Book Review
The AMS does not provide abstracts of book reviews.
You may download the entire review from the links below.
Full text of review:
PDF
This review is available free of charge.
Book Information:
Authors:
Linda Rass and
John Radcliffe
Title:
Spatial deterministic epidemics
Additional book information:
Mathematical Surveys and Monographs, vol. 102, Amer. Math. Soc.,
Providence, RI,
2003,
x+261 pp.,
ISBN 0-8218-0499-5,
$69.00$
Editors:
H. T. Banks and
Carlos Castillo-Chavez
Title:
Bioterrorism: Mathematical modeling applications in homeland security
Additional book information:
edited by
H. T. Banks and
Carlos Castillo-Chavez,
SIAM,
Philadelphia, PA,
2003,
x+240 pp.,
ISBN 0-89871-549-0,
$78.00$
1. Anderson, R.M. and May, R.M. (1991) Infectious Diseases of Humans : Dynamics and Control. Oxford University Press.
D. G. Aronson and H. F. Weinberger, Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, Partial differential equations and related topics (Program, Tulane Univ., New Orleans, La., 1974) Lecture Notes in Math., Vol. 446, Springer, Berlin, 1975, pp. 5–49. MR 0427837
D. G. Aronson and H. F. Weinberger, Multidimensional nonlinear diffusion arising in population genetics, Adv. in Math. 30 (1978), no. 1, 33–76. MR 511740, DOI 10.1016/0001-8708(78)90130-5
G. I. Barenblatt, Podobie, avtomodel′nost′, promezhutochnaya asimptotika, “Gidrometeoizdat”, Leningrad, 1978 (Russian). Teoriya i prilozheniya k geofizicheskoĭ gidrodinamike. [Theory and applications to geophysical hydrodynamics]. MR 556235
Grigory Isaakovich Barenblatt, Scaling, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 2003. With a foreword by Alexandre Chorin. MR 2034052, DOI 10.1017/CBO9780511814921
M. A. Omara, Hydrodynamic forces on a moving cylinder in presence of vortices, Proc. Math. Phys. Soc. Egypt 1 (1939), no. 3, 15–18. MR 14889
Maury Bramson, Convergence of solutions of the Kolmogorov equation to travelling waves, Mem. Amer. Math. Soc. 44 (1983), no. 285, iv+190. MR 705746, DOI 10.1090/memo/0285
8. Cantrell, R.S. and Cosner, C. (2003) Spatial Ecology via Reaction-Diffusion Models. Wiley, Chichester.
9. Cliff, A.D. and Haggett, P. (1988) Atlas of Disease Distributions: Analytical Approaches to Epidemiological Data. Blackwell, Oxford.
10. Cliff, A.D., Haggett, P. and Smallman-Raynor, M. (1993) Measles: An Historical Geography, Pion, London.
11. Diamond, J. (1997) Guns, Germs and Steel. Vintage, Random House, London.
12. Dieckmann, U., Law, R. and Metz, J.A.J., eds. (2000) The Geometry of Ecological Interactions. Cambridge University Press.
13. Dieckmann, U., Metz, J.A.J., Sabelis, M.W. and Sigmund, K. (2002) Adaptive Dynamics of Infectious Diseases : In Pursuit of Virulence Management. Cambridge University Press.
Odo Diekmann and J. A. P. Heesterbeek, Mathematical epidemiology of infectious diseases, Wiley Series in Mathematical and Computational Biology, John Wiley & Sons, Ltd., Chichester, 2000. Model building, analysis and interpretation. MR 1882991
P. van den Driessche and James Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180 (2002), 29–48. John A. Jacquez memorial volume. MR 1950747, DOI 10.1016/S0025-5564(02)00108-6
16. Ewald, P.W. (1994) Evolution of Infectious Disease. Oxford University Press.
17. Ferguson, N.M., Donnelly, C.A. and Anderson, R.M. (2001) Transmission intensity and impact of control policies on the foot and mouth epidemic in Great Britain. Nature 413 : 542-548.
18. Fisher, R.A. (1937) The wave of advance of advantageous genes. Ann. Eugen. London 7 : 355-369.
19. Garrett, L. (1994) The Coming Plague. Penguin Books, London.
20. Haccou, P., Jagers, P. and Vatutin, V.A. (2005) Branching Processes : Variation, Growth and Extinction of Populations. Cambridge University Press.
21. Hengeveld, R. (1989) Dynamics of Biological Invasions. Chapman and Hall, London.
Herbert W. Hethcote, The mathematics of infectious diseases, SIAM Rev. 42 (2000), no. 4, 599–653. MR 1814049, DOI 10.1137/S0036144500371907
23. Keeling, M.J. et al. (2003) Modelling vaccination strategies against foot-and-mouth disease. Nature 421 : 136-142.
24. Kendall D.G. (1965) Mathematical models of the spread of infection. pp. 213-225 in : Mathematics and Computer Science in Biology and Medicine, HMSO, London.
