Mathematical Biology An Introduction

ISBN-10: 0387952233

ISBN-13: 9780387952239

Edition: 3rd 2002 (Revised)

Authors: James D. Murray

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It has been over a decade since the release of the now classic original edition of Murray's Mathematical Biology. Since then mathematical biology has grown at an astonishing rate and is well established as a distinct discipline. Mathematical modeling is now being applied in every major discipline in the biomedical sciences. Though the field has become increasingly large and specialized, this book remains important as a text that introduces some of the exciting problems that arise in biology and gives some indication of the wide spectrum of questions that modeling can address. Due to the tremendous development in the field this book is being published in two volumes. This first volume is an introduction to the field, the mathematics mainly involves ordinary differential equations that are suitable for undergraduate and graduate courses at different levels. For this new edition Murray is covering certain items in depth, giving new applications such as modeling marital interactions and temperature dependence sex determination. SIAM, 2004: "Murray's Mathematical Biology is a classic that belongs on the shelf of any serious student or researcher in the field. Together the two volumes contain well over 1000 references, a rich source of material, together with an excellent index to help readers quickly find key words. ... I recommend the new and expanded third edition to any serious young student interested in mathematical biology who already has a solid basis in applied mathematics."
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Book details

List price: $99.00
Edition: 3rd
Copyright year: 2002
Publisher: Springer
Publication date: 2/2/2011
Binding: Hardcover
Pages: 553
Size: 6.00" wide x 9.75" long x 1.25" tall
Weight: 2.090
Language: English

James D. Murray is Professor Emeritus of Applied Mathematics at the University of Washington.

Preface to the Third Edition
Preface to the First Edition
Continuous Population Models for Single Species
Continuous Growth Models
Insect Outbreak Model: Spruce Budworm
Delay Models
Linear Analysis of Delay Population Models: Periodic Solutions
Delay Models in Physiology: Periodic Dynamic Diseases
Harvesting a Single Natural Population
Population Model with Age Distribution
Discrete Population Models for a Single Species
Introduction: Simple Models
Cobwebbing: A Graphical Procedure of Solution
Discrete Logistic-Type Model: Chaos
Stability, Periodic Solutions and Bifurcations
Discrete Delay Models
Fishery Management Model
Ecological Implications and Caveats
Tumour Cell Growth
Models for Interacting Populations
Predator-Prey Models: Lotka-Volterra Systems
Complexity and Stability
Realistic Predator-Prey Models
Analysis of a Predator-Prey Model with Limit Cycle Periodic Behaviour: Parameter Domains of Stability
Competition Models: Competitive Exclusion Principle
Mutualism or Symbiosis
General Models and Cautionary Remarks
Threshold Phenomena
Discrete Growth Models for Interacting Populations
Predator-Prey Models: Detailed Analysis
Temperature-Dependent Sex Determination (TSD)
Biological Introduction and Historical Asides on the Crocodilia
Nesting Assumptions and Simple Population Model
Age-Structured Population Model for Crocodilia
Density-Dependent Age-Structured Model Equations
Stability of the Female Population in Wet Marsh Region I
Sex Ratio and Survivorship
Temperature-Dependent Sex Determination (TSD) Versus Genetic Sex Determination (GSD)
Related Aspects on Sex Determination
Modelling the Dynamics of Marital Interaction: Divorce Prediction and Marriage Repair
Psychological Background and Data: Gottman and Levenson Methodology
Marital Typology and Modelling Motivation
Modelling Strategy and the Model Equations
Steady States and Stability
Practical Results from the Model
Benefits, Implications and Marriage Repair Scenarios
Reaction Kinetics
Enzyme Kinetics: Basic Enzyme Reaction
Transient Time Estimates and Nondimensionalisation
Michaelis-Menten Quasi-Steady State Analysis
Suicide Substrate Kinetics
Cooperative Phenomena
Autocatalysis, Activation and Inhibition
Multiple Steady States, Mushrooms and Isolas
Biological Oscillators and Switches
Motivation, Brief History and Background
Feedback Control Mechanisms
Oscillators and Switches with Two or More Species: General Qualitative Results
Simple Two-Species Oscillators: Parameter Domain Determination for Oscillations
Hodgkin-Huxley Theory of Nerve Membranes: FitzHugh-Nagumo Model
Modelling the Control of Testosterone Secretion and Chemical Castration
BZ Oscillating Reactions
Belousov Reaction and the Field-Koros-Noyes (FKN) Model
Linear Stability Analysis of the FKN Model and Existence of Limit Cycle Solutions
Nonlocal Stability of the FKN Model
Relaxation Oscillators: Approximation for the Belousov-Zhabotinskii Reaction
Analysis of a Relaxation Model for Limit Cycle Oscillations in the Belousov-Zhabotinskii Reaction
Perturbed and Coupled Oscillators and Black Holes
Phase Resetting in Oscillators
Phase Resetting Curves
Black Holes
Black Holes in Real Biological Oscillators
Coupled Oscillators: Motivation and Model System
Phase Locking of Oscillations: Synchronisation in Fireflies
Singular Perturbation Analysis: Preliminary Transformation
Singular Perturbation Analysis: Transformed System
Singular Perturbation Analysis: Two-Time Expansion
Analysis of the Phase Shift Equation and Application to Coupled Belousov-Zhabotinskii Reactions
Dynamics of Infectious Diseases
Historical Aside on Epidemics
Simple Epidemic Models and Practical Applications
Modelling Venereal Diseases
Multi-Group Model for Gonorrhea and Its Control
AIDS: Modelling the Transmission Dynamics of the Human Immunodeficiency Virus (HIV)
HIV: Modelling Combination Drug Therapy
Delay Model for HIV Infection with Drug Therapy
Modelling the Population Dynamics of Acquired Immunity to Parasite Infection
Age-Dependent Epidemic Model and Threshold Criterion
Simple Drug Use Epidemic Model and Threshold Analysis
Bovine Tuberculosis Infection in Badgers and Cattle
Modelling Control Strategies for Bovine Tuberculosis in Badgers and Cattle
Reaction Diffusion, Chemotaxis, and Nonlocal Mechanisms
Simple Random Walk and Derivation of the Diffusion Equation
Reaction Diffusion Equations
Models for Animal Dispersal
Nonlocal Effects and Long Range Diffusion
Cell Potential and Energy Approach to Diffusion and Long Range Effects
Oscillator-Generated Wave Phenomena
Belousov-Zhabotinskii Reaction Kinematic Waves
Central Pattern Generator: Experimental Facts in the Swimming of Fish
Mathematical Model for the Central Pattern Generator
Analysis of the Phase Coupled Model System
Biological Waves: Single-Species Models
Background and the Travelling Waveform
Fisher-Kolmogoroff Equation and Propagating Wave Solutions
Asymptotic Solution and Stability of Wavefront Solutions of the Fisher-Kolmogoroff Equation
Density-Dependent Diffusion-Reaction Diffusion Models and Some Exact Solutions
Waves in Models with Multi-Steady State Kinetics: Spread and Control of an Insect Population
Calcium Waves on Amphibian Eggs: Activation Waves on Medaka Eggs
Invasion Wavespeeds with Dispersive Variability
Species Invasion and Range Expansion
Use and Abuse of Fractals
Fractals: Basic Concepts and Biological Relevance
Examples of Fractals and Their Generation
Fractal Dimension: Concepts and Methods of Calculation
Fractals or Space-Filling?
Phase Plane Analysis
Routh-Hurwitz Conditions, Jury Conditions, Descartes' Rule of Signs, and Exact Solutions of a Cubic
Polynomials and Conditions
Descartes' Rule of Signs
Roots of a General Cubic Polynomial
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
General Results for the Laplacian Operator in Bounded Domains
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