Abstract
Many biological phenomena, at all levels of organization, can be modeled by treating them as random processes, behaving much like the diffusion of ink in a container of water. In this chapter we discuss some biological aspects of random processes, namely the movement of oxygen across a human placenta and the spread of infectious diseases. While these processes might seem to be quite different at first glance, they actually act according to very similar models.
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References and Suggested Further Reading
Membrane structure: William S. Beck, Karel F. Liem and George Gaylord Simpson; Life: An Introduction to Biology, 3rd ed., Harper Collins Publishers, New York, 1991.
Membrane transport: Edward K. Yeargers, Basic Biophysics for Biology, CRC Press, Inc., Boca Raton, 1992.
Diffusion: Russell K. Hobbie, Intermediate Physics for Medicine and Biology, John Wiley and Sons, 2nd ed, New York, p. 65, 1988.
Diffusion: H. C. Berg, Random Walks in Biology, Princeton University Press, Princeton, NJ, 1993
Diffusion in Biology: J. D. Murray, Mathematical Biology, Springer-Verlag, New York. 1989.
Fluid resistance: S.I. Rubinow, Introduction to Mathematical Biology, John Wiley and Sons, New York, 1975.
Diffusion across a slab: David L. Powers, Boundary Value Problems, Academic Press, New York, 1979.
Oxygen dissociation curves, fetal blood: William T. Keeton and James L. Gould, Biological Science, 5th ed. W. W. Norton and Company, New York, 1993.
Placenta: H. Bartels, W. Moll, J. Metcalfe, Physiology of gas exchange in the human placenta, Am. J. Obstet. Gynecol. 84, 1714–1730, 1962.
Placenta: J. Metcalfe, H. Bartels, W. Moll, “Gas Exchange in the Pregnant Uterus,” Physio. L Rev. 47, 782–838, 1967.
Placenta: R. E. Forster II, “Some Principles Governing Maternal—Foetal Transfer in the Placenta,” Foetal and Neonatal Physiology, Cambridge University Press, Cambridge, 223–237, 1973.
Placenta: K. S. Comline, K. W. Cross, G. S. Dawes, P. W. Nathanielsz, Foetal and Neonatal Physiology, Cambridge University Press. Cambridge. 1973.
Placenta: F. C. Battaglia, G. Meschia, An Introduction to Fetal Physiology, Academic Press, Inc., Harcourt Brace Jovannovich, New York, 1986.
Placenta: A. Guettouche, et. al., Mathematical Modeling of the Human Fetal Arterial Blood Circulation, Int. J. Biomed. Comput. 31, 127–139, 1992.
Placenta: A. Costa, M. L. Costantino, R. Fumero, Oxygen exchange mechanisms in the human placenta: mathematical modelling and simulation, J. Biomed. Eng. 14, 85–389, 1992.
Epidemiology: John P. Fox, Carrie E. Hall and Lila R. Elveback, Epidemiology: Man and Disease, The Macmillan Company, New York, 1970.
Epidemiology and disease: Julius P. Krier and Richard F. Mortenson, Infection, Resistance and Immunity, Harper and Row, Publishers, New York, 1990.
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© 1996 Springer Science+Business Media New York
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Yeargers, E.K., Shonkwiler, R.W., Herod, J.V. (1996). Random Movements in Space and Time. In: An Introduction to the Mathematics of Biology: with Computer Algebra Models. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-1095-3_6
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DOI: https://doi.org/10.1007/978-1-4757-1095-3_6
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4757-1097-7
Online ISBN: 978-1-4757-1095-3
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