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BK

New York : Springer, 2000

ix,137 s.

ISBN 0-387-95050-8 (brož.)

Lecture notes in statistics ; [vol.] 151

Obsahuje předmluvu, rejstřík, údaje o autorech

Bibliografie: s. 127-133

Epidemiologie - modely matematické - studie

Modely stochastické - epidemiologie - studie

000105932

This book gives a presentation of stochastic epidemic models and their statistical analysis. It focuses on simple epidemic models making use of modern probabilistic and statistical methods such as coupling, diffusion approximation, random graphs, likelihood theory for counting processes, martingales, the EM-algorithm, and MCMC methods. These methods are presented in a general form keeping the technical level at a minimum and then applied to epidemic models. The reader will learn about the theory of epidemic models and be introduced to many useful general techniques from probability and statistics. The lecture notes require an undergraduate-level knowledge of probability and statistics and is well suited for a one-semester graduate course. // Hŕkan Andersson works as a risk analyst in a Swedish bank. Previously, he was a researcher in the Department of Mathematics at Stockholm University, Sweden; models of epidemic spread were his main research field. He has published several papers on epidemic modelling in applied probability journals. // Tom Britton is associate professor at the Department of Mathematics at Uppsala University, Sweden. He is the author of a dozen papers in epidemic modelling and its statistical analysis. He is also director of undergraduate studies at the Department of Mathematics at Uppsala University and secretary of the Swedish Statistical Association. // Springer-Verlag // 175 Fifth Avenue, New York, New York 10010, USA Heidelberger Platz 3, 1000 Berlin 33,

Germany Tiergartenstrasse 17, D-69121 Heidelberg, Germany 13-3, Hongo 3-chome, Bunkyo-ku, Tokyo 113, Japan Provenga, 388, la planta, E-08025 Barcelona, Spain // Room 701 Mirror Tower, 61, Mody Road, Tsimshatsui, Kowloon, Hong Kong 8 Alexandra Road, Wimbledon, London SW19 7JZ, England Via Podgora 4,1-20122 Milano, Italy 26, rue de Carmes, F-75005 Paris, France # 04-01 Cencon I, 1 Tannery Road, Singapore 1334 // ISBN 978-0-387-95050-1 // 9 ___ ___ // www.springer-ny.com // Part I: STOCHASTIC MODELLING // 1 // Chapter 1, Introduction 3 // 1.1. Stochastic versus deterministic models 3 // 1.2. A simple epidemic model: The Reed-Frost model 4 // 1.3. Stochastic epidemics in large communities 6 // 1.4. History of epidemic modelling 7 // Exercises 9 // Chapter 2. The standard SIR epidemic model 11 // 2.1. Definition of the model 11 // 2.2. The Sellke construction 12 // 2.3. The Markovian case 14 // 2.4. Exact results 15 // Exercises 18 // Chapter 3. Coupling methods 19 // 3.1. First examples 19 // 3.2. Definition of coupling 22 // 3.3. Applications to epidemics 22 // Exercises 26 // Chapter 4. The threshold limit theorem 27 // 4.1. The imbedded process 27 // 4.2. Preliminary convergence results 28 // Contents // viii // 4.3. The case mn/n ->/i>0asn—>oo 30 // 4.4. The case mn = m for all n 32 // 4.5. Duration of the Markovian SIR epidemic 34 // Exercises 36 // Chapter 5. Density dependent jump Markov processes 39 // 5.1. An example: A simple birth and death process 39 // 5.2. The general

model 40 // 5.3. The Law of Large Numbers 41 // 5.4. The Central Limit Theorem 43 // 5.5. Applications to epidemic models 46 // Exercises 48 // Chapter 6. Multitype epidemics 51 // 6.1. The standard SIR multitype epidemic model 51 // 6.2. Large population limits 53 // 6.3. Household model 55 // 6.4. Comparing equal and varying susceptibility 56 // Exercises 61 // Chapter 7. Epidemics and graphs 63 // 7.1. Random graph interpretation 64 // 7.2. Constant infectious period 65 // 7.3. Epidemics and social networks 66 // 7.4. The two-dimensional lattice 70 // Exercises 72 // Chapter 8. Models for endemic diseases 73 // 8.1. The SIR model with demography 73 // 8.2. The SIS model 77 // Exercises 83 // Part II: ESTIMATION 85 // Chapter 9. Complete observation of the epidemic process 87 // 9.1. Martingales and log-likelihoods of counting processes 87 // 9.2. ML-estimation for the standard SIR epidemic 91 // Exercises 94 // Chapter 10. Estimation in partially observed epidemics 99 // 10.1. Estimation based on martingale methods 99 // 10.2. Estimation based on the EM-algorithm 103 // Exercises 105 // Chapter 11. Markov Chain Monte Carlo methods 107 // 11.1. Description of the techniques 107 // 11.2. Important examples 109 // 11.3. Practical implementation issues 111 // 11.4. Bayesian inference for epidemics 113 // Exercises 114 // Chapter 12. Vaccination 117 // 12.1. Estimating vaccination policies based on one epidemic 117 // 12.2. Estimating vaccination policies for endemic diseases 120

// 12.3. Estimation of vaccine efficacy 123 // Exercises 124 // References 127 // Subject index 135