Spatiotemporal patterns in ecology and epidemiology: theory, models, and simulation
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boca Raton
Chapman & Hall/CRC
2008
|
| Schriftenreihe: | Chapman & Hall/CRC mathematical and computational biology
17 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | 443 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
Internformat
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| 245 | 1 | 0 | |a Spatiotemporal patterns in ecology and epidemiology |b theory, models, and simulation |c Horst Malchow ... |
| 264 | 1 | |a Boca Raton |b Chapman & Hall/CRC |c 2008 | |
| 300 | |a 443 S. |b Ill., graph. Darst. |e 1 CD-ROM (12 cm) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Chapman & Hall/CRC mathematical and computational biology |v 17 | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 7 | |a Biologia (aplicações) |2 larpcal | |
| 650 | 7 | |a Biomatemática |2 larpcal | |
| 650 | 7 | |a Dinâmica de populações |2 larpcal | |
| 650 | 7 | |a Ecologia matemática |2 larpcal | |
| 650 | 7 | |a Epidemiologia |2 larpcal | |
| 650 | 7 | |a Sistemas dinâmicos |2 larpcal | |
| 650 | 4 | |a Écologie - Modèles mathématiques | |
| 650 | 4 | |a Épidémiologie - Modèles mathématiques | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Ökologie | |
| 650 | 4 | |a Ecology |x Mathematical models | |
| 650 | 4 | |a Epidemiology |x Mathematical models | |
| 650 | 0 | 7 | |a Epidemiologie |0 (DE-588)4015016-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematisches Modell |0 (DE-588)4114528-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Populationsdynamik |0 (DE-588)4046803-3 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Epidemiologie |0 (DE-588)4015016-1 |D s |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016256648 | ||
Datensatz im Suchindex
| _version_ | 1804137287246675968 |
|---|---|
| adam_text | Contents
I Introduction
1
1
Ecological patterns in time and space
3
1.1
Local structures
......................... 3
1.2
Spatial and
spatiotemporal
structures
............. 6
2
An overview of modeling approaches
11
II Models of temporal dynamics
19
3
Classical one population models
21
3.1
Isolated populations models
.................. 21
3.1.1
Scaling
.......................... 25
3.2
Migration models
........................ 27
3.2.1
Harvesting
........................ 30
3.3
Glance at discrete models
.................... 44
3.4
Peek into chaos
......................... 46
4
Interacting populations
49
4.1
Two-species prey predator population model
......... 50
4.2
Classical
Lotka-
Volterra model
................. 57
4.2.1
More on prey-predator models
............. 58
4.2.2
Scaling
.......................... 59
4.3
Other types of population communities
............ 60
4.3.1
Competing populations
................. 60
4.3.2
Symbiotic populations
.................. 62
4.3.3
Leslie-Gower model
................... 64
4.3.4
Classical Holling-Tanner model
............. 65
4.3.5
Other growth models
................... 66
4.3.6
Models with prey switching
............... 66
4.4
Global stability
......................... 68
4.4.1
General quadratic prey-predator system
........ 71
4.4.2
Mathematical tools for analyzing limit cycles
..... 72
4.4.3
Routh-Hurwitz conditions
................ 74
4.4.4
Criterion for
Hopf
bifurcation
.............. 75
4.4.5
Instructive example
................... 76
4.4.6
-Poincaré
map
....................... 77
4.5
Food web
............................. 80
4.6
More about chaos
........................ 87
4.7
Age-dependent populations
................... 91
4.7.1
Prey-predator, age-dependent populations
....... 95
4.7.2
More about age-dependent populations
........ 96
4.7.3
Simulations and brief discussion
............ 108
5
Case study: biological pest control in vineyards 111
5.1
First model
............................ 112
5.1.1
Modeling the human activity
.............. 114
5.2
More sophisticated model
.................... 116
5.2.1
Models comparison
.................... 122
5.3
Modeling the ballooning effect
................. 124
5.3.1
Spraying effects and human intervention
........ 134
5.3.2
Ecological discussion
................... 134
6
Epidemic models
137
6.1
Basic epidemic models
...................... 137
6.1.1
Simplest models
..................... 139
6.1.2
Standard incidence
.................... 141
6.2
Other classical epidemic models
................ 145
6.3
Age- and stage-dependent epidemic system
