生物数学

contents, volume i

preface to the third edition

preface to the first edition

1. continuous population models for single species

1.1 continuous growth models

1.2 insect outbreak model： spruce budworm

1.3 delay models

1.4 linear analysis of delay population models： periodic solutions

1.5 delay models in physiology： periodic dynamic diseases

1.6 harvesting a single natural population

1.7 population model with age distribution

exercises

2. discrete population models for a single species

2.1 introduction： simple models

2.2 cobwebbing： a graphical procedure of solution

2.3 discrete logistic-type model： chaos

2.4 stability, periodic solutions and bifurcations

2.5 discrete delay models

2.6 fishery management model

.2.7 ecological implications and caveats

2.8 tumour cell growth

exercises

3. models for interacting populations

3.1 predator-prey models： lotka-volterra systems

3.2 complexity and stability

3.3 realistic predator-prey models

3.4 analysis of a predator-prey model with limit cycle periodic behaviour： parameter domains of stability

3.5 competition models： competitive exclusion principle

3.6 mutualism or symbiosis

3.7 general models and cautionary remarks

3.8 threshold phenomena

3.9 discrete growth models for interacting populations

3.10 predator-prey models： detailed analysis

exercises

4. temperature-dependent sex determination （tsd）

4.1 biological introduction and historical asides on the crocodilia.

4.2 nesting assumptions and simple population model

4.3 age-structured population model for crocodilia

4.4 density-dependent age-structured model equations

4.5 stability of the female population in wet marsh region l

4.6 sex ratio and survivorship

4.7 temperature-dependent sex determination （tsd） versus genetic sex determination （gsd）

4.8 related aspects on sex determination

exercise

5. modelling the dynamics of marital interaction： divorce prediction and marriage repair

5.1 psychological background and data： gottman and levenson methodology

5.2 marital typology and modelling motivation

5.3 modelling strategy and the model equations

5.4 steady states and stability

5.5 practical results from the model

5.6 benefits, implications and marriage repair scenarios

6. reaction kinetics

6.1 enzyme kinetics： basic enzyme reaction

6.2 transient time estimates and nondimensionalisation

6.3 michaelis-menten quasi-steady state analysis

6.4 suicide substrate kinetics

6.5 cooperative phenomena

6.6 autocatalysis, activation and inhibition

6.7 multiple steady states, mushrooms and isolas

exercises

7. biological oscillators and switches

7.1 motivation, brief history and background

7.2 feedback control mechanisms

7.3 oscillators and switches with two or more species： general qualitative results

7.4 simple two-species oscillators： parameter domain determination for oscillations

7.5 hodgkin-huxley theory of nerve membranes：fitzhugh-nagumo model

7.6 modelling the control of testosterone secretion and chemical castration

exercises

8. bz oscillating reactions

8.1 belousov reaction and the field-koros-noyes （fkn） model

8.2 linear stability analysis of the fkn model and existence of limit cycle solutions

8.3 nonlocal stability of the fkn model

8.4 relaxation oscillators： approximation for the belousov-zhabotinskii reaction

8.5 analysis of a relaxation model for limit cycle oscillations in the belousov-zhabotinskii reaction

exercises

9. perturbed and coupled oscillators and black holes

9.1 phase resetting in oscillators

9.2 phase resetting curves

9.3 black holes

9.4 black holes in real biological oscillators

9.5 coupled oscillators： motivation and model system

9.6 phase locking of oscillations： synchronisation in fireflies

9.7 singular perturbation analysis： preliminary transformation

9.8 singular perturbation analysis： transformed system

9.9 singular perturbation analysis： two-time expansion

9.10 analysis of the phase shift equation and application to coupled belousov-zhabotinskii reactions

exercises

10. dynamics of infectious diseases

10.1 historical aside on epidemics

10.2 simple epidemic models and practical applications

10.3 modelling venereal diseases

10.4 multi-group model for gonorrhea and its control

10.5 aids： modelling the transmission dynamics of the human immunodeficiency virus （hiv）

10.6 hiv： modelling combination drug therapy

10.7 delay model for hiv infection with drug therapy

10.8 modelling the population dynamics of acquired immunity to parasite infection

