Mathematics in population biology:
"The formulation, analysis, and re-evaluation of mathematical models in population biology has become a valuable source of insight to mathematicians and biologists alike. This book presents an overview and selected sample of these results and ideas, organized by biological theme rather than mat...
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton, NJ
Princeton University Press
2003
|
| Series: | Princeton series in theoretical and computational biology
|
| Subjects: | |
| Online Access: | Publisher description Inhaltsverzeichnis |
| Summary: | "The formulation, analysis, and re-evaluation of mathematical models in population biology has become a valuable source of insight to mathematicians and biologists alike. This book presents an overview and selected sample of these results and ideas, organized by biological theme rather than mathematical concept, with an emphasis on helping the reader develop appropriate modeling skills through use of well-chosen and varied examples."--BOOK JACKET. |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XVIII, 543 S. graph. Darst. |
| ISBN: | 0691092907 0691092915 |
Staff View
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| adam_text | Titel: Mathematics in population biology
Autor: Thieme, Horst R.
Jahr: 2003
Contents
Preface xiü
Chapter 1. Some General Remarks on Mathematical Modeling 1
Bibliographic Remarks 3
PART1. BASIC POPULATION GROWTH MODELS 5
Chapter 2. Birth, Death, and Migration 7
2.1 The Fundamental Balance Equation of Population Dynamics 7
2.2 Birth Date Dependent Life Expectancies 9
2.3 The Probability of Lifetime Emigration 11
Chapter 3. Unconstrained Population Growth for Single Species 13
3.1 Closed Populations 13
3.1.1 The Average Intrinsic Growth Rate for Periodic Environments 14
3.1.2 The Average Intrinsic Growth Rate for Nonperiodic Environments 17
3.2 Open Populations 19
3.2.1 Nonzero Average Intrinsic Growth Rate 21
3.2.2 Zero Average Intrinsic Growth Rate 28
Chapter 4. Von Bertalanffy Growth of Body Size 33
Chapter 5. Classic Models of Density-Dependent Population Growth for
Single Species 37
5.1 The Bernoulli and the Verhulst Equations 37
5.2 The Beverton-Holt and Smith Differential Equation 39
5.2.1 Derivation from a Resource-Consumer Model 40
5.2.2 Derivation from Cannibalism of Juveniles by Adults 42
5.3 The Ricker Differential Equation 45
5.4 The Gompertz Equation 47
5.5 A First Comparison of the Various Equations 47
Chapter 6. Sigmoid Growth 51
6.1 General Conditions for Sigmoid Growth 52
6.2 Fitting Sigmoid Population Data 57
Viii CONTENTS
Chapter 7. The Allee Effect 65
7.1 First Model Derivation: Search for a Mate 65
7.2 Second Model Derivation: Impact of a Satiating Generalist Predator 67
7.3 Model Analysis 69
Chapter 8. Nonautonomous Population Growth: Asymptotic Equality of
Population Sizes 75
Chapter 9. Discrete-Time Single-Species Models 81
9.1 The Discrete Analog of the Verhulst (Logistic) and the
Bernoulli Equation: the Beverton-Holt Difference
Equation and Its Generalization 81
9.2 The Ricker Difference Equation 83
9.3 Some Analytic Results for Scalar Difference Equations 84
9.4 Some Remarks Concerning the Quadratic Difference Equation 99
Bibliographic Remarks 104
