One Hundred Years (or so) of Epidemiological Modeling

Overview

The year 2027 marks the centenary of one of the most influential papers in mathematical biology: W. O. Kermack and A. G. McKendrick’s 1927 “A Contribution to the Mathematical Theory of Epidemics.” Building on earlier insights of Ronald Ross and Hilda Hudson, Kermack and McKendrick introduced an age-of-infection model, established the celebrated threshold theorem — the principle that an epidemic can take hold only when the density of susceptibles exceeds a critical value — and derived the final-size equation governing the eventual size of an outbreak. The compartmental SIR structure popularised by their work remains, a hundred years later, the conceptual backbone of quantitative epidemiology.

This six-week programme takes the centenary as an occasion to survey how the field has grown from those foundations and to chart where it is heading. Over the twentieth century the deterministic theory was complemented by stochastic models — branching processes, Markov chains, random graphs — that capture the randomness of transmission in finite and heterogeneous populations, while advances in statistical inference made it possible to estimate epidemiological quantities such as the basic reproduction number R₀ directly from data. The turn of the century brought network and agent-based models, phylogenetic reconstruction of transmission chains, and Bayesian methods for fitting increasingly complex models to noisy, high-dimensional, and incomplete observations. The COVID-19 pandemic then placed the entire enterprise under intense scrutiny, demonstrating both the value of real-time forecasting, ensemble modelling, and data integration, and the difficulty of communicating uncertainty and translating model outputs into timely public-health decisions.

The programme is organised around three connected themes. The first, “Mathematical Foundations”, concerns the theory of transmission dynamics, from classical compartmental models to spatial, household, and network formulations and their stochastic and deterministic limits. The second, “Computational and Statistical Tools”, addresses inference from imperfect data, model selection and validation, uncertainty quantification, forecasting, and the integration of genomic and epidemiological information. The third, “From Models to Policy”, examines how modelling informs interventions such as vaccination, contact tracing, and non-pharmaceutical measures, alongside health economics, decision-making under uncertainty, ethics, and pandemic preparedness. Each two-week block pairs introductory tutorials with a research workshop, with ample time reserved in between for collaboration and informal discussion.

By bringing together mathematicians, probabilists, statisticians, computational scientists, and public-health researchers, the programme aims to celebrate a century of progress, to strengthen the dialogue between theory and practice, and to identify the challenges that will shape the next century of epidemiological modelling — among them the assimilation of multi-scale and digital data, the integration of behaviour and pathogen evolution into models, One Health approaches to emerging threats, and the role of machine learning. Hosted at IMS, with strong participation from the regional infectious-disease modelling community, it offers a particularly valuable opportunity for early-career researchers to engage with leaders in the field.