GPH 44: Mathematical Modelling of Infectious Disease

In this episode, Medlock Holmes enters the world of dynamic systems - where infections move not randomly, but according to patterns that can be described, simulated, and sometimes predicted.Mathematical modelling of infectious disease seeks to answer urgent questions:How fast will an outbreak grow?When will it peak?What level of vaccination is needed for herd immunity?What impact will school closures or travel restrictions have?Holmes introduces the classic SIR framework - Susceptible, Infectious, Recovered - and explores how compartmental models describe the flow of individuals between disease states. We examine the meaning and significance of the basic reproduction number, R₀, and how it determines whether an epidemic expands or collapses.The episode moves beyond simple models to consider:* SEIR extensions (including exposed/incubation periods)* Stochastic vs deterministic models* Agent-based models* Contact networks and heterogeneity* Time-varying transmission rates* Vaccination thresholds and herd immunityHolmes emphasises that models are not crystal balls. They are structured assumptions made explicit. Their power lies in clarifying scenarios, testing policy options, and illuminating uncertainty - not predicting exact futures.We also explore the ethical dimensions of modelling during pandemics: how projections influence public behaviour, political decision-making, and resource allocation.In infectious disease control, modelling is both science and strategy.Key Takeaways* Mathematical models describe how infections move through populations.* The basic reproduction number (R₀) determines epidemic potential.* Compartmental models simplify complex transmission dynamics.* Stochastic models incorporate randomness and uncertainty.* Models depend on assumptions - transparency is essential.* Modelling supports scenario planning and policy decisions.* Interpretation requires humility as well as technical skill. This is a public episode. If you'd like to discuss this with other subscribers or get access to bonus episodes, visit drmanaankarray.substack.com/subscribe