Chapter 10. Dynamics of an Aquatic Population Interacting with a
Polluted Environment 107
10.1 Modeling Toxicant and Population Dynamics 108
10.2 Open Loop Toxicant Input 114
10.3 Feedback Loop Toxicant Input 117
10.4 Extinction and Persistence Equilibria and a
Threshold Condition for Population Extinction 120
10.5 Stability of Equilibria and Global Behavior of Solutions 125
10.6 Multiple Extinction Equilibria, Bistability and Periodic Oscillations 135
10.7 Linear Dose Response 139
Bibliographic Remarks 149
Chapter 11. Population Growth Under Basic Stage Structure 151
11.1 A Most Basic Stage-Structured Model 151
11.2 Well-Posedness and Dissipativity 153
11.3 Equilibria and Reproduction Ratios 155
11.4 Basic Reproduction Ratios and Threshold Conditions for
Extinction versus Persistence 156
11.5 Weakly Density-Dependent Stage-Transition Rates and
Global Stability of Nontrivial Equilibria 157
11.6 The Number and Nature of Possible Multiple Nontrivial Equilibria 160
11.7 Strongly Density-Dependent Stage-Transition Rates and
Periodic Oscillations 162
11.8 An Example for Multiple Periodic Orbits and Both
Supercritical and Subcriticai Hopf Bifurcation 166
11.9 Multiple Interior Equilibria, Bistability, and Many Bifurcations for
Pure Intrastage Competition 168
Bibliographic Remarks 181
CONTENTS ¡X
PART 2. STAGE TRANSITIONS AND DEMOGRAPHICS 183
Chapter 12. The Transition Through a Stage 185
12.1 The Sojourn Function 185
12.2 Mean Sojourn Time, Expected Exit Age, and Expectation of Life 187
12.3 The Variance of the Sojourn Time, Moments and Central Moments 189
12.4 Remaining Sojourn Time and Its Expectation 190
12.5 Fixed Stage Durations 197
12.6 Per Capita Exit Rates (Mortality Rates) 199
12.7 Exponentially Distributed Stage Durations 201
12.8 Log-Normally Distributed Stage Durations 202
12.9 A Stochastic Interpretation of Stage Transition 206
Bibliographic Remarks 209
Chapter 13. Stage Dynamics with Given Input 211
13.1 Input and Stage-Age Density 211
13.2 The Partial Differential Equation Formulation 212
13.3 Stage Content and Average Stage Duration 217
13.4 Average Stage Age 219
13.5 Stage Exit Rates 221
13.5.1 The Fundamental Balance Equation of Stage Dynamics 222
13.5.2 Average Age at Stage Exit 224
13.6 Stage Outputs 226
13.7 Which Recruitment Curves Can Be Explained by
Cannibalism of Newborns by Adults? 230
Bibliographic Remarks 237
Chapter 14. Demographics in an Unlimiting Constant Environment 239
14.1 The Renewal Equation 240
14.2 Balanced Exponential Growth 241
14.3 The Renewal Theorem: Approach to Balanced Exponential Growth 244
Chapter 15. Some Demographic Lessons from Balanced Exponential Growth 255
15.1 Inequalities and Estimates for the Malthusian Parameter 255
15.2 Average Age and Average Age at Death in a Population at Balanced
Exponential Growth. Average Per Capita Death Rate 262
15.3 Ratio of Population Size and Birth Rate 266
15.4 Consequences of an Abrupt Shift in Maternity:
Momentum of Population Growth 267
Bibliographic Remarks 270
Chapter 16. Some Nonlinear Demographics 273
16.1 A Demographic Model with a Juvenile and an Adult Stage 274
16.2 A Differential Delay Equation 277
Bibliographic Remarks 279
X CONTENTS
PART 3. HOST-PARASITE POPULATION GROWTH:
