Stochastic epidemic models and their statistical analysis:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York ; Berlin ; Heidelberg ; Barcelona ; Hong Kong ; London ; Milan ; Paris ; Singapore ; Tokyo
Springer
2000
|
| Series: | Lecture notes in statistics
151 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 137 S. graph. Darst. |
| ISBN: | 0387950508 |
Staff View
MARC
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| 245 | 1 | 0 | |a Stochastic epidemic models and their statistical analysis |c Håkan Andersson ; Tom Britton |
| 264 | 1 | |a New York ; Berlin ; Heidelberg ; Barcelona ; Hong Kong ; London ; Milan ; Paris ; Singapore ; Tokyo |b Springer |c 2000 | |
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| 650 | 4 | |a Épidémiologie - Méthodes statistiques | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Epidemiologic Methods | |
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Record in the Search Index
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| adam_text | Contents
Preface v
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
viii Contents
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
Contents ix
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
|
| any_adam_object | 1 |
| author | Andersson, Håkan Britton, Tom 1965- |
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| author_facet | Andersson, Håkan Britton, Tom 1965- |
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| building | Verbundindex |
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| dewey-full | 614.4/01/5118 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 614 - Forensic medicine; incidence of disease |
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| id | DE-604.BV013331941 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:43:56Z |
| institution | BVB |
| isbn | 0387950508 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009090618 |
| oclc_num | 44118177 |
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| physical | IX, 137 S. graph. Darst. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
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| publisher | Springer |
| record_format | marc |
| series | Lecture notes in statistics |
| series2 | Lecture notes in statistics |
| spelling | Andersson, Håkan Verfasser aut Stochastic epidemic models and their statistical analysis Håkan Andersson ; Tom Britton New York ; Berlin ; Heidelberg ; Barcelona ; Hong Kong ; London ; Milan ; Paris ; Singapore ; Tokyo Springer 2000 IX, 137 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in statistics 151 Analyse stochastique Analyse stochastique ram Epidemiologie gtt Epidémiologie - Modèles mathématiques ram Epidémiologie - Méthodes statistiques ram Statistische methoden gtt Stochastische analyse gtt Wiskundige modellen gtt Épidémiologie - Modèles mathématiques Épidémiologie - Méthodes statistiques Mathematisches Modell Epidemiologic Methods Epidemiology Mathematical models Epidemiology Statistical methods Models, Statistical Stochastic Processes Stochastic analysis Stochastisches Modell (DE-588)4057633-4 gnd rswk-swf Schätzung (DE-588)4193791-0 gnd rswk-swf Epidemiologie (DE-588)4015016-1 gnd rswk-swf Epidemiologie (DE-588)4015016-1 s Stochastisches Modell (DE-588)4057633-4 s Schätzung (DE-588)4193791-0 s DE-604 Britton, Tom 1965- Verfasser (DE-588)173410766 aut Lecture notes in statistics 151 (DE-604)BV002447846 151 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009090618&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Andersson, Håkan Britton, Tom 1965- Stochastic epidemic models and their statistical analysis Lecture notes in statistics Analyse stochastique Analyse stochastique ram Epidemiologie gtt Epidémiologie - Modèles mathématiques ram Epidémiologie - Méthodes statistiques ram Statistische methoden gtt Stochastische analyse gtt Wiskundige modellen gtt Épidémiologie - Modèles mathématiques Épidémiologie - Méthodes statistiques Mathematisches Modell Epidemiologic Methods Epidemiology Mathematical models Epidemiology Statistical methods Models, Statistical Stochastic Processes Stochastic analysis Stochastisches Modell (DE-588)4057633-4 gnd Schätzung (DE-588)4193791-0 gnd Epidemiologie (DE-588)4015016-1 gnd |
| subject_GND | (DE-588)4057633-4 (DE-588)4193791-0 (DE-588)4015016-1 |
| title | Stochastic epidemic models and their statistical analysis |
| title_auth | Stochastic epidemic models and their statistical analysis |
| title_exact_search | Stochastic epidemic models and their statistical analysis |
| title_full | Stochastic epidemic models and their statistical analysis Håkan Andersson ; Tom Britton |
| title_fullStr | Stochastic epidemic models and their statistical analysis Håkan Andersson ; Tom Britton |
| title_full_unstemmed | Stochastic epidemic models and their statistical analysis Håkan Andersson ; Tom Britton |
| title_short | Stochastic epidemic models and their statistical analysis |
| title_sort | stochastic epidemic models and their statistical analysis |
| topic | Analyse stochastique Analyse stochastique ram Epidemiologie gtt Epidémiologie - Modèles mathématiques ram Epidémiologie - Méthodes statistiques ram Statistische methoden gtt Stochastische analyse gtt Wiskundige modellen gtt Épidémiologie - Modèles mathématiques Épidémiologie - Méthodes statistiques Mathematisches Modell Epidemiologic Methods Epidemiology Mathematical models Epidemiology Statistical methods Models, Statistical Stochastic Processes Stochastic analysis Stochastisches Modell (DE-588)4057633-4 gnd Schätzung (DE-588)4193791-0 gnd Epidemiologie (DE-588)4015016-1 gnd |
| topic_facet | Analyse stochastique Epidemiologie Epidémiologie - Modèles mathématiques Epidémiologie - Méthodes statistiques Statistische methoden Stochastische analyse Wiskundige modellen Épidémiologie - Modèles mathématiques Épidémiologie - Méthodes statistiques Mathematisches Modell Epidemiologic Methods Epidemiology Mathematical models Epidemiology Statistical methods Models, Statistical Stochastic Processes Stochastic analysis Stochastisches Modell Schätzung |
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