Mathematical biology
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Mathematical biology or biomathematics is an interdisciplinary field of academic study which aims at modelling natural, biological processes using mathematical techniques and tools. It has both practical and theoretical applications in biological research.
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Research
Below is a list of some areas of research in mathematical biology and links to related projects in various universities:
- Modelling of arterial disease [1] (http://www.maths.gla.ac.uk/~nah/research_interests.html)
- Modelling of neurons and carcinogenesis [2] (http://www.maths.gla.ac.uk/research/groups/biology/kal.htm)
- Mechanics of biological tissues [3] (http://www.maths.gla.ac.uk/~rwo/research_areas.htm)
- Theoretical enzymology and enzyme kinetics [4] (http://www.informatics.indiana.edu/schnell/research/enzymology.asp)
- Cancer modelling and simulation [5] (http://calvino.polito.it/~biomat/)
- Swarming behaviour [6] (http://www.math.ubc.ca/people/faculty/keshet/research.html)
- Multi-scale modelling of the heart [7] (http://www.integrativebiology.ox.ac.uk/heartmodel.html)
- Travelling waves in a wound-healing assay [8] (http://www.maths.ox.ac.uk/~maini/public/gallery/twwha.htm)
- The mechanochemical theory of morphogenesis [9] (http://www.maths.ox.ac.uk/~maini/public/gallery/mctom.htm)
- Biological pattern formation [10] (http://www.maths.ox.ac.uk/~maini/public/gallery/bpf.htm)
- Modelling the movement of interacting cell populations [11] (http://www.ma.hw.ac.uk/~jas/researchinterests/index.html)
- Mathematical modelling of scar tissue formation [12] (http://www.ma.hw.ac.uk/~jas/researchinterests/scartissueformation.html)
These examples are characterised by complex, nonlinear mechanisms and it is being increasingly recognised that the result of such interactions may only be understood through mathematical and computational models. Due to the wide diversity of specific knowledge involved, biomathematical research is often done in collaboration between mathematicians, physicists, biologists, physicians, zoologists, chemists etc.
Bibliographical references
- J.D. Murray, Mathematical Biology. Springer-Verlag, 3rd ed. in 2 vols.: Mathematical Biology: I. An Introduction, 2002 ISBN 0387952233; Mathematical Biology: II. Spatial Models and Biomedical Applications, 2003 ISBN 0387952284.
- L. Edelstein-Keshet, Mathematical Models in Biology. SIAM, 2004. ISBN 0075549506
- L.A. Segel, Modeling dynamic phenomena in molecular and cellular biology. C.U.P., 1984. ISBN 052127477X
- F. Hoppensteadt, Mathematical theories of populations: demographics, genetics and epidemics. SIAM, Philadelphia, 1975 (reprinted 1993). ISBN 0898710170
- S.I. Rubinow, Introduction to mathematical biology. John Wiley, 1975. ISBN 0471744468
- A. Goldbeter, Biochemical oscillations and cellular rhythms. C.U.P., 1996. ISBN 0521599466
- E. Renshaw, Modelling biological populations in space and time. C.U.P., 1991. ISBN 0521448557
- P.G. Drazin, Nonlinear systems. C.U.P., 1992. ISBN 0521406684
- D.W. Jordan and P. Smith, Nonlinear ordinary differential equations, 2nd ed. O.U.P., 1987. ISBN 0198565623
External references
- F. Hoppensteadt, Getting Started in Mathematical Biology (http://www.ams.org/notices/199509/hoppensteadt.pdf). Notices of American Mathematical Society, Sept. 1995.
- M. C. Reed, Why Is Mathematical Biology So Hard? (http://www.resnet.wm.edu/~jxshix/math490/reed.pdf) Notices of American Mathematical Society, March, 2004.
- R. M. May, Uses and Abuses of Mathematics in Biology (http://www.resnet.wm.edu/~jxshix/math490/may.pdf). Science, February 6, 2004.
- J. D. Murray, How the leopard gets its spots? (http://www.resnet.wm.edu/~jxshix/math490/murray.doc) Scientific American, 258(3): 80-87, 1988.
Internal links
- Bioinformatics, biologically-inspired computing, biostatistics, cellular automata, excitable medium, Ewens's sampling formula, Lotka-Volterra equation, mathematical model, morphometrics, population dynamics, population genetics, theoretical biology.
External links
- Society for Mathematical Biology (http://www.smb.org/)
- European Society for Mathematical and Theoretical Biology (http://www.esmtb.org/)
- Centre for Mathematical Biology at Oxford University (http://www.maths.ox.ac.uk/cmb/)
- Mathematical Biology at the National Institute for Medical Research (http://mathbio.nimr.mrc.ac.uk/)
- Institute for Medical BioMathematics (http://www.imbm.org/)
- Mathematical Biology Systems of Differential Equations (http://eqworld.ipmnet.ru/en/solutions/syspde/spde-toc2.pdf) from EqWorld: The World of Mathematical Equations
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