EPIDEMIOLOGY OF INFECTIOUS DISEASES 281
Chapter 17. Background 283
17.1 Impact of Infectious Diseases in Past and Present Time 284
17.2 Epidemiological Terms and Principles 289
Bibliographic Remarks 291
Chapter 18. The Simplified Kermack-McKendrick Epidemic Model 293
18.1 A Model with Mass-Action Incidence 293
18.2 Phase-Plane Analysis of the Model Equations.
The Epidemic Threshold Theorem 295
18.3 The Final Size of the Epidemic. Alternative Formulation of
the Threshold Theorem 297
Chapter 19. Generalization of the Mass-Action Law of Infection 305
19.1 Population-Size Dependent Contact Rates 305
19.2 Model Modification 306
19.3 The Generalized Epidemic Threshold Theorem 307
Chapter 20. The Kermack-McKendrick Epidemic Model with
Variable Infectivity 311
20.1 A Stage-Age Structured Model 311
20.2 Reduction to a Scalar Integral Equation 313
Bibliographic Remarks 316
Chapter 21. SEIR (-? S) Type Endemic Models for Childhood Diseases 317
21.1 The Model and Its WeU-Posedness 318
21.2 Equilibrium States and the Basic Replacement Ratio 321
21.3 The Disease Dynamics in the Vicinities of
the Disease-Free and the Endemic Equilibrium:
Local Stability and the Interepidemic Period 325
21.4 Some Global Results: Extinction, Persistence of the Disease;
Conditions for Attraction to the Endemic Equilibrium 332
Bibliographic Remarks 339
Chapter 22. Age-Structured Models for Endemic Diseases and
Optimal Vaccination Strategies 341
22.1 A Model with Chronological Age-Structure 341
22.2 Disease-Free and Endemic Equilibrium: the Replacement Ratio 348
22.3 The Net Replacement Ratio, and Disease Extinction and Persistence 351
22.4 Cost of Vaccinations and Optimal Age Schedules 358
CONTENTS Xi
22.5 Estimating the Net Replacement Ratio: Average Duration of
Susceptibility and Average Age at Infection.
Optimal Vaccination Schedules Revisited 366
Bibliographic Remarks 381
Chapter 23. Endemic Models with Multiple Groups or Populations 383
23.1 The Model 384
23.2 Equilibrium Solutions 388
23.3 Local Asymptotic Stability of Strongly Endemic Equilibria 394
23.4 Extinction or Persistence of the Disease? 399
23.5 The Basic Replacement Matrix, Alias Next-Generation Matrix 404
23.6 The Basic Replacement Ratio as Spectral Radius of
the Basic Replacement Matrix 406
23.7 Some Special Cases of Mixing 411
Bibliographic Remarks 416
PART 4. TOOLBOX 419
Appendix A Ordinary Differential Equations 421
A.I Conservation of Positivity and Boundedness 421
A.2 Planar Ordinary Differential Equation Systems 424
A.3 The Method of Fluctuations 428
A.4 Behavior in the Vicinity of an Equilibrium 433
A.5 Elements of Persistence Theory 436
Bibliographic Remarks 441
A.6 Global Stability of a Compact Minimal Set 442
A.7 Hopf Bifurcation 444
A.8 Perron-Frobenius Theory of Positive Matrices and Associated Linear
Dynamical Systems 446
Bibliographic Remarks 451
Appendix B Integration, Integral Equations, and Some Convex Analysis 453
B.I The Stieltjes Integral of Regulated Functions - 453
B.2 Some Elements from Measure Theory 465
B.3 Some Elements from Convex Analysis 472
B.4 Lebesgue-Stieltjes Integration 475
B.5 Jensen s Inequality and Related Material 483
B.6 Volterra Integral Equations 486
B.7 Critical and Regular Values of a Function 490
Bibliographic Remarks 491
Appendix C Some MAPLE Worksheets with Comments for Part 1 493
C.I Fitting the Growth of the World Population (Figure 3.1) 493
C.2 Periodic Modulation of Exponential Growth in Closed Populations
(Figures 3.2 and 3.3) 496
XÜ CONTENTS
C.3 Fitting Sigmoid Population-Growth Curves (Figures 6.1 and 6.2) 498
C.4 Fitting Bernoulli s Equation to Population Data of Sweden (Figure 6.3) 507
C.5 Illustrating the Allee Effect (Figures 7.2-7.4) 510
C.6 Dynamics of an Aquatic Population Interacting with a
Polluted Environment (Figure 10.3E) 513
References 519
Index 537
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| id | DE-604.BV014893498 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T19:08:30Z |
| institution | BVB |
| isbn | 0691092907 0691092915 |
| language | English |
| lccn | 2002192472 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010070018 |
