Mathematical biology:
Saved in:
| Format: | Book |
|---|---|
| Language: | English |
| Published: |
Providence, RI
American Math. Soc., Inst. for Advanced Study
2009
|
| Series: | IAS Park City mathematics series
14 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | X, 398 S. Ill., graph. Darst. |
| ISBN: | 9780821847657 |
Staff View
MARC
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| 245 | 1 | 0 | |a Mathematical biology |c Mark A. Lewis ... [et al.], editors |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface
ix
M. A. Lewis
and J. Keener
Introduction
1
James P. Keener
Introduction to Dynamics of Biological Systems
7
1.
Rates of reaction
9
2.
Thresholds and
bist
ability
14
3.
Excitability
17
4.
Summary
21
Bibliography
23
Mark A. Lewis, Thomas Hillen, and Frithjof
Lutscher
Spatial Dynamics in Ecology
25
1.
Introduction
27
2.
Deriving the model
28
2.1.
Conservation law derivation
28
2.2.
The Fokker-Planck equation
30
2.3.
Fundamental solution to the diffusion equation
32
3.
Population spread
34
4.
Critical domain size problem
40
4.1.
Classical problem
40
4.2.
Critical domain size problem in a stream
42
Bibliography
45
J. M. Cushing
Matrix Models and Population Dynamics
47
Introduction
49
Lecture
1.
Matrix models
51
Lecture
2.
Bifurcations
67
Lecture
3.
Experimental case studies
81
vi
CONTENTS
Lecture
4.
Periodically fluctuating environments
115
Lecture
5.
Competitive interactions
135
Bibliography
147
David J. Earn
Mathematical Epidemiology of Infectious Diseases
151
1.
Introduction
153
2.
Describing epidemics
154
2.1.
Plague
154
2.2.
Measles and other childhood diseases
155
2.3.
Influenza
157
2.4.
Statistical description of epidemic time series
157
2.5.
Exercises
163
3.
Modelling epidemics
163
3.1.
Statistical modelling
163
3.2.
Mechanistic modelling
166
3.3.
Demographic stochasticity
170
3.4.
Seasonal forcing
171
3.5.
Exercises
174
4.
Predicting epidemics
175
4.1.
Exercises
181
5.
Manipulating epidemics
182
6.
Conclusions and take-home messages
183
Bibliography
183
Leon Glass
Topological Approaches to Biological Dynamics
187
Lecture
1.
Linear stability and the
Poincaré
Hopf
theorem applied to
biology
191
Lecture
2.
Discontinuous phase resetting
195
Lecture
3.
Fixed points and the entrainment of biological oscillations
201
Lecture
4.
Fixed points in phase maps with applications to development
and spiral waves on spheres
205
Lecture
5.
Unique stable limit cycles in model genetic networks
209
Lecture
6.
Projects: Resetting and entraining biological oscillations
213
Bibliography
215
CONTENTS
vii
Helen Byrne
Mathematical Modelling of Solid Tumour Growth:
from Avascular to Vascular, via Angiogenesis
217
1.
Introduction
219
2.
Background biology
220
3.
ODE models
222
3.1.
Introduction
222
3.2.
Growth of homogeneous solid tumours
223
3.3.
Chemotherapy
224
3.4.
Radiotherapy
229
3.5.
Heterogeneous tumour growth
234
3.6.
Discussion
236
3.7.
Exercises
237
4.
Avascular tumours: radially-symmetric growth
238
4.1.
Introduction
238
4.2.
Model development
239
4.3.
Model analysis
242
4.4.
Discussion
244
4.5.
Exercises
245
5.
Symmetry breaking and invasion
246
5.1.
Introduction
246
5.2.
The model equations
247
5.3.
Radially-symmetric model solutions
248
5.4.
Linear stability analysis
249
5.5.
Discussion
251
5.6.
Exercises
252
Appendix
253
6.
Avascular tumours: multiphase models
254
6.1.
Introduction
254
6.2.
Model development
254
6.3.
Model simplification
257
6.4.
Discussion
259
7.
Angiogenesis and vascular tumour growth
261
7.1.
Introduction
261
7.2.
Angiogenesis: model development
261
7.3.
Angiogenesis: caricature model
262
7.4.
Multiscale modelling of vascular tumour growth
265
7.5.