10.9 age-dependent epidemic model and threshold criterion

10.10 simple drug use epidemic model and threshold analysis

10.11 bovine tuberculosis infection in badgers and caule

10.12 modelling control strategies for bovine tuberculosis in badgers and cattle

exercises

11. reaction diffusion, chemotaxis, and noniocal mechanisms

11.1 simple random walk and derivation of the diffusion equation

11.2 reaction diffusion equations

11.3 models for animal dispersal

11.4 chemotaxis

11.5 nonlocal effects and long range diffusion

11.6 cell potential and energy approach to diffusion and long range effects

exercises

12. oscillator-generated wave phenomena

12. i belousov-zhabotinskii reaction kinematic waves

12.2 central pattern generator： experimental facts in the swimming of fish

12.3 mathematical model for the central pattern generator

12.4 analysis of the phase coupled model system

exercises

13. biological waves： single-species models

13. l background and the travelling waveform

13.2 fisher-kolmogoroff equation and propagating wave solutions

13.3 asymptotic solution and stability of wavefront solutions of the fisher-kolmogoroff equation

13.4 density-dependent diffusion-reaction diffusion models and some exact solutions

13.5 waves in models with multi-steady state kinetics： spread and control of an insect population

13.6 calcium waves on amphibian eggs： activation waves on medaka eggs

13.7 invasion wavespeeds with dispersive variability

13.8 species invasion and range expansion

exercises

14. use and abuse of fractals

14.1 fractals： basic concepts and biological relevance

14.2 examples of fractals and their generation

14.3 fractal dimension： concepts and methods of calculation

14.4 fractals or space-filling?

appendices

a. phase plane analysis

b. routh-hurwitz conditions, jury conditions, descartes'

rule of signs, and exact solutions of a cubic

b.1 polynomials and conditions

b.2 descartes' rule of signs

b.3 roots of a general cubic polynomial

bibliography

index

contents, volume ii

j.d. murray： mathematical biology, ii： spatial models and biomedical applications

preface to the third edition

preface to the first edition

1. multi-species waves and practical applications

1.1 intuitive expectations

1.2 waves of pursuit and evasion in predator-prey systems

1.3 competition model for the spatial spread of the grey squirrel in britain

1.4 spread of genetically engineered organisms

1.5 travelling fronts in the belousov-zhabotinskii reaction

1.6 waves in excitable media

1.7 travelling wave trains in reaction diffusion systems with oscillatory kinetics

1.8 spiral waves

1.9 spiral wave solutions of x-co reaction diffusion systems

2. spatial pattern formation with reaction diffusion systems

2.1 role of pattern in biology

2.2 reaction diffusion （turing） mechanisms

2.3 general conditions for diffusion-driven instability：linear stability analysis and evolution of spatial pattern

2.4 detailed analysis of pattern initiation in a reaction diffusion mechanism

2.5 dispersion relation, turing space, scale and geometry effects in pattern formation models

2.6 mode selection and the dispersion relation

2.7 pattern generation with single-species models： spatial heterogeneity with the spruce budworm model

2.8 spatial patterns in scalar population interaction diffusion equations with convection： ecological control strategies

2.9 nonexistence of spatial patterns in reaction diffusion systems： general and particular results

3. animal coat patterns and other practical applications of reactiondiffusion mechanisms

3.1 mammalian coat patterns--'how the leopard got its spots'

3.2 teratologies： examples of animal coat pattern abnormalities

3.3 a pattern formation mechanism for butterfly wing patterns

3.4 modelling hair patterns in a whorl in acetabularia

4. pattern formation on growing domains： alligators and snakes

4. i stripe pattern formation in the alligator： experiments

4.2 modelling concepts： determining the time of stripe formation

4.3 stripes and shadow stripes on the alligator

4.4 spatial patterning of teeth primordia in the alligator：background and relevance

4.5 biology of tooth initiation

4.6 modelling tooth primordium initiation： background

4.7 model mechanism for alligator teeth patterning

4.8 results and comparison with experimental data

4.9 prediction experiments

4.10 concluding remarks on alligator tooth spatial patterning

4.11 pigmentation pattern formation on snakes

4.12 cell-chemotaxis model mechanism

4.13 simple and complex snake pattern elements

4.14 propagating pattern generation with the celi-chemotaxis system

5. bacterial patterns and chemotaxis

5.1 background and experimental results

5.2 model mechanism for e. coli in the semi-solid experiments

5.3 liquid phase model： intuitive analysis of pattern formation

5.4 interpretation of the analytical results and numerical solutions

5.5 semi-solid phase model mechanism for s. typhimurium

5.6 linear analysis of the basic semi-solid model

5.7 brief outline and results of the nonlinear analysis

5.8 simulation results, parameter spaces, basic patterns

5.9 numerical results with initial conditions from the experiments

5.10 swarm ring patterns with the semi-solid phase model mechanism

5.11 branching patterns in bacillus subtilis

6. mechanical theory for generating pattern and form in development

6.1 introduction, motivation and background biology

6.2 mechanical model for mesenchymal morphogenesis

6.3 linear analysis, dispersion relation and pattern formation potential

6.4 simple mechanical models which generate spatial patterns with complex dispersion relations

