Stochastic Epidemic Models and Their Statistical Analysis

1. Front Matter

   Pages i-ix

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2. Stochastic Modelling

   1. Front Matter

      Pages 1-2

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   2. Introduction

      • Håkan Andersson, Tom Britton

      Pages 3-9

   3. The standard SIR epidemic model

      • Håkan Andersson, Tom Britton

      Pages 11-18

   4. Coupling methods

      • Håkan Andersson, Tom Britton

      Pages 19-26

   5. The threshold limit theorem

      • Håkan Andersson, Tom Britton

      Pages 27-37

   6. Density dependent jump Markov processes

      • Håkan Andersson, Tom Britton

      Pages 39-49

   7. Multitype epidemics

      • Håkan Andersson, Tom Britton

      Pages 51-61

   8. Epidemics and graphs

      • Håkan Andersson, Tom Britton

      Pages 63-72

   9. Models for endemic diseases

      • Håkan Andersson, Tom Britton

      Pages 73-83

3. Estimation

   1. Front Matter

      Pages 85-86

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   2. Complete observation of the epidemic process

      • Håkan Andersson, Tom Britton

      Pages 87-97

   3. Estimation in partially observed epidemics

      • Håkan Andersson, Tom Britton

      Pages 99-106

   4. Markov Chain Monte Carlo

      • Håkan Andersson, Tom Britton

      Pages 107-115

   5. Vaccination

      • Håkan Andersson, Tom Britton

      Pages 117-125

4. Back Matter

   Pages 127-140

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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.

• Analysis
• Markov
• Markov chain
• Markov process
• epidemics
• model
• modeling

• Group Financial Risk Control, SwedBank, Stockholm, Sweden

  Håkan Andersson

• Department of Mathematics, Uppsala University, Uppsala, Sweden

  Tom Britton

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