Inferring epidemics from multiple dependent data via pseudo-marginal methods

Health-policy planning requires evidence on the burden that epidemics place on healthcare systems. Multiple, often dependent, datasets provide a noisy and fragmented signal from the unobserved epidemic process including transmission and severity dynamics. This paper explores important challenges to the use of state-space models for epidemic inference when multiple dependent datasets are analysed. We propose a new semistochastic model that exploits deterministic approximations for large-scale transmission dynamics while retaining stochasticity in the occurrence and reporting of relatively rare severe events. This model is suitable for many real-time situations including large seasonal epidemics and pandemics. Within this context we develop algorithms to provide exact parameter inference and test them via simulation. Finally, we apply our joint model and the proposed algorithm to several surveillance data on the 2017–18 influenza epidemic in England to reconstruct transmission dynamics and estimate the daily new influenza infections as well as severity indicators such as the case-hospitalisation risk and the hospital-intensive care risk.