Stochastic Epidemic Models with Inference

by Tom Britton, Frank Ball, Etienne Pardoux, Catherine Larédo

Overview

Focussing on shastic models for the spread of infectious diseases in a human population, this book is the outcome of a two-week ICPAM/CIMPA school on "Shastic 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.

Product Details

ISBN-13:	9783030308995
Publisher:	Springer International Publishing
Publication date:	12/01/2019
Series:	Lecture Notes in Mathematics , #2255
Edition description:	1st ed. 2019
Pages:	474
Product dimensions:	6.10(w) x 9.25(h) x (d)

About the Author

Tom Britton is professor at the Department of Mathematics at Skholm University. His research focuses on shastic modelling, and inference procedures, for biological and medical problems, in particular models for the spread of infectious diseases, networks and phylogenetics. He is the author of more than 100 publications, and two monographs about models and analysis of infectious disease spreading.

Etienne Pardoux is professor emeritus at the Institut de Mathématiques de Marseille, within Aix Marseille Univ. His research has covered several topics of shastic analysis, in particular shastic partial differential equations, backward shastic differential equations and homogenization. More recently, he has turned his interests towards evolutionary biology and modeling of infectious diseases. He is the author of more than 160 publications, including four books.

Table of Contents

- Part I Shastic Epidemics in a Homogeneous Community. - Introduction. - Shastic Epidemic Models. - Markov Models. - General Closed Models. - Open Markov Models. - Part II Shastic SIR Epidemics in Structured Populations. - Introduction. - Single Population Epidemics. - The Households Model. - A General Two-Level Mixing Model. - Part III Shastic 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.