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[1] and sweeping in scope.[2]

Mathematical Biology II: Spatial Models and Biomedical Applications
AuthorJames D. Murray
CountryUnited States
LanguageEnglish
Subject Mathematical biology
Publisher Springer
Publication date
  • 1989
  • Second edition in 1993
  • Third edition in 2003
Media typePrint
Pages811
ISBN0-387-95228-4
Mathematical Biology I: An Introduction
AuthorJames D. Murray
CountryUnited States
LanguageEnglish
Subject Mathematical biology
Publisher Springer
Publication date
  • 1989
  • Second edition in 1993
  • Third edition in 2002
Media typePrint
Pages551
ISBN0-387-95223-3

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[3][4]
  • 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[5]
  • 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[6][7]
  • Chapter 10: Dermal Wound Healing
  • Chapter 11: Growth and Control of Brain Tumours[8]
  • Chapter 12: Neural Models of Pattern Formation
  • Chapter 13: Geographic Spread and Control of Epidemics[9]
  • 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.[10]

References
  1. Edelstein-Keshet, Leah (2004). Murray, James D. (ed.). "Featured Review: Mathematical Biology". SIAM Review. 46 (1): 143–147. ISSN 0036-1445. JSTOR 20453477.
  2. Bell, Jonathan G. (1990). "Mathematical Biology (J. D. Murray)". SIAM Review. 32 (3): 487–489. doi:10.1137/1032093. ISSN 0036-1445.
  3. Cook, J.; Tyson, R.; White, J.; Rushe, R.; Gottman, J.; Murray, J. (1995). "Mathematics of Marital Conflict: Qualitative Dynamic Mathematical Modeling of Marital Interaction". Journal of Family Psychology. 9 (2): 110–130. doi:10.1037/0893-3200.9.2.110. S2CID 122029386.
  4. Gottman, J.; Swanson, C.; Murray, J. (1999). "The Mathematics of Marital Conflict: Dynamic Mathematical Nonlinear Modeling of Newlywed Marital Interaction". Journal of Family Psychology. 13 (1): 3–19. doi:10.1037/0893-3200.13.1.3. S2CID 53410111.
  5. Murray, J. D.; Myerscough, M. R. (1991-04-07). "Pigmentation pattern formation on snakes". Journal of Theoretical Biology. 149 (3): 339–360. Bibcode:1991JThBi.149..339M. doi:10.1016/S0022-5193(05)80310-8. ISSN 0022-5193. PMID 2062100.
  6. Sherratt, Jonathan A.; Murray, James Dickson; Clarke, Bryan Campbell (1990-07-23). "Models of epidermal wound healing". Proceedings of the Royal Society of London. Series B: Biological Sciences. 241 (1300): 29–36. doi:10.1098/rspb.1990.0061. PMID 1978332. S2CID 20717487.
  7. Sherratt, J. A.; Murray, J. D. (1991-04-01). "Mathematical analysis of a basic model for epidermal wound healing". Journal of Mathematical Biology. 29 (5): 389–404. doi:10.1007/BF00160468. ISSN 1432-1416. PMID 1831488. S2CID 37551844.
  8. Swanson, Kristin R.; Bridge, Carly; Murray, J. D.; Alvord, Ellsworth C. (2003-12-15). "Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion". Journal of the Neurological Sciences. 216 (1): 1–10. doi:10.1016/j.jns.2003.06.001. ISSN 0022-510X. PMID 14607296. S2CID 15744550.
  9. Källén, A.; Arcuri, P.; Murray, J. D. (1985-10-07). "A simple model for the spatial spread and control of rabies". Journal of Theoretical Biology. 116 (3): 377–393. Bibcode:1985JThBi.116..377K. doi:10.1016/S0022-5193(85)80276-9. ISSN 0022-5193. PMID 4058027.
  10. Maini, Philip K.; Chaplain, Mark A. J.; Lewis, Mark A.; Sherratt, Jonathan A. (2021-12-04). "Special Collection: Celebrating J.D. Murray's Contributions to Mathematical Biology". Bulletin of Mathematical Biology. 84 (1): 13. doi:10.1007/s11538-021-00955-8. ISSN 1522-9602. PMID 34865189. S2CID 244897975.
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