This thesis explores the joint estimation of transmission and severity of infectious diseases, focussing on the specific case of influenza. Transmission governs the speed and magnitude of viral spread in a population, while severity determines morbidity and mortality and the resulting effect on health care facilities. Their quantification is crucial to inform public health policies, motivating the routine collection of data on influenza cases.

The estimation of severity is compromised by the high degree of censoring affecting the data early during the epidemic. The challenge of estimating transmission is that each influenza data source is often affected by noise and selection bias and individually provides only partial information on the underlying process.

To address severity estimation with high censored data, new methods, inspired by demographic models and by parametric survival analysis, are formulated. A comprehensive review of these methods and existing methods is also carried out.

To jointly estimate transmission and severity, an initial Bayesian epidemic model is fitted to historical data on severe cases, assuming a deterministic severity process and using a single data source. This model is then extended to describe a more stochastic and hence more realistic process of severe events, with the data generating process governed by hidden random variables in a state-space framework. Such increased realism necessitates the use of multiple data sources to enhance parameter identifiability, in a Bayesian evidence synthesis context. In contrast to the literature in the field, the model introduced accounts for dependencies between datasets. The added stochasticity and unmeasured dependencies result in an intractable likelihood. Inference therefore requires a new approach based on Monte Carlo methods.

The method proposed proves its potential and usefulness in the concluding application to real data from the latest (2017/18) epidemic of influenza in England.