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| physical | XVIII, 543 S. graph. Darst. |
| publishDate | 2003 |
| publishDateSearch | 2003 |
| publishDateSort | 2003 |
| publisher | Princeton University Press |
| record_format | marc |
| series2 | Princeton series in theoretical and computational biology |
| spelling | Thieme, Horst R. 1948- Verfasser (DE-588)111523559 aut Mathematics in population biology Horst R. Thieme Princeton, NJ Princeton University Press 2003 XVIII, 543 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Princeton series in theoretical and computational biology Includes bibliographical references and index "The formulation, analysis, and re-evaluation of mathematical models in population biology has become a valuable source of insight to mathematicians and biologists alike. This book presents an overview and selected sample of these results and ideas, organized by biological theme rather than mathematical concept, with an emphasis on helping the reader develop appropriate modeling skills through use of well-chosen and varied examples."--BOOK JACKET. Biologie des populations - Modèles mathématiques Maladies infectieuses - Modèles mathématiques Populatiedynamica gtt Populaties (biologie) gtt Wiskundige modellen gtt Mathematisches Modell Biology methods Communicable diseases Mathematical models Epidemiologic Methods Models, Theoretical Population Dynamics Population biology Mathematical models Populationsbiologie (DE-588)4046800-8 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Demökologie (DE-588)4149059-9 gnd rswk-swf Populationsbiologie (DE-588)4046800-8 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Demökologie (DE-588)4149059-9 s Erscheint auch als Online-Ausgabe 978-0-691-18765-5 http://www.loc.gov/catdir/description/prin031/2002192472.html Publisher description HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010070018&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Thieme, Horst R. 1948- Mathematics in population biology Biologie des populations - Modèles mathématiques Maladies infectieuses - Modèles mathématiques Populatiedynamica gtt Populaties (biologie) gtt Wiskundige modellen gtt Mathematisches Modell Biology methods Communicable diseases Mathematical models Epidemiologic Methods Models, Theoretical Population Dynamics Population biology Mathematical models Populationsbiologie (DE-588)4046800-8 gnd Mathematisches Modell (DE-588)4114528-8 gnd Demökologie (DE-588)4149059-9 gnd |
| subject_GND | (DE-588)4046800-8 (DE-588)4114528-8 (DE-588)4149059-9 |
| title | Mathematics in population biology |
| title_auth | Mathematics in population biology |
| title_exact_search | Mathematics in population biology |
| title_full | Mathematics in population biology Horst R. Thieme |
| title_fullStr | Mathematics in population biology Horst R. Thieme |
| title_full_unstemmed | Mathematics in population biology Horst R. Thieme |
| title_short | Mathematics in population biology |
| title_sort | mathematics in population biology |
| topic | Biologie des populations - Modèles mathématiques Maladies infectieuses - Modèles mathématiques Populatiedynamica gtt Populaties (biologie) gtt Wiskundige modellen gtt Mathematisches Modell Biology methods Communicable diseases Mathematical models Epidemiologic Methods Models, Theoretical Population Dynamics Population biology Mathematical models Populationsbiologie (DE-588)4046800-8 gnd Mathematisches Modell (DE-588)4114528-8 gnd Demökologie (DE-588)4149059-9 gnd |
| topic_facet | Biologie des populations - Modèles mathématiques Maladies infectieuses - Modèles mathématiques Populatiedynamica Populaties (biologie) Wiskundige modellen Mathematisches Modell Biology methods Communicable diseases Mathematical models Epidemiologic Methods Models, Theoretical Population Dynamics Population biology Mathematical models Populationsbiologie Demökologie |
| url | http://www.loc.gov/catdir/description/prin031/2002192472.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010070018&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT thiemehorstr mathematicsinpopulationbiology |