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Mathematical Biology

Mathematical Biology is a two-part monograph on mathematical biology first published in 1989 by the applied mathematician James D. Murray. It is considered to be a classic in the field and sweeping in scope.

Part I: An Introduction

Part I of Mathematical Biology covers population dynamics, reaction kinetics, oscillating reactions, and reaction-diffusion equations.

Chapter 1: Continuous Population Models for Single Species
Chapter 2: Discrete Population Models for a Single Species
Chapter 3: Models for Interacting Populations
Chapter 4: Temperature-Dependent Sex Determination (TSD)
Chapter 5: Modelling the Dynamics of Marital Interaction: Divorce Prediction and Marriage Repair
Chapter 6: Reaction Kinetics
Chapter 7: Biological Oscillators and Switches
Chapter 8: BZ Oscillating Reactions
Chapter 9: Perturbed and Coupled Oscillators and Black Holes
Chapter 10: Dynamics of Infectious Diseases
Chapter 11: Reaction Diffusion, Chemotaxis, and Nonlocal Mechanisms
Chapter 12: Oscillator-Generated Wave Phenomena
Chapter 13: Biological Waves: Single-Species Models
Chapter 14: Use and Abuse of Fractals

Part II: Spatial Models and Biomedical Applications

Part II of Mathematical Biology focuses on pattern formation and applications of reaction-diffusion equations. Topics include: predator-prey interactions, chemotaxis, wound healing, epidemic models, and morphogenesis.

Chapter 1: Multi-Species Waves and Practical Applications
Chapter 2: Spatial Pattern Formation with Reaction Diffusion Systems
Chapter 3: Animal Coat Patterns and Other Practical Applications of Reaction Diffusion Mechanisms
Chapter 4: Pattern Formation on Growing Domains: Alligators and Snakes
Chapter 5: Bacterial Patterns and Chemotaxis
Chapter 6: Mechanical Theory for Generating Pattern and Form in Development
Chapter 7: Evolution, Morphogenetic Laws, Developmental Constraints and Teratologies
Chapter 8: A Mechanical Theory of Vascular Network Formation
Chapter 9: Epidermal Wound Healing
Chapter 10: Dermal Wound Healing
Chapter 11: Growth and Control of Brain Tumours
Chapter 12: Neural Models of Pattern Formation
Chapter 13: Geographic Spread and Control of Epidemics
Chapter 14: Wolf Territoriality, Wolf-Deer Interaction and Survival

Impact

Since its initial publication, the monograph has come to be seen as a highly influential work in the field of mathematical biology. It serves as the essential text for most high level mathematical biology courses around the world, and is credited with transforming the field from a niche subject into a standard research area of applied mathematics.