Mathematical epidemiology of infectious diseases: model building, analysis and interpretation
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester [u.a.]
Wiley
2000
|
| Schriftenreihe: | Wiley series in mathematical and computational biology
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVI, 303 S. |
| ISBN: | 0471986828 0471492418 |
Internformat
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| 245 | 1 | 0 | |a Mathematical epidemiology of infectious diseases |b model building, analysis and interpretation |c O. Diekmann ; J. A. P. Heesterbeek |
| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 2000 | |
| 300 | |a XVI, 303 S. | ||
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| 490 | 0 | |a Wiley series in mathematical and computational biology | |
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Datensatz im Suchindex
| _version_ | 1805079062300852224 |
|---|---|
| adam_text |
Contents
Preface, Creed and Apology xi
What it is all about and what not xi
The top down approach xi
A workbook xii
Portrait of the reader as a young person xiii
A brief outline of the book xiii
Acknowledgements xiv
And what about reality? xv
I The bare bones: basic issues explained in the simplest
context 1
1 The epidemic in a closed population 3
1.1 The questions (and the underlying assumptions) 3
1.2 Initial growth 4
1.2.1 Initial growth on a generation basis 4
1.2.2 The influence of demographic stochasticity 5
1.2.3 Initial growth in real time 9
1.3 The final size 12
1.3.1 The standard final size equation 12
1.3.2 Derivation of the standard final size equation (and reflection
upon the underlying assumptions) 15
1.3.3 The final size of epidemics within herds 18
1.3.4 The final size in a finite population 22
1.4 The epidemic in a closed population: summary 26
2 Heterogeneity: the art of averaging 31
2.1 Differences in infectivity 31
2.2 Differences in infectivity and susceptibility 37
2.3 Heterogeneity: a preliminary conclusion 39
vi CONTENTS
3 Dynamics at the demographic time scale 41
3.1 Repeated outbreaks versus persistence 41
3.2 Fluctuations around the endemic steady state 43
3.3 Regulation of host populations 55
3.4 Beyond a single outbreak: summary 59
3.5 Some evolutionary considerations about virulence 60
II Structured populations 63
4 The concept of state 65
4.1 i states 65
4.1.1 d states 66
4.1.2 h states 68
4.2 p states 69
4.3 Recapitulation, problem formulation and outlook 70
5 The basic reproduction ratio 73
5.1 The definition of Ro 73
5.2 General h state 77
5.3 On conditions that simplify the computation of Ro 79
5.3.1 One dimensional range 80
5.3.2 Additional within group contacts 81
5.3.3 Finite dimensional range 82
5.4 Submodels for the kernel 83
5.5 Extended example: two diseases 85
5.6 Pair formation models 91
5.7 Summary: a recipe for Ro 95
6 And everything else 99
6.1 Partially vaccinated populations (a first example) 99
6.2 The intrinsic growth rate r 103
6.3 Some generalities 108
6.4 Separable mixing 110
7 Age structure H3
7.1 Demography 113
7.2 Contacts 115
7.3 The next generation operator 115
7.4 Interval decomposition 117
7.5 Inferring parameters from endemic data 117
7.6 Vaccination 122
CONTENTS vii
8 Spatial spread 125
8.1 Posing the problem 125
8.2 Warming up: the linear diffusion equation 125
8.3 Verbal reflections suggesting robustness 128
8.4 Linear structured population models 130
8.5 The nonlinear situation 132
8.6 How to make the theory operational? 134
8.7 Summary: The speed of propagation 134
9 Macroparasites 137
9.1 Introduction 137
9.2 Counting parasite load 139
9.3 The calculation of Ro for life cycles 146
9.4 Seasonality and Ro 148
9.5 A 'pathological' model 149
10 What is contact? 153
10.1 Introduction 153
10.2 Contact duration 154
10.3 Consistency conditions 159
10.4 Effects of subdivision 162
10.4.1 Aggregation 162
10.4.2 What is a core group? 165
10.5 Network models (an idiosyncratic survey) 166
10.5.1 Reflections: what do we want and why? 166
10.5.2 A network with hardly any structure 169
