• Source: 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.


      References




      External links


      Mathematical Biology I: An Introduction
      Mathematical Biology II: Spatial Models and Biomedical Applications

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