  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 semi-stochastic 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 as
the case-hospitalisation risk and the hospital-intensive care risk.
