This course presents a concise outline of the stochastic models used in epidemiology to describe the evolution of infectious diseases that can be transmitted within a population and the statistical methods suitable for the type of data encountered in this area of application. In particular, it aims to help students grasp simple Markov models of stratified populations, the "large population" asymptotics which dominates in statistical applications and probabilistic tools such as coupling for analysing these models.
Session 1 – General introduction to the course. Deterministic modelling. The Reed-Frost model.
Session 2 – The SIR model. Construction and extensions.
Session 3 – More on Markov models and coupling. Applications to the study of epidemiological models
Session 4 – Large population asymptotics for SIR models.
Session 5 – Density-dependent epidemiological Markov models with jumps
Session 6 – Statistical estimation.
Session 7 – Statistical estimation (continued).