25. Kolmogorov, A., Petrovski, I. and Piscounov, N. (1937) Étude de l'équation de la diffusion avec croissance de la quantité de matière et son application a un problème biologique. Moscow Univ. Bull. Ser. International Sect. A 1 (6) : 1-25.
26. McNeill, W.H. (1979) Plagues and Peoples. Penguin Books, London.
27. Mollison, D. (1977) Spatial contact models for ecological and epidemic spread. J. Roy. Stat. Soc. B 39 : 283-326.
Ingemar Nåsell, Hybrid models of tropical infections, Lecture Notes in Biomathematics, vol. 59, Springer-Verlag, Berlin, 1985. MR 812057, DOI 10.1007/978-3-662-01609-1
M. E. J. Newman, The structure and function of complex networks, SIAM Rev. 45 (2003), no. 2, 167–256. MR 2010377, DOI 10.1137/S003614450342480
30. Noble, J.V. (1974) Geographic and temporal development of plagues. Nature 250 : 726-728.
Akira Okubo and Simon A. Levin, Diffusion and ecological problems: modern perspectives, 2nd ed., Interdisciplinary Applied Mathematics, vol. 14, Springer-Verlag, New York, 2001. MR 1895041, DOI 10.1007/978-1-4757-4978-6
32. van Saarloos, W. (2003) Front propagation into unstable states. Physics Reports 386 : 29-222.
33. Shigesada, N. and Kawasaki, K. (1997) Biological Invasions: Theory and Practice. Oxford University Press.
J. G. Skellam, Random dispersal in theoretical populations, Biometrika 38 (1951), 196–218. MR 43440, DOI 10.1093/biomet/38.1-2.196
M. S. Bartlett and R. W. Hiorns (eds.), The mathematical theory of the dynamics of biological populations, Academic Press, London-New York, 1973. Based on a Conference held in Oxford, September, 1972. MR 0504003
Horst R. Thieme, Mathematics in population biology, Princeton Series in Theoretical and Computational Biology, Princeton University Press, Princeton, NJ, 2003. MR 1993355
37. Tilman, D. and Kareiva, P. (1997) Spatial Ecology : The Role of Space in Population Dynamics and Interspecific Interactions. Princeton University Press.
H. F. Weinberger, Long-time behavior of a class of biological models, SIAM J. Math. Anal. 13 (1982), no. 3, 353–396. MR 653463, DOI 10.1137/0513028
39. Winslow, C.E.A. (1980) The Conquest of Epidemic Disease. A Chapter in History of Ideas. University of Wisconsin Press, Madison.
- 1.
- Anderson, R.M. and May, R.M. (1991) Infectious Diseases of Humans : Dynamics and Control. Oxford University Press.
- 2.
- Aronson D.G. and Weinberger, H.F. (1975) Nonlinear diffusion in population genetics, combustion and nerve pulse propagation. pp. 5-49 in : Partial Differential Equations and Related Topics, Goldstein J.A., ed. Springer Lecture Notes in Mathematics 446. MR 0427837
- 3.
- Aronson D.G. and Weinberger, H.F. (1978) Multidimensional nonlinear diffusion arising in population genetics. Adv. Math. 30 : 33-76.MR 0511740
- 4.
- Barenblatt, G.I. (1979) Similarity, Self-similarity and Intermediate Asymptotics. Plenum, New York. MR 0556235
- 5.
- Barenblatt, G.I. (2003) Scaling. Cambridge University Press. MR 2034052
- 6.
- Becker, N.G. (1989) Analysis of Infectious Disease Data. Chapman and Hall, London. MR 0014889
- 7.
- Bramson, M. (1983) Convergence of Solutions of the Kolmogorov Equation to Travelling Waves. Memoir of the AMS 44 : 285. MR 0705746
- 8.
- Cantrell, R.S. and Cosner, C. (2003) Spatial Ecology via Reaction-Diffusion Models. Wiley, Chichester.
- 9.
- Cliff, A.D. and Haggett, P. (1988) Atlas of Disease Distributions: Analytical Approaches to Epidemiological Data. Blackwell, Oxford.
- 10.
- Cliff, A.D., Haggett, P. and Smallman-Raynor, M. (1993) Measles: An Historical Geography, Pion, London.
- 11.
- Diamond, J. (1997) Guns, Germs and Steel. Vintage, Random House, London.
- 12.
- Dieckmann, U., Law, R. and Metz, J.A.J., eds. (2000) The Geometry of Ecological Interactions. Cambridge University Press.
- 13.
- Dieckmann, U., Metz, J.A.J., Sabelis, M.W. and Sigmund, K. (2002) Adaptive Dynamics of Infectious Diseases : In Pursuit of Virulence Management. Cambridge University Press.
- