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 SpeciesChapter 2: Discrete Population Models for a Single SpeciesChapter 3: Models for Interacting PopulationsChapter 4: Temperature-Dependent Sex Determination Chapter 5: Modelling the Dynamics of Marital Interaction: Divorce Prediction and Marriage RepairChapter 6: Reaction KineticsChapter 7: Biological Oscillators and SwitchesChapter 8: BZ Oscillating ReactionsChapter 9: Perturbed and Coupled Oscillators and Black HolesChapter 10: Dynamics of Infectious DiseasesChapter 11: Reaction Diffusion, Chemotaxis, and Nonlocal MechanismsChapter 12: Oscillator-Generated Wave PhenomenaChapter 13: Biological Waves: Single-Species ModelsChapter 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 ApplicationsChapter 2: Spatial Pattern Formation with Reaction Diffusion SystemsChapter 3: Animal Coat Patterns and Other Practical Applications of Reaction Diffusion MechanismsChapter 4: Pattern Formation on Growing Domains: Alligators and SnakesChapter 5: Bacterial Patterns and ChemotaxisChapter 6: Mechanical Theory for Generating Pattern and Form in DevelopmentChapter 7: Evolution, Morphogenetic Laws, Developmental Constraints and TeratologiesChapter 8: A Mechanical Theory of Vascular Network FormationChapter 9: Epidermal Wound HealingChapter 10: Dermal Wound HealingChapter 11: Growth and Control of Brain TumoursChapter 12: Neural Models of Pattern FormationChapter 13: Geographic Spread and Control of EpidemicsChapter 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.