6.5 periodic patterns of feather germs

6.6 cartilage condensation in limb morphogenesis and morphogenetic rules

6.7 embryonic fingerprint formation

6.8 mechanochemical model for the epidermis

6.9 formation of microvilli

6.10 complex pattern formation and tissue interaction models

7. evolution, morphogenetic laws, developmental constraints and teratologies

7.1 evolution and morphogenesis

7.2 evolution and morphogenetic rules in cartilage formation in the vertebrate limb

7.3 teratologies （monsters）

7.4 developmental constraints, morphogenetic rules and the consequences for evolution

8.a mechanical theory of vascular network formation

8.1 biological background and motivation

8.2 cell-extracellular matrix interactions for vasculogenesis

8.3 parameter values

8.4 analysis of the model equations

8.5 network patterns： numerical simulations and conclusions

9. epidermal wound healing

9.1 brief history of wound healing

9.2 biological background： epidermal wounds

9.3 model for epidermal wound healing

9.4 nondimensional form, linear stability and parameter values

9.5 numerical solution for the epidermal wound repair model

9.6 travelling wave solutions for the epidermal model

9.7 clinical implications of the epidermal wound model

9.8 mechanisms of epidermal repair in embryos

9.9 actin alignment in embryonic wounds： a mechanical model

9.10 mechanical model with stress alignment of the actin filaments in two dimensions

10. dermal wound healing

10.1 background and motivation---general and biological

10.2 logic of wound healing and initial models

10.3 brief review of subsequent developments

10.4 model for fibroblast-driven wound healing： residual strain and tissue remodelling

10.5 solutions of the model equation solutions and comparison with experiment

10.6 wound healing model of cook （1995）

10.7 matrix secretion and degradation

10.8 cell movement in an oriented environment

10.9 model system for dermal wound healing with tissue structure

10.10 one-dimensional model for the structure of pathological scars

10.11 open problems in wound healing

10.12 concluding remarks on wound healing

11. growth and control of brain tumours

11.1 medical background

11.2 basic mathematical model of glioma growth and invasion

11.3 tumour spread in vitro： parameter estimation

11.4 tumour invasion in the rat brain

11.5 tumour invasion in the human brain

11.6 modelling treatment scenarios： general comments

11.7 modelling tumour resection （removal） in homogeneous tissue

11.8 analytical solution for tumour recurrence after resection

11.9 modelling surgical resection with brain tissue heterogeneity

11.10 modelling the effect of chemotherapy on tumour growth

11.11 modeling tumour polyclonality and cell mutation

12. neural models of pattern formation

12.1 spatial patterning in neural firing with a simple activation-inhibition model

12.2 a mcchanism for stripe formation in the visual cortex

12.3 a model for the brain mechanism underlying visual hallucination patterns

12.4 neural activity model for shell patterns

12.5 shamanism and rock art

13. geographic spread and control of epidemics

13.1 simple model for the spatial spread of an epidemic

13.2 spread of the black death in europe 1347-1350

13.3 brief history of rabies： facts and myths

13.4 the spatial spread of rabies among foxes i： background and simple model

13.5 spatial spread of rabies among foxes ii：three-species （sir） model

13.6 control strategy based on wave propagation into a non-epidemic region： estimate of width of a rabies barrier

13.7 analytic approximation for the width of the rabies control break

13.8 two-dimensional epizootic fronts and effects ot variable fox densitics： quantitative predictions for a rabies outbreak in england

13.9 effect of fox immunity on spatial spread of rabies

14. wolf territoriality, wolf-deer interaction and survival

14.1 introduction and wolf ecology

14.2 models for wolf pack territory formation： single pack--home range model

14.3 multi-wolf pack territorial model

14.4 wolf-deer predator-prey model

14.5 concluding remarks on-wolf territoriality and deer survival

14.6 coyote home range patterns

14.7 chippewa and sioux intertribal conflict c1750-1850

appendix

a. general results for the laplacian operator in bounded domains

bibliography

index

《生物数学·第1卷（第3版）》是近代生物数学方面的名著。这是第一卷，第三版，在原来版本的基础上做了全面修订。近年来这个科目的茁壮成长和新知识点的不断涌现，新的版本将原来的一卷集分成上下两卷，扩大了知识容量，第二卷绝大多数是新增知识点。书中对生物学中的反应扩散方程和形态发生学的数学理论及最新研究成果作了全面介绍，是学习与研究生物数学的一部不可多得的参考书。