.......... 147
6.4
Case study: Aujeszky disease
................. 151
6.5
Analysis of a disease with two states
.............. 156
7
Ecoepidemic systems
165
7.1
Prey-diseased-predator interactions
.............. 165
7.1.1
Some biological considerations
............. 176
7.2
Predator-diseased-prey interactions
.............. 178
7.3
Diseased competing species models
.............. 184
7.3.1
Simulation discussion
.................. 189
7.4
Ecoepidemics models of symbiotic communities
........ 191
7.4.1
Disease effects on the symbiotic system
........ 194
7.4.2
Disease control by use of a symbiotic species
..... 195
III
Spatiotemporal
dynamics and pattern formation:
deterministic approach
197
8
Spatial aspect: diffusion as a paradigm
199
9
Instabilities and dissipative structures
205
9.1
Turing patterns
......................... 206
9.1.1
Turing patterns in a multispecies system
........ 218
9.2
Differential flow instability
................... 223
9.3
Ecological example:
semiarid
vegetation patterns
....... 231
9.3.1
Pattern formation due to nonlocal interactions
.... 236
9.4
Concluding remarks
....................... 245
10
Patterns in the wake of invasion
247
10.1
Invasion in a prey-predator system
.............. 248
10.2
Dynamical stabilization of an unstable equilibrium
...... 260
10.2.1,
A bifurcation approach
................. 261
10.2.2
Comparison of wave speeds
............... 266
10.3
Patterns in a competing species community
.......... 269
10.4
Concluding remarks
....................... 277
11
Biological turbulence
281
11.1
Self-organized patchiness and the wave of chaos
....... 283
11.1.1
Stability diagram and the hierarchy of regimes
.... 290
11.1.2
Patchiness in a two-dimensional case
.......... 294
11.2
Spatial structure and spatial correlations
........... 296
11.2.1
Intrinsic lengths and scaling
............... 300
11.3
Ecological implications
..................... 308
11.3.1
Plankton patchiness on a biological scale
........ 308
11.3.2
Self-organized patchiness, desynchronization, and the
paradox of enrichment
.................. 312
11.4
Concluding remarks
....................... 321
12
Patchy invasion
325
12.1
Allee
effect, biological control, and one-dimensional patterns of
species invasion
......................... 326
12.1.1
Patterns of species spread
................ 331
12.2
Invasion and control in the two-dimensional case
....... 338
12.2.1
Properties of the patchy invasion
............ 344
12.3
Biological control through infectious diseases
......... 350
12.3.1
Patchy spread in SIR model
............... 353
12.4
Concluding remarks
....................... 358
IV
Spatiotemporal
patterns and noise
363
13
Generic model of stochastic population dynamics
365
14
Noise-induced pattern transitions
369
14.1
Transitions in a patchy environment
.............. 369
14.1.1
No noise
.......................... 370
14.1.2
Noise-induced pattern transition
............ 370
14.2
Transitions in a uniform environment
............. 372
14.2.1·
Standing waves driven by noise
............. 373
15
Epidemie
spread
in a stochastic environment
375
15.1
Model
............................... 376
15.2
Strange periodic attractors in the lytic regime
........ 379
15.3
Local dynamics in the lysogenic regime
............ 382
15.4
Deterministic and stochastic spatial dynamics
........ 383
15.5
Local dynamics with deterministic switch from lysogeny to lysis
385
15.6
Spatiotemporal
dynamics with switches from lysogeny to lysis
390
15-.6.1 Deterministic switching from lysogeny to lysis
..... 391
15.6.2
Stochastic switching
................... 393
16
Noise-induced pattern formation
397
References
403
Index
443
|
| adam_txt |
Contents
I Introduction
1
1
Ecological patterns in time and space
3
1.1
Local structures
. 3
1.2
Spatial and
spatiotemporal
structures
. 6
2
An overview of modeling approaches
11
II Models of temporal dynamics
19
3
Classical one population models
21
3.1
Isolated populations models
. 21
3.1.1
Scaling
. 25
3.2
Migration models
. 27
3.2.1
Harvesting
. 30
3.3
Glance at discrete models
. 44
3.4
Peek into chaos
. 46
4
Interacting populations
49
4.1
Two-species prey predator population model
. 50
4.2
Classical
Lotka-
Volterra model
. 57
4.2.1
More on prey-predator models
. 58
4.2.2
Scaling
. 59
4.3
Other types of population communities
. 60
4.3.1
Competing populations
. 60
4.3.2
Symbiotic populations
. 62
4.3.3
Leslie-Gower model
. 64
4.3.4
Classical Holling-Tanner model
. 65
4.3.5
Other growth models
. 66
4.3.6
Models with prey switching
. 66
4.4
Global stability
. 68
4.4.1
General quadratic prey-predator system
. 71
4.4.2
Mathematical tools for analyzing limit cycles
. 72
4.4.3
Routh-Hurwitz conditions
. 74
4.4.4
Criterion for
Hopf
bifurcation
. 75
4.4.5
Instructive example
. 76
4.4.6
-Poincaré
map
. 77
4.5
Food web
. 80
4.6
More about chaos
. 87
4.7
Age-dependent populations
. 91
4.7.1
Prey-predator, age-dependent populations
. 95
4.7.2
More about age-dependent populations
. 96
4.7.3
Simulations and brief discussion
. 108
5
Case study: biological pest control in vineyards 111
5.1
First model
. 112
5.1.1
Modeling the human activity
. 114
5.2
More sophisticated model
. 116
5.2.1
Models comparison
. 122
5.3
Modeling the ballooning effect
. 124
5.3.1
Spraying effects and human intervention
. 134
5.3.2
Ecological discussion
. 134
6
Epidemic models
137
6.1
Basic epidemic models
. 137
6.1.1
Simplest models
. 139
6.1.2
Standard incidence
. 141
6.2
Other classical epidemic models
. 145
6.3
Age- and stage-dependent epidemic system
. 147
6.4
Case study: Aujeszky disease
. 151
6.5
Analysis of a disease with two states
. 156
7
Ecoepidemic systems
165
7.1
Prey-diseased-predator interactions
. 165
7.1.1
Some biological considerations
. 176
7.2
Predator-diseased-prey interactions
. 178
7.3
Diseased competing species models
. 184
7.3.1
Simulation discussion
. 189
7.4
Ecoepidemics models of symbiotic communities
. 191
7.4.1
Disease effects on the symbiotic system
. 194
7.4.2
Disease control by use of a symbiotic species
. 195
III
Spatiotemporal
dynamics and pattern formation:
deterministic approach
197
8
Spatial aspect: diffusion as a paradigm
199
9
Instabilities and dissipative structures
205
9.1
Turing patterns
. 206
9.1.1
Turing patterns in a multispecies system
. 218
9.2
Differential flow instability
. 223
9.3
Ecological example:
semiarid
vegetation patterns
. 231
9.3.1
Pattern formation due to nonlocal interactions
. 236
9.4
Concluding remarks
. 245
10
Patterns in the wake of invasion
247
10.1
Invasion in a prey-predator system
. 248
10.2
Dynamical stabilization of an unstable equilibrium
. 260
10.2.1,
A bifurcation approach
. 261
10.2.2
Comparison of wave speeds
. 266
10.3
Patterns in a competing species community
. 269
10.4
Concluding remarks
. 277
11
Biological turbulence
281
11.1
Self-organized patchiness and the wave of chaos
. 283
11.1.1
Stability diagram and the hierarchy of regimes
. 290
11.1.2
Patchiness in a two-dimensional case
. 294
11.2
Spatial structure and spatial correlations
. 296
11.2.1
Intrinsic lengths and scaling
. 300
11.3
Ecological implications
. 308
11.3.1
Plankton patchiness on a biological scale
. 308
11.3.2
Self-organized patchiness, desynchronization, and the
paradox of enrichment
. 312
11.4
Concluding remarks
. 321
12
Patchy invasion
325
12.1
Allee
effect, biological control, and one-dimensional patterns of
species invasion
. 326
12.1.1
Patterns of species spread
. 331
12.2
Invasion and control in the two-dimensional case
. 338
12.2.1
Properties of the patchy invasion
. 344
12.3
Biological control through infectious diseases
. 350
12.3.1
Patchy spread in SIR model
. 353
12.4
Concluding remarks
. 358
IV
Spatiotemporal
patterns and noise
363
13
Generic model of stochastic population dynamics
365
14
Noise-induced pattern transitions
369
14.1
Transitions in a patchy environment
. 369
14.1.1
No noise
. 370
14.1.2
Noise-induced pattern transition
. 370
14.2
Transitions in a uniform environment
. 372
14.2.1·
Standing waves driven by noise
. 373
15
Epidemie
spread
in a stochastic environment
375
15.1
Model
. 376
15.2
Strange periodic attractors in the lytic regime
. 379
15.3
Local dynamics in the lysogenic regime
. 382
15.4
Deterministic and stochastic spatial dynamics
. 383
15.5
Local dynamics with deterministic switch from lysogeny to lysis
385
15.6
Spatiotemporal
dynamics with switches from lysogeny to lysis
390
15-.6.1 Deterministic switching from lysogeny to lysis
. 391
15.6.2
Stochastic switching
. 393
16
Noise-induced pattern formation
397
References
403
Index
443 |
| any_adam_object | 1 |
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| author | Malchow, Horst |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
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| discipline | Biologie Mathematik |
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| id | DE-604.BV023053309 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:25:34Z |
