Mathematical tools for understanding infectious disease dynamics:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton [u.a.]
Princeton Univ. Press
2013
|
| Series: | Princeton series in theoretical and computational biology
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XIV, 502 S. |
| ISBN: | 9780691155395 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Contents
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
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
viii CONTENTS
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
β
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 i?o
161
7.2
NGM for compartmental systems
166
7.3
General h-state
173
7.4
Conditions that simplify the computation of
ño
175
7.5
Sub-models for the kernel
179
7.6
Sensitivity analysis of
До
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
CONTENTS ix
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
Ло
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 Ro derived from mechanistic models
309
13.1
Introduction
309
13.2
Final size and age-structured data
311
13.3
Estimating
До
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
З68
16.3
Elaborations for Chapter
3 375
16.4
Elaborations for Chapter
4
З8О
16.5
Elaborations for Chapter
5 402
X
CONTENTS
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
4G5
18
Elaborations for Part III
483
18.1
Elaborations for Chapter
13 483
18.2
Elaborations for Chapter
15 488
Bibliography
491
Index
497
Mathematical Tools for Understanding
Infectious Disease
Dynamics
Mathematical modeling is critical to our understanding of how infectious diseases spread at the individual
and population levels. This book gives readers the necessary skills to correctly formulate and analyze math¬
ematical models in infectious disease epidemiology, and is the first treatment of the subject to integrate
deterministic and stochastic models and methods.
Mathematical Tools for Understanding Infectious Disease Dynamics fully explains how to translate
biological assumptions into mathematics to construct useful and consistent models, and how to use the
biological interpretation and mathematical reasoning to analyze these models. It shows how to relate
models to data through statistical inference, and how to gain important insights into infectious disease
dynamics by translating mathematical results back to biology. This comprehensive and accessible book
also features numerous detailed exercises throughout; full elaborations to all exercises are provided.
■
Covers the latest research in mathematical modeling of infectious disease epidemiology
■
Integrates deterministic and stochastic approaches
■
Teaches skills in model construction, analysis, inference, and interpretation
■
Features numerous exercises and their detailed elaborations
■
Motivated by real-world applications throughout
Odo
Diekmann is professor of applied analysis at Utrecht University. Hans
Heesterbeek
is professor of
theoretical epidemiology at Utrecht University. Tom
Britton
is professor of mathematical statistics at
Stockholm University.
|
| any_adam_object | 1 |
| author | Diekmann, Odo 1948- Heesterbeek, J. A. P. 1960- Britton, Tom 1965- |
| author_GND | (DE-588)1031802193 (DE-588)1031802304 (DE-588)173410766 |
| author_facet | Diekmann, Odo 1948- Heesterbeek, J. A. P. 1960- Britton, Tom 1965- |
| author_role | aut aut aut |
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| dewey-full | 614.4 |
| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 614 - Forensic medicine; incidence of disease |
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| discipline | Biologie Mathematik Medizin |
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| spelling | Diekmann, Odo 1948- Verfasser (DE-588)1031802193 aut Mathematical tools for understanding infectious disease dynamics Odo Diekmann, Hans Heesterbeek, and Tom Britton Princeton [u.a.] Princeton Univ. Press 2013 XIV, 502 S. txt rdacontent n rdamedia nc rdacarrier Princeton series in theoretical and computational biology Mathematisches Modell Medizin Epidemiology Mathematical models Congresses Epidemiology Mathematical models Communicable diseases Mathematical models SCIENCE / Life Sciences / Biology / General bisacsh MATHEMATICS / Applied bisacsh MEDICAL / Infectious Diseases bisacsh Infektionskrankheit (DE-588)4026879-2 gnd rswk-swf Epidemiologie (DE-588)4015016-1 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Mathematisches Modell (DE-588)4114528-8 s Epidemiologie (DE-588)4015016-1 s Infektionskrankheit (DE-588)4026879-2 s DE-604 Heesterbeek, J. A. P. 1960- Verfasser (DE-588)1031802304 aut Britton, Tom 1965- Verfasser (DE-588)173410766 aut Erscheint auch als Online-Ausgabe 978-1-400-84562-0 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025932051&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025932051&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Diekmann, Odo 1948- Heesterbeek, J. A. P. 1960- Britton, Tom 1965- Mathematical tools for understanding infectious disease dynamics Mathematisches Modell Medizin Epidemiology Mathematical models Congresses Epidemiology Mathematical models Communicable diseases Mathematical models SCIENCE / Life Sciences / Biology / General bisacsh MATHEMATICS / Applied bisacsh MEDICAL / Infectious Diseases bisacsh Infektionskrankheit (DE-588)4026879-2 gnd Epidemiologie (DE-588)4015016-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4026879-2 (DE-588)4015016-1 (DE-588)4114528-8 (DE-588)1071861417 |
| title | Mathematical tools for understanding infectious disease dynamics |
| title_auth | Mathematical tools for understanding infectious disease dynamics |
| title_exact_search | Mathematical tools for understanding infectious disease dynamics |
| title_full | Mathematical tools for understanding infectious disease dynamics Odo Diekmann, Hans Heesterbeek, and Tom Britton |
| title_fullStr | Mathematical tools for understanding infectious disease dynamics Odo Diekmann, Hans Heesterbeek, and Tom Britton |
| title_full_unstemmed | Mathematical tools for understanding infectious disease dynamics Odo Diekmann, Hans Heesterbeek, and Tom Britton |
| title_short | Mathematical tools for understanding infectious disease dynamics |
| title_sort | mathematical tools for understanding infectious disease dynamics |
| topic | Mathematisches Modell Medizin Epidemiology Mathematical models Congresses Epidemiology Mathematical models Communicable diseases Mathematical models SCIENCE / Life Sciences / Biology / General bisacsh MATHEMATICS / Applied bisacsh MEDICAL / Infectious Diseases bisacsh Infektionskrankheit (DE-588)4026879-2 gnd Epidemiologie (DE-588)4015016-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Mathematisches Modell Medizin Epidemiology Mathematical models Congresses Epidemiology Mathematical models Communicable diseases Mathematical models SCIENCE / Life Sciences / Biology / General MATHEMATICS / Applied MEDICAL / Infectious Diseases Infektionskrankheit Epidemiologie Konferenzschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025932051&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025932051&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT diekmannodo mathematicaltoolsforunderstandinginfectiousdiseasedynamics AT heesterbeekjap mathematicaltoolsforunderstandinginfectiousdiseasedynamics AT brittontom mathematicaltoolsforunderstandinginfectiousdiseasedynamics |