Speaker: Jonathan Fintzi, Graduate Student, UW Biostatistics
Abstract: Stochastic epidemic models (SEMs) describe the transmission dynamics of infectious diseases. The task of fitting a SEM, often represented as a Markov jump process (MJP), is complicated by the limited extent of incidence data, which are recorded at discrete times and usually capture only a fraction of cases. The absence of complete subject-level disease histories makes analytically integrating over the missing data impossible. Furthermore, even with complete subject-level data, the computational burden of repeatedly evaluating the MJP likelihood makes it cumbersome to perform exact Bayesian inference for SEM parameters in large populations. Approximate inference via the linear noise approximation (LNA) has recently been proposed as a way of approximating the MJP transition density in the case of partially observed prevalence counts. However, analyzing partially observed incidence using the LNA is challenging since the data reflect the new infections in each inter-observation interval, while the SEM dynamics of the process are driven by the model compartment counts. We demonstrate how a reparameterization of the SEM in terms of its constituent counting processes, along with a transformation of the approximating diffusion, on which the LNA is based, can be used to adapt the LNA for fitting SEMs to partially observed incidence data.