Vascular tumour growth: numerical simulations and model
predictions
269
7.6.
Conclusions
270
7.7.
Exercises
276
8.
Summary and future directions
278
Bibliography
281
viii CONTENTS
Paul
С.
Bressloff
Lectures in Mathematical
Neuroscience
289
Lecture
1.
Single neuron models
293
1.1.
Conductance-based models
293
1.2.
Periodically forced neural oscillator
296
1.3.
Integrate-and-fire models
303
Lecture
2.
Synaptic and dendritic processing
315
2.1.
Excitatory and inhibitory synapses
315
2.2.
Kinetic model of a synapse
318
2.3.
Dendritic filtering of synaptic inputs
322
2.4.
Synaptic plasticity
325
Lecture
3.
Firing rates, spike statistics and the neural code
337
3.1.
The neural code
337
3.2.
Spike statistics and the
Poisson
process
341
3.3.
Stochastically driven IF neuron
344
3.4.
Homogeneous population of IF neurons
348
Lecture
4.
Network oscillations and synchrony
353
4.1.
Phase reduction for synaptically coupled neural oscillators
354
4.2.
Phase-locked solutions
357
4.3.
Oscillations in large homogeneous networks
364
Lecture
5.
Neural pattern formation
369
5.1.
Reduction to rate models
369
5.2.
Turing mechanism for cortical pattern formation
371
5.3.
Persistent localized states
377
5.4.
Traveling waves
383
Bibliography
391
Each summer the IAS/Park City Mathematics Institute Graduate Summer School gathers
some of the best researchers and educators in a particular field to present lectures on
a major area of mathematics. A unifying theme of the mathematical biology courses
presented here is that the study of biology involves dynamical systems. Introductory
chapters by Jim Keener and Mark Lewis describe the biological dynamics of reactions
and of spatial processes.
Each remaining chapter stands alone, as a snapshot of in-depth research within a sub-
area of mathematical biology. Jim Cushing writes about the role of nonlinear dynamical
systems in understanding complex dynamics of insect populations. Epidemiology, and
the interplay of data and differential equations, is the subject of David Earn s chapter
on dynamic diseases. Topological methods for understanding dynamical systems are
the focus of the chapter by Leon Glass on perturbed biological oscillators. Helen Byrne
introduces the reader to cancer modeling and shows how mathematics can describe
and predict complex movement patterns of tumors and cells. In the final chapter, Paul
Bressloff couples nonlinear dynamics to nonlocal oscillations, to provide insight to the
form and function of the brain.
The book provides a state-of-the-art picture of some current research in mathematical
biology. Our hope is that the excitement and richness of the topics covered here will
encourage readers to explore further in mathematical biology, pursuing these topics and
others on their own.
The level is appropriate for graduate students and research scientists. Each chapter is
based on a series of lectures given by a leading researcher and develops methods and
theory of mathematical biology from first principles. Exercises are included for those
who wish to delve further into the material.
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| dewey-tens | 570 - Biology |
| discipline | Biologie |
| format | Book |
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| indexdate | 2024-07-09T21:31:39Z |
| institution | BVB |
| isbn | 9780821847657 |
| language | English |
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| spelling | Mathematical biology Mark A. Lewis ... [et al.], editors Providence, RI American Math. Soc., Inst. for Advanced Study 2009 X, 398 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier IAS Park City mathematics series 14 Mathematisches Modell Biology Mathematical models Biomathematik (DE-588)4139408-2 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 2005 Princeton NJ gnd-content Biomathematik (DE-588)4139408-2 s DE-604 Lewis, Mark 1962- Sonstige (DE-588)138665591 oth IAS Park City mathematics series 14 (DE-604)BV010402400 14 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017144364&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=017144364&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
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| title | Mathematical biology |
| title_auth | Mathematical biology |
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| title_full | Mathematical biology Mark A. Lewis ... [et al.], editors |
| title_fullStr | Mathematical biology Mark A. Lewis ... [et al.], editors |
| title_full_unstemmed | Mathematical biology Mark A. Lewis ... [et al.], editors |
| title_short | Mathematical biology |
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| topic | Mathematisches Modell Biology Mathematical models Biomathematik (DE-588)4139408-2 gnd |
| topic_facet | Mathematisches Modell Biology Mathematical models Biomathematik Konferenzschrift 2005 Princeton NJ |
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