A Likelihood Approach for Real-Time Calibration of Stochastic Compartmental Epidemic Models

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. In this manuscript, we describe a calibration and prediction framework for stochastic compartmental transmission models of epidemics. The proposed method, Multiple Shooting for Stochastic systems (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 outbreaks of a novel viral pathogen, we evaluate the accuracy of MSS for real-time parameter estimation and prediction during epidemics. We assume that weekly counts for the number of new diagnosed cases are available and serve as an imperfect proxy of incidence. We show that MSS produces accurate estimates of key epidemic parameters (i.e. mean duration of infectiousness, R0, and Reff) and can provide an accurate estimate of the unobserved number of infectious individuals during the course of an epidemic. MSS also allows for accurate prediction of the number and timing of future hospitalizations and the overall attack rate. We 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. We find that MSS significantly outperforms each of these three benchmark methods in the majority of epidemic scenarios tested. In summary, MSS is a promising method that may improve on current approaches for calibration and prediction using stochastic models of epidemics.Author Summary: The sporadic emergence and spread of novel human pathogens poses a continuing threat to global public health. Early and accurate prediction of epidemic behavior is needed to inform effective public health policy decisions which much balance the risk of major outbreaks with the substantial costs of interventions. Key parameters governing the behavior of epidemics, however, cannot be directly observed and hence computational techniques are required for parameter estimation and prediction on the basis of imperfect surveillance data. In this paper, we develop a method (Multiple Shooting for Stochastic Systems, MSS) that utilizes accumulating epidemic data to estimate in real-time (1) key epidemic parameters including the average number of secondary cases and the mean duration of infectiousness, (2) the future number of cases, and (3) the unobserved number of infected individuals in the population. Employing comprehensive simulation experiments, we demonstrate that MSS outperforms the existing state-of-the-art calibration and prediction techniques in the majority of simulated scenarios. MSS may thus allow policy makers to respond more effectively and use resources more efficiently in the face of emerging epidemic threats.