| indexdate | 2024-07-09T21:09:54Z |
| institution | BVB |
| language | English |
| lccn | 2007040410 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016256648 |
| oclc_num | 174112652 |
| open_access_boolean | |
| owner | DE-384 DE-19 DE-BY-UBM |
| owner_facet | DE-384 DE-19 DE-BY-UBM |
| physical | 443 S. Ill., graph. Darst. 1 CD-ROM (12 cm) |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series | Chapman & Hall/CRC mathematical and computational biology |
| series2 | Chapman & Hall/CRC mathematical and computational biology |
| spelling | Malchow, Horst Verfasser aut Spatiotemporal patterns in ecology and epidemiology theory, models, and simulation Horst Malchow ... Boca Raton Chapman & Hall/CRC 2008 443 S. Ill., graph. Darst. 1 CD-ROM (12 cm) txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC mathematical and computational biology 17 Includes bibliographical references and index Biologia (aplicações) larpcal Biomatemática larpcal Dinâmica de populações larpcal Ecologia matemática larpcal Epidemiologia larpcal Sistemas dinâmicos larpcal Écologie - Modèles mathématiques Épidémiologie - Modèles mathématiques Mathematisches Modell Ökologie Ecology Mathematical models Epidemiology Mathematical models Epidemiologie (DE-588)4015016-1 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Populationsdynamik (DE-588)4046803-3 gnd rswk-swf Epidemiologie (DE-588)4015016-1 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Populationsdynamik (DE-588)4046803-3 s Chapman & Hall/CRC mathematical and computational biology 17 (DE-604)BV021728115 17 Digitalisierung UB Augsburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016256648&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Malchow, Horst Spatiotemporal patterns in ecology and epidemiology theory, models, and simulation Chapman & Hall/CRC mathematical and computational biology Biologia (aplicações) larpcal Biomatemática larpcal Dinâmica de populações larpcal Ecologia matemática larpcal Epidemiologia larpcal Sistemas dinâmicos larpcal Écologie - Modèles mathématiques Épidémiologie - Modèles mathématiques Mathematisches Modell Ökologie Ecology Mathematical models Epidemiology Mathematical models Epidemiologie (DE-588)4015016-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Populationsdynamik (DE-588)4046803-3 gnd |
| subject_GND | (DE-588)4015016-1 (DE-588)4114528-8 (DE-588)4046803-3 |
| title | Spatiotemporal patterns in ecology and epidemiology theory, models, and simulation |
| title_auth | Spatiotemporal patterns in ecology and epidemiology theory, models, and simulation |
| title_exact_search | Spatiotemporal patterns in ecology and epidemiology theory, models, and simulation |
| title_exact_search_txtP | Spatiotemporal patterns in ecology and epidemiology theory, models, and simulation |
| title_full | Spatiotemporal patterns in ecology and epidemiology theory, models, and simulation Horst Malchow ... |
| title_fullStr | Spatiotemporal patterns in ecology and epidemiology theory, models, and simulation Horst Malchow ... |
| title_full_unstemmed | Spatiotemporal patterns in ecology and epidemiology theory, models, and simulation Horst Malchow ... |
| title_short | Spatiotemporal patterns in ecology and epidemiology |
| title_sort | spatiotemporal patterns in ecology and epidemiology theory models and simulation |
| title_sub | theory, models, and simulation |
| topic | Biologia (aplicações) larpcal Biomatemática larpcal Dinâmica de populações larpcal Ecologia matemática larpcal Epidemiologia larpcal Sistemas dinâmicos larpcal Écologie - Modèles mathématiques Épidémiologie - Modèles mathématiques Mathematisches Modell Ökologie Ecology Mathematical models Epidemiology Mathematical models Epidemiologie (DE-588)4015016-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Populationsdynamik (DE-588)4046803-3 gnd |
| topic_facet | Biologia (aplicações) Biomatemática Dinâmica de populações Ecologia matemática Epidemiologia Sistemas dinâmicos Écologie - Modèles mathématiques Épidémiologie - Modèles mathématiques Mathematisches Modell Ökologie Ecology Mathematical models Epidemiology Mathematical models Epidemiologie Populationsdynamik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016256648&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV021728115 |
| work_keys_str_mv | AT malchowhorst spatiotemporalpatternsinecologyandepidemiologytheorymodelsandsimulation |