Stochastic transmission dynamic models are especially useful for studying the early emergence of novel pathogens given the importance of chance events when the number of infectious individuals is small. However, methods for parameter estimation and prediction for these types of stochastic models remain limited. This paper describes a calibration and prediction framework for stochastic compartmental transmission models of epidemics.
The proposed method 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 outbreaks of a novel viral pathogen, the authors evaluate the accuracy of this method (multiple shooting for stochastic systems or MSS) for real-time parameter estimation and prediction during epidemics. They assume that weekly counts for the number of new diagnosed cases are available and serve as an imperfect proxy of incidence.
The authors compare the performance of MSS to three state-of-the-art benchmark methods: 1) a likelihood approximation with an assumption of independent Poisson observations; 2) a particle filtering method; and 3) an ensemble Kalman filter method. They find that MSS significantly outperforms each of these three benchmark methods in the majority of epidemic scenarios tested.
Zimmer C, Yaesoubi R, Cohen T. A Likelihood Approach for Real-Time Calibration of Stochastic Compartmental Epidemic Models. PLoS Computational Biology 2017; 13 (1): e1005257. https://doi.org/10.1371/journal.pcbi.1005257