III The hard part: elaborations to (almost) all exercises 175
11 Elaborations for Part I 177
11.1 Elaborations for Chapter 1 177
11.2 Elaborations for Chapter 2 197
11.3 Elaborations for Chapter 3 203
12 Elaborations for Part II 221
12.1 Elaborations for Chapter 5 221
12.2 Elaborations for Chapter 6 241
12.3 Elaborations for Chapter 7 252
12.4 Elaborations for Chapter 8 261
12.5 Elaborations for Chapter 9 265
12.6 Elaborations for Chapter 10 277
viii CONTENTS
Appendix A Stochastic basis of the Kermack McKendrick
ODE model 291
Appendix B Bibliographic skeleton 297
Epidemic modelling 297
Population dynamics 299
Non negative matrices and operators 299
Dynamical systems and bifurcations 300
Analysis 300
Stochastic processes , 300
Index 301 |
| any_adam_object | 1 |
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| dewey-tens | 610 - Medicine and health |
| discipline | Biologie Mathematik Medizin |
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| id | DE-604.BV012467872 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-20T06:39:00Z |
| institution | BVB |
| isbn | 0471986828 0471492418 |
| language | English |
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| physical | XVI, 303 S. |
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| spelling | Diekmann, Odo 1948- Verfasser (DE-588)1031802193 aut Mathematical epidemiology of infectious diseases model building, analysis and interpretation O. Diekmann ; J. A. P. Heesterbeek Chichester [u.a.] Wiley 2000 XVI, 303 S. txt rdacontent n rdamedia nc rdacarrier Wiley series in mathematical and computational biology Epidemiologie - Infektionskrankheit - Mathematisches Modell Epidemiologie (DE-588)4015016-1 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Infektionskrankheit (DE-588)4026879-2 gnd rswk-swf Infektionskrankheit (DE-588)4026879-2 s Epidemiologie (DE-588)4015016-1 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Heesterbeek, J. A. P. 1960- Sonstige (DE-588)1031802304 oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008461530&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Diekmann, Odo 1948- Mathematical epidemiology of infectious diseases model building, analysis and interpretation Epidemiologie - Infektionskrankheit - Mathematisches Modell Epidemiologie (DE-588)4015016-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Infektionskrankheit (DE-588)4026879-2 gnd |
| subject_GND | (DE-588)4015016-1 (DE-588)4114528-8 (DE-588)4026879-2 |
| title | Mathematical epidemiology of infectious diseases model building, analysis and interpretation |
| title_auth | Mathematical epidemiology of infectious diseases model building, analysis and interpretation |
| title_exact_search | Mathematical epidemiology of infectious diseases model building, analysis and interpretation |
| title_full | Mathematical epidemiology of infectious diseases model building, analysis and interpretation O. Diekmann ; J. A. P. Heesterbeek |
| title_fullStr | Mathematical epidemiology of infectious diseases model building, analysis and interpretation O. Diekmann ; J. A. P. Heesterbeek |
| title_full_unstemmed | Mathematical epidemiology of infectious diseases model building, analysis and interpretation O. Diekmann ; J. A. P. Heesterbeek |
| title_short | Mathematical epidemiology of infectious diseases |
| title_sort | mathematical epidemiology of infectious diseases model building analysis and interpretation |
| title_sub | model building, analysis and interpretation |
| topic | Epidemiologie - Infektionskrankheit - Mathematisches Modell Epidemiologie (DE-588)4015016-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Infektionskrankheit (DE-588)4026879-2 gnd |
| topic_facet | Epidemiologie - Infektionskrankheit - Mathematisches Modell Epidemiologie Mathematisches Modell Infektionskrankheit |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008461530&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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