Mathematical Biology

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

Mathematical Biology I: An Introduction
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 Biologyis a two-part monograph onmathematical biologyfirst published in 1989 by theapplied mathematician James D. Murray.It is considered to be a classic in the field^[1]and sweeping in scope.^[2]

Part I: An Introduction

Part I ofMathematical Biologycoverspopulation dynamics,reaction kinetics,oscillating reactions,andreaction-diffusionequations.

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 ofFractals

Part II: Spatial Models and Biomedical Applications

Part II ofMathematical Biologyfocuses onpattern formationand applications of reaction-diffusion equations. Topics include:predator-preyinteractions,chemotaxis,wound healing,epidemic models,andmorphogenesis.

Chapter 1:Multi-Species Waves and Practical Applications
Chapter 2:Spatial Pattern Formation with Reaction Diffusion Systems
Chapter 3:Animal Coat Patternsand 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 andTeratologies
Chapter 8:A Mechanical Theory of VascularNetwork 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 ofapplied mathematics.^[10]

References

^Edelstein-Keshet, Leah (2004). Murray, James D. (ed.)."Featured Review: Mathematical Biology".SIAM Review.46(1): 143–147.ISSN 0036-1445.JSTOR 20453477.
^Bell, Jonathan G. (1990)."Mathematical Biology (J. D. Murray)".SIAM Review.32(3): 487–489.doi:10.1137/1032093.ISSN 0036-1445.
^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.
^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.
^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.
^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.
^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.
^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.
^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.
^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

[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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