| |
| Preface to the Third Edition | p. vii |
| Preface to the First Edition | p. xi |
| Continuous Population Models for Single Species | p. 1 |
| Continuous Growth Models | p. 1 |
| Insect Outbreak Model: Spruce Budworm | p. 7 |
| Delay Models | p. 13 |
| Linear Analysis of Delay Population Models: Periodic Solutions | p. 17 |
| Delay Models in Physiology: Periodic Dynamic Diseases | p. 21 |
| Harvesting a Single Natural Population | p. 30 |
| Population Model with Age Distribution | p. 36 |
| Exercises | p. 40 |
| Discrete Population Models for a Single Species | p. 44 |
| Introduction: Simple Models | p. 44 |
| Cobwebbing: A Graphical Procedure of Solution | p. 49 |
| Discrete Logistic-Type Model: Chaos | p. 53 |
| Stability, Periodic Solutions and Bifurcations | p. 59 |
| Discrete Delay Models | p. 62 |
| Fishery Management Model | p. 67 |
| Ecological Implications and Caveats | p. 69 |
| Tumour Cell Growth | p. 72 |
| Exercises | p. 75 |
| Models for Interacting Populations | p. 79 |
| Predator-Prey Models: Lotka-Volterra Systems | p. 79 |
| Complexity and Stability | p. 83 |
| Realistic Predator-Prey Models | p. 86 |
| Analysis of a Predator-Prey Model with Limit Cycle Periodic Behaviour: Parameter Domains of Stability | p. 88 |
| Competition Models: Competitive Exclusion Principle | p. 94 |
| Mutualism or Symbiosis | p. 99 |
| General Models and Cautionary Remarks | p. 101 |
| Threshold Phenomena | p. 105 |
| Discrete Growth Models for Interacting Populations | p. 109 |
| Predator-Prey Models: Detailed Analysis | p. 110 |
| Exercises | p. 115 |
| Temperature-Dependent Sex Determination (TSD) | p. 119 |
| Biological Introduction and Historical Asides on the Crocodilia | p. 119 |
| Nesting Assumptions and Simple Population Model | p. 124 |
| Age-Structured Population Model for Crocodilia | p. 130 |
| Density-Dependent Age-Structured Model Equations | p. 133 |
| Stability of the Female Population in Wet Marsh Region I | p. 135 |
| Sex Ratio and Survivorship | p. 137 |
| Temperature-Dependent Sex Determination (TSD) Versus Genetic Sex Determination (GSD) | p. 139 |
| Related Aspects on Sex Determination | p. 142 |
| Exercise | p. 144 |
| Modelling the Dynamics of Marital Interaction: Divorce Prediction and Marriage Repair | p. 146 |
| Psychological Background and Data: Gottman and Levenson Methodology | p. 147 |
| Marital Typology and Modelling Motivation | p. 150 |
| Modelling Strategy and the Model Equations | p. 153 |
| Steady States and Stability | p. 156 |
| Practical Results from the Model | p. 164 |
| Benefits, Implications and Marriage Repair Scenarios | p. 170 |
| Reaction Kinetics | p. 175 |
| Enzyme Kinetics: Basic Enzyme Reaction | p. 175 |
| Transient Time Estimates and Nondimensionalisation | p. 178 |
| Michaelis-Menten Quasi-Steady State Analysis | p. 181 |
| Suicide Substrate Kinetics | p. 188 |
| Cooperative Phenomena | p. 197 |
| Autocatalysis, Activation and Inhibition | p. 201 |
| Multiple Steady States, Mushrooms and Isolas | p. 208 |
| Exercises | p. 215 |
| Biological Oscillators and Switches | p. 218 |
| Motivation, Brief History and Background | p. 218 |
| Feedback Control Mechanisms | p. 221 |
| Oscillators and Switches with Two or More Species: General Qualitative Results | p. 226 |
| Simple Two-Species Oscillators: Parameter Domain Determination for Oscillations | p. 234 |
| Hodgkin-Huxley Theory of Nerve Membranes: FitzHugh-Nagumo Model | p. 239 |
| Modelling the Control of Testosterone Secretion and Chemical Castration | p. 244 |
| Exercises | p. 253 |
| BZ Oscillating Reactions | p. 257 |
| Belousov Reaction and the Field-Koros-Noyes (FKN) Model | p. 257 |
| Linear Stability Analysis of the FKN Model and Existence of Limit Cycle Solutions | p. 261 |
| Nonlocal Stability of the FKN Model | p. 265 |
| Relaxation Oscillators: Approximation for the Belousov-Zhabotinskii Reaction | p. 268 |
