Mathematical Biology

Mathematical Biology I: An Introduction

Second edition
Author	James D. Murray
Language	English
Subject	Mathematical biology
Publisher	Springer
Publication date	1989 Second edition in 1993 Third edition in 2002
Publication place	United States
Media type	Print
Pages	551
ISBN	0-387-95223-3

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

Author	James D. Murray
Language	English
Subject	Mathematical biology
Publisher	Springer
Publication date	1989 Second edition in 1993 Third edition in 2003
Publication place	United States
Media type	Print
Pages	811
ISBN	0-387-95228-4

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.

External links

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