displayed in Figures B-F confirms that for the majority of scenarios studied here, MSS statistically outperforms the three competing benchmark methods.

Conclusions:

MSS improves on current approaches for model-based parameter estimation and prediction for epidemics and may thus allow for policy makers to respond more effectively and use resources more efficiently in the face of emerging epidemic threats.