E-Book, Englisch, Band 7, 520 Seiten
Reihe: Princeton Series in Theoretical and Computational Biology
Diekmann / Heesterbeek / Britton Mathematical Tools for Understanding Infectious Disease Dynamics
Course Book
ISBN: 978-1-4008-4562-0
Verlag: De Gruyter
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
E-Book, Englisch, Band 7, 520 Seiten
Reihe: Princeton Series in Theoretical and Computational Biology
ISBN: 978-1-4008-4562-0
Verlag: De Gruyter
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
No detailed description available for "Mathematical Tools for Understanding Infectious Disease Dynamics".
Autoren/Hrsg.
Fachgebiete
- Medizin | Veterinärmedizin Medizin | Public Health | Pharmazie | Zahnmedizin Medizin, Gesundheitswesen Epidemiologie, Medizinische Statistik
- Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
Weitere Infos & Material
Preface xi
A brief outline of the book xii
I The bare bones: Basic issues 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
- 1.3 The final size 14
- 1.4 The epidemic in a closed population: summary 28
2 Heterogeneity: The art of averaging 33
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- 2.1 Differences in infectivity 33
- 2.2 Differences in infectivity and susceptibility 39
- 2.3 The pitfall of overlooking dependence 41
- 2.4 Heterogeneity: a preliminary conclusion 43
3 Stochastic modeling: The impact of chance 45
- 3.1 The prototype stochastic epidemic model 46
- 3.2 Two special cases 48
- 3.3 Initial phase of the stochastic epidemic 51
- 3.4 Approximation of the main part of the epidemic 58
- 3.5 Approximation of the final size 60
- 3.6 The duration of the epidemic 69
- 3.7 Stochastic modeling: summary 71
4 Dynamics at the demographic time scale 73
- 4.1 Repeated outbreaks versus persistence 73
- 4.2 Fluctuations around the endemic steady state 75
- 4.3 Vaccination 84
- 4.4 Regulation of host populations 87
- 4.5 Tools for evolutionary contemplation 91
- 4.6 Markov chains: models of infection in the ICU 101
- 4.7 Time to extinction and critical community size 107
- 4.8 Beyond a single outbreak: summary 124
5 Inference, or how to deduce conclusions from data 127
- 5.1 Introduction 127
- 5.2 Maximum likelihood estimation 127
- 5.3 An example of estimation: the ICU model 130
- 5.4 The prototype stochastic epidemic model 134
- 5.5 ML-estimation of a and ß in the ICU model 146
- 5.6 The challenge of reality: summary 148
II Structured populations 151
- 6 The concept of state 153
- 6.1 i-states 153
- 6.2 p-states 157
- 6.3 Recapitulation, problem formulation and outlook 159
7 The basic reproduction number 161
- 7.1 The definition of R0 161
- 7.2 NGM for compartmental systems 166
- 7.3 General h-state 173
- 7.4 Conditions that simplify the computation of R0 175
- 7.5 Sub-models for the kernel 179
- 7.6 Sensitivity analysis of R0 181
- 7.7 Extended example: two diseases 183
- 7.8 Pair formation models 189
- 7.9 Invasion under periodic environmental conditions 192
- 7.10 Targeted control 199
- 7.11 Summary 203
8 Other indicators of severity 205
- 8.1 The probability of a major outbreak 205
- 8.2 The intrinsic growth rate 212
- 8.3 A brief look at final size and endemic level 219
- 8.4 Simplifications under separable mixing 221
9 Age structure 227
- 9.1 Demography 227
- 9.2 Contacts 228
- 9.3 The next-generation operator 229
- 9.4 Interval decomposition 232
- 9.5 The endemic steady state 233
- 9.6 Vaccination 234
10 Spatial spread 239
- 10.1 Posing the problem 239
- 10.2 Warming up: the linear diffusion equation 240
- 10.3 Verbal reflections suggesting robustness 242
- 10.4 Linear structured population models 244
- 10.5 The nonlinear situation 246
- 10.6 Summary: the speed of propagation 248
- 10.7 Addendum on local finiteness 249
11 Macroparasites 251
- 11.1 Introduction 251
- 11.2 Counting parasite load 253
- 11.3 The calculation of R0 for life cycles 260
- 11.4 A 'pathological' model 261
12 What is contact? 265
- 12.1 Introduction 265
- 12.2 Contact duration 265
- 12.3 Consistency conditions 272
- 12.4 Effects of subdivision 274
- 12.5 Stochastic final size and multi-level mixing 278
- 12.6 Network models (an idiosyncratic view) 286
- 12.7 A primer on pair approximation 302
III Case studies on inference 307
13 Estimators of R0 derived from mechanistic models 309
- 13.1 Introduction 309
- 13.2 Final size and age-structured data 311
- 13.3 Estimating R0 from a transmission experiment 319
- 13.4 Estimators based on the intrinsic growth rate 320
14 Data-driven modeling of hospital infections 325
- 14.1 Introduction 325
- 14.2 The longitudinal surveillance data 326
- 14.3 The Markov chain bookkeeping framework 327
- 14.4 The forward process 329
- 14.5 The backward process 333
- 14.6 Looking both ways 334
15 A brief guide to computer intensive statistics 337
- 15.1 Inference using simple epidemic models 337
- 15.2 Inference using 'complicated' epidemic models 338
- 15.3 Bayesian statistics 339
- 15.4 Markov chain Monte Carlo methodology 341
- 15.5 Large simulation studies 344
IV Elaborations 347
16 Elaborations for Part I 349
- 16.1 Elaborations for Chapter 1 349
- 16.2 Elaborations for Chapter 2 368
- 16.3 Elaborations for Chapter 3 375
- 16.4 Elaborations for Chapter 4 380
- 16.5 Elaborations for Chapter 5 402
17 Elaborations for Part II 407
- 17.1 Elaborations for Chapter 7 407
- 17.2 Elaborations for Chapter 8 432
- 17.3 Elaborations for Chapter 9 445
- 17.4 Elaborations for Chapter 10 451
- 17.5 Elaborations for Chapter 11 455
- 17.6 Elaborations for Chapter 12 465
18 Elaborations for Part III 483
- 18.1 Elaborations for Chapter 13 483
- 18.2 Elaborations for Chapter 15 488
Bibliography 491
Index 497