Stochastic Epidemic Models with Inference

Focussing on stochastic models for the spread of infectious diseases in a human population, this book is the outcome of a two-week ICPAM/CIMPA school on Stochastic models of epidemics which took place in Ziguinchor, Senegal, December 5–16, 2015. The text is divided into four parts, each based on one of the courses given at the school: homogeneous models (Tom Britton and Etienne Pardoux), two-level mixing models (David Sirl and Frank Ball), epidemics on graphs (Viet Chi Tran), and statistics for epidemic models (Catherine Larédo).The CIMPA school was aimed at PhD students and Post Docs in the mathematical sciences. Parts (or all) of this book can be used as the basis for traditional or individual reading courses on the topic. For this reason, examples and exercises (some with solutions) are provided throughout.

- Part I Stochastic Epidemics in a Homogeneous Community. - Introduction. - Stochastic Epidemic Models. - Markov Models. - General Closed Models. - Open Markov Models. - Part II Stochastic SIR Epidemics in Structured Populations. - Introduction. - Single Population Epidemics. - The Households Model. - A General Two-Level Mixing Model. - Part III Stochastic Epidemics in a Heterogeneous Community. - Introduction. - Random Graphs. - The Reproduction Number R0. - SIR Epidemics on Configuration Model Graphs. - Statistical Description of Epidemics Spreading on Networks: The Case of Cuban HIV. - Part IV Statistical Inference for Epidemic Processes in a Homogeneous Community. - Introduction. - Observations and Asymptotic Frameworks. - Inference for Markov Chain Epidemic Models. - Inference Based on the Diffusion Approximation of Epidemic Models. - Inference for Continuous Time SIR models.