# Stochastic Epidemic Models and Their Statistical Analysis

• Tom Britton
Book

Part of the Lecture Notes in Statistics book series (LNS, volume 151)

1. Front Matter
Pages i-ix
2. ### Stochastic Modelling

1. Front Matter
Pages 1-2
Pages 3-9
Pages 11-18
Pages 19-26
Pages 27-37
Pages 39-49
Pages 51-61
Pages 63-72
Pages 73-83
3. ### Estimation

1. Front Matter
Pages 85-86
Pages 87-97
Pages 99-106
Pages 107-115
Pages 117-125
4. Back Matter
Pages 127-140

### Introduction

The present lecture notes describe stochastic epidemic models and methods for their statistical analysis. Our aim is to present ideas for such models, and methods for their analysis; along the way we make practical use of several probabilistic and statistical techniques. This will be done without focusing on any specific disease, and instead rigorously analyzing rather simple models. The reader of these lecture notes could thus have a two-fold purpose in mind: to learn about epidemic models and their statistical analysis, and/or to learn and apply techniques in probability and statistics. The lecture notes require an early graduate level knowledge of probability and They introduce several techniques which might be new to students, but our statistics. intention is to present these keeping the technical level at a minlmum. Techniques that are explained and applied in the lecture notes are, for example: coupling, diffusion approximation, random graphs, likelihood theory for counting processes, martingales, the EM-algorithm and MCMC methods. The aim is to introduce and apply these techniques, thus hopefully motivating their further theoretical treatment. A few sections, mainly in Chapter 5, assume some knowledge of weak convergence; we hope that readers not familiar with this theory can understand the these parts at a heuristic level. The text is divided into two distinct but related parts: modelling and estimation.

### Keywords

Analysis Markov Markov chain Markov process epidemics model modeling

#### Authors and affiliations

• 1
• Tom Britton
• 2
1. 1.Group Financial Risk ControlSwedBankStockholmSweden
2. 2.Department of MathematicsUppsala UniversityUppsalaSweden

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-1158-7
• Copyright Information Springer-Verlag New York, Inc. 2000
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-0-387-95050-1
• Online ISBN 978-1-4612-1158-7
• Series Print ISSN 0930-0325
• Buy this book on publisher's site