Mathematical models of infectious diseases are important for informing public health decisions. Recent progress in computational techniques, along with increased access to surveillance data, has enabled more advanced modelling approaches. In particular, central to this thesis is the integration of Bayesian inference with mechanistic epidemic models to address real-world problems such as reporting delays, intervention evaluation, and parameter uncertainty. This thesis consists of four papers, each with the aim of strengthening the theoretical and practical aspects of epidemic modelling for real-time monitoring, retrospective evaluation, and future preparedness.

Paper I presents a Bayesian nowcasting model to estimate real-time COVID-19-related fatalities in Sweden, where observed death counts are delayed due to reporting lags. This paper introduces the use of additional data streams, here ICU admissions and reported cases, to enhance predictive accuracy. Retrospective evaluation over the second and third COVID-19 waves (October 2020–May 2021) shows that the proposed model improves accuracy compared to a baseline model that does not use additional data streams. All code and data are publicly available, and nowcasts were updated weekly during the pandemic on the webpage: https://staff.math.su.se/fanny.bergstrom/covid19-nowcasting/.

Paper II conducts a counterfactual analysis of Sweden’s national COVID-19 vaccination campaign in 2021 using an age-stratified susceptible-infectious-exposed-recovered (SEIR) model within a Bayesian framework. The model incorporates age-specific incidence data, vaccine uptake, and demographic contact patterns. It estimates that approximately 31,600 deaths related to COVID-19 were averted during 2021, of which 5,170 were due to direct protection and 26,400 from indirect effects (that is, reduced transmission). These findings underscore the importance of community-level vaccine-induced immunity. The study also includes sensitivity analyses to test robustness under various assumptions, such as reporting rates and pre-existing immunity.

Paper III enhances the World Health Organization’s Global Situational Alert System (GSAS), which supports real-time risk assessments at the country level. The paper introduces a hierarchical Bayesian model that accounts for transmission dynamics and reporting delays using case and death data. A three-part model includes components for case growth, delay-adjusted case-to-death mapping, and excess mortality-based calibration. The system assigns alert levels based on projected deaths per capita. Retrospective evaluation shows that modelling reporting delays improve forecast accuracy.

Paper IV focuses on a fundamental issue in epidemic modelling: the identifiability of parameters. Using a modified susceptible-infectious-recovered (SIR) model, the paper shows that under-reporting rates, pre-existing immunity levels, and transmission rates cannot be uniquely inferred from case data alone. An analytical proof of the unidentifiability is provided. Through a simulation study, the paper demonstrates that identifiability can be restored if data, such as sample survey data on population immunity or prevalence, are available for at least one parameter. This finding has implications for model design and data collection strategies, highlighting the need for identifiability analysis to ensure reliable inference.