| Analysis of a Relaxation Model for Limit Cycle Oscillations in the Belousov-Zhabotinskii Reaction | p. 271 |
| Exercises | p. 277 |
| Perturbed and Coupled Oscillators and Black Holes | p. 278 |
| Phase Resetting in Oscillators | p. 278 |
| Phase Resetting Curves | p. 282 |
| Black Holes | p. 286 |
| Black Holes in Real Biological Oscillators | p. 288 |
| Coupled Oscillators: Motivation and Model System | p. 293 |
| Phase Locking of Oscillations: Synchronisation in Fireflies | p. 295 |
| Singular Perturbation Analysis: Preliminary Transformation | p. 299 |
| Singular Perturbation Analysis: Transformed System | p. 302 |
| Singular Perturbation Analysis: Two-Time Expansion | p. 305 |
| Analysis of the Phase Shift Equation and Application to Coupled Belousov-Zhabotinskii Reactions | p. 310 |
| Exercises | p. 313 |
| Dynamics of Infectious Diseases | p. 315 |
| Historical Aside on Epidemics | p. 315 |
| Simple Epidemic Models and Practical Applications | p. 319 |
| Modelling Venereal Diseases | p. 327 |
| Multi-Group Model for Gonorrhea and Its Control | p. 331 |
| AIDS: Modelling the Transmission Dynamics of the Human Immunodeficiency Virus (HIV) | p. 333 |
| HIV: Modelling Combination Drug Therapy | p. 341 |
| Delay Model for HIV Infection with Drug Therapy | p. 350 |
| Modelling the Population Dynamics of Acquired Immunity to Parasite Infection | p. 351 |
| Age-Dependent Epidemic Model and Threshold Criterion | p. 361 |
| Simple Drug Use Epidemic Model and Threshold Analysis | p. 365 |
| Bovine Tuberculosis Infection in Badgers and Cattle | p. 369 |
| Modelling Control Strategies for Bovine Tuberculosis in Badgers and Cattle | p. 379 |
| Exercises | p. 393 |
| Reaction Diffusion, Chemotaxis, and Nonlocal Mechanisms | p. 395 |
| Simple Random Walk and Derivation of the Diffusion Equation | p. 395 |
| Reaction Diffusion Equations | p. 399 |
| Models for Animal Dispersal | p. 402 |
| Chemotaxis | p. 405 |
| Nonlocal Effects and Long Range Diffusion | p. 408 |
| Cell Potential and Energy Approach to Diffusion and Long Range Effects | p. 413 |
| Exercises | p. 416 |
| Oscillator-Generated Wave Phenomena | p. 418 |
| Belousov-Zhabotinskii Reaction Kinematic Waves | p. 418 |
| Central Pattern Generator: Experimental Facts in the Swimming of Fish | p. 422 |
| Mathematical Model for the Central Pattern Generator | p. 424 |
| Analysis of the Phase Coupled Model System | p. 431 |
| Exercises | p. 436 |
| Biological Waves: Single-Species Models | p. 437 |
| Background and the Travelling Waveform | p. 437 |
| Fisher-Kolmogoroff Equation and Propagating Wave Solutions | p. 439 |
| Asymptotic Solution and Stability of Wavefront Solutions of the Fisher-Kolmogoroff Equation | p. 444 |
| Density-Dependent Diffusion-Reaction Diffusion Models and Some Exact Solutions | p. 449 |
| Waves in Models with Multi-Steady State Kinetics: Spread and Control of an Insect Population | p. 460 |
| Calcium Waves on Amphibian Eggs: Activation Waves on Medaka Eggs | p. 467 |
| Invasion Wavespeeds with Dispersive Variability | p. 471 |
| Species Invasion and Range Expansion | p. 478 |
| Exercises | p. 482 |
| Use and Abuse of Fractals | p. 484 |
| Fractals: Basic Concepts and Biological Relevance | p. 484 |
| Examples of Fractals and Their Generation | p. 487 |
| Fractal Dimension: Concepts and Methods of Calculation | p. 490 |
| Fractals or Space-Filling? | p. 496 |
| Appendices | p. 501 |
| Phase Plane Analysis | p. 501 |
| Routh-Hurwitz Conditions, Jury Conditions, Descartes' Rule of Signs, and Exact Solutions of a Cubic | p. 507 |
| Polynomials and Conditions | p. 507 |
| Descartes' Rule of Signs | p. 509 |
| Roots of a General Cubic Polynomial | p. 510 |
| Bibliography | p. 513 |
| Index | p. 537 |
| J.D. Murray: Mathematical Biology, II: Spatial Models and Biomedical Applications | |
| Preface to the Third Edition | |
| Preface to the First Edition | |
| Multi-Species Waves and Practical Applications | |
| Intuitive Expectations | |
| Waves of Pursuit and Evasion in Predator-Prey Systems | |
| Competition Model for the Spatial Spread of the Grey Squirrel in Britain | |
| Spread of Genetically Engineered Organisms | |
| Travelling Fronts in the Belousov-Zhabotinskii Reaction | |
| Waves in Excitable Media | |
| Travelling Wave Trains in Reaction Diffusion Systems with Oscillatory Kinetics | |
| Spiral Waves | |
| Spiral Wave Solutions of [lambda]-[omega] Reaction Diffusion Systems | |
| Spatial Pattern Formation with Reaction Diffusion Systems | |
| Role of Pattern in Biology | |
| Reaction Diffusion (Turing) Mechanisms | |
| General Conditions for Diffusion-Driven Instability: Linear Stability Analysis and Evolution of Spatial Pattern | |
| Detailed Analysis of Pattern Initiation in a Reaction Diffusion Mechanism | |
| Dispersion Relation, Turing Space, Scale and Geometry Effects in Pattern Formation Models | |
| Mode Selection and the Dispersion Relation | |
| Pattern Generation with Single-Species Models: Spatial Heterogeneity with the Spruce Budworm Model | |
| Spatial Patterns in Scalar Population Interaction Diffusion Equations with Convection: Ecological Control Strategies | |
| Nonexistence of Spatial Patterns in Reaction Diffusion Systems: General and Particular Results | |
| Animal Coat Patterns and Other Practical Applications of Reaction Diffusion Mechanisms | |
| Mammalian Coat Patterns--'How the Leopard Got Its Spots' | |
| Teratologies: Examples of Animal Coat Pattern Abnormalities | |
| A Pattern Formation Mechanism for Butterfly Wing Patterns | |
| Modelling Hair Patterns in a Whorl in Acetabularia | |
| Pattern Formation on Growing Domains: Alligators and Snakes | |
| Stripe Pattern Formation in the Alligator: Experiments | |
| Modelling Concepts: Determining the Time of Stripe Formation | |
| Stripes and Shadow Stripes on the Alligator | |
| Spatial Patterning of Teeth Primordia in the Alligator: Background and Relevance | |
| Biology of Tooth Initiation | |
| Modelling Tooth Primordium Initiation: Background | |
| Model Mechanism for Alligator Teeth Patterning | |
| Results and Comparison with Experimental Data | |
| Prediction Experiments | |
| Concluding Remarks on Alligator Tooth Spatial Patterning | |
| Pigmentation Pattern Formation on Snakes | |
| Cell-Chemotaxis Model Mechanism | |
| Simple and Complex Snake Pattern Elements | |
| Propagating Pattern Generation with the Cell-Chemotaxis System | |
| Bacterial Patterns and Chemotaxis | |
| Background and Experimental Results | |
| Model Mechanism for E. coli in the Semi-Solid Experiments | |
| Liquid Phase Model: Intuitive Analysis of Pattern Formation | |
| Interpretation of the Analytical Results and Numerical Solutions | |
| Semi-Solid Phase Model Mechanism for S. typhimurium | |
| Linear Analysis of the Basic Semi-Solid Model | |
| Brief Outline and Results of the Nonlinear Analysis | |
| Simulation Results, Parameter Spaces, Basic Patterns | |
| Numerical Results with Initial Conditions from the Experiments | |
| Swarm Ring Patterns with the Semi-Solid Phase Model Mechanism | |
| Branching Patterns in Bacillus subtilis | |
| Mechanical Theory for Generating Pattern and Form in Development | |
| Introduction, Motivation and Background Biology | |
| Mechanical Model for Mesenchymal Morphogenesis | |
| Linear Analysis, Dispersion Relation and Pattern | |
| Simple Mechanical Models Which Generate Spatial Patterns with Complex Dispersion Relations | |
| Periodic Patterns of Feather Germs | |
| Cartilage Condensation in Limb Morphogenesis and Morphogenetic Rules | |
| Embryonic Fingerprint Formation | |
| Mechanochemical Model for the Epidermis | |
| Formation of Microvilli | |
| Complex Pattern Formation and Tissue Interaction Models | |
| Evolution, Morphogenetic Laws, Developmental Constraints and Teratologies | |
| Evolution and Morphogenesis | |
| Evolution and Morphogenetic Rules in Cartilage Formation in the Vertebrate Limb | |
| Teratologies (Monsters) | |
| Developmental Constraints, Morphogenetic Rules and the Consequences for Evolution | |
| A Mechanical Theory of Vascular Network Formation | |
| Biological Background and Motivation | |
| Cell-Extracellular Matrix Interactions for Vasculogenesis | |
| Parameter Values | |
| Analysis of the Model Equations | |
| Network Patterns: Numerical Simulations and Conclusions | |
| Epidermal Wound Healing | |
| Brief History of Wound Healing | |
| Biological Background: Epidermal Wounds | |
| Model for Epidermal Wound Healing | |
| Nondimensional Form, Linear Stability and Parameter Values | |
| Numerical Solution for the Epidermal Wound Repair Model | |
| Travelling Wave Solutions for the Epidermal Model | |
| Clinical Implications of the Epidermal Wound Model | |
| Mechanisms of Epidermal Repair in Embryos | |
| Actin Alignment in Embryonic Wounds: A Mechanical Model | |
| Mechanical Model with Stress Alignment of the Actin Filaments in Two Dimensions | |
| Dermal Wound Healing | |
| Background and Motivation--General and Biological | |
| Logic of Wound Healing and Initial Models | |
| Brief Review of Subsequent Developments | |
| Model for Fibroblast-Driven Wound Healing: Residual Strain and Tissue Remodelling | |
| Solutions of the Model Equation Solutions and Comparison with Experiment | |
| Wound Healing Model of Cook (1995) | |
| Matrix Secretion and Degradation | |
| Cell Movement in an Oriented Environment | |
| Model System for Dermal Wound Healing with Tissue Structure | |
| One-Dimensional Model for the Structure of Pathological Scars | |
| Open Problems in Wound Healing | |
| Concluding Remarks on Wound Healing | |
| Growth and Control of Brain Tumours | |
| Medical Background | |
| Basic Mathematical Model of Glioma Growth and Invasion | |
| Tumour Spread In Vitro: Parameter Estimation | |
| Tumour Invasion in the Rat Brain | |
| Tumour Invasion in the Human Brain | |
| Modelling Treatment Scenarios: General Comments | |
| Modelling Tumour Resection (Removal) in Homogeneous Tissue | |
| Analytical Solution for Tumour Recurrence After Resection | |
| Modelling Surgical Resection with Brain Tissue Heterogeneity | |
| Modelling the Effect of Chemotherapy on Tumour Growth | |
| Modeling Tumour Polyclonality and Cell Mutation | |
| Neural Models of Pattern Formation | |
| Spatial Patterning in Neural Firing with a Simple Activation-Inhibition Model | |
| A Mechanism for Stripe Formation in the Visual Cortex | |
| A Model for the Brain Mechanism Underlying Visual Hallucination Patterns | |
| Neural Activity Model for Shell Patterns | |
| Shamanism and Rock Art | |
| Geographic Spread and Control of Epidemics | |
| Simple Model for the Spatial Spread of an Epidemic | |
| Spread of the Black Death in Europe 1347-1350 | |
| Brief History of Rabies: Facts and Myths | |
| The Spatial Spread of Rabies Among Foxes I: Background and Simple Model | |
| Spatial Spread of Rabies Among Foxes II: Three-Species (SIR) Model | |
| Control Strategy Based on Wave Propagation into a Non-epidemic Region: Estimate of Width of a Rabies Barrier | |
| Analytic Approximation for the Width of the Rabies Control Break | |
| Two-Dimensional Epizootic Fronts and Effects of Variable Fox Densitics: Quantitative Predictions for a Rabies Outbreak in England | |
| Effect of Fox Immunity on Spatial Spread of Rabies | |
| Wolf Territoriality, Wolf-Deer Interaction and Survival | |
| Introduction and Wolf Ecology | |
| Models for Wolf Pack Territory Formation: Single Pack--Home Range Model | |
| Multi-Wolf Pack Territorial Model | |
| Wolf-Deer Predator-Prey Model | |
| Concluding Remarks on Wolf Territoriality and Deer Survival | |
| Coyote Home Range Patterns | |
| Chippewa and Sioux Intertribal Conflict c1750-1850 | |
| Appendix | |
| General Results for the Laplacian Operator in Bounded Domains | |
| Bibliography | |
| Index | |
| Table of Contents provided by Rittenhouse. All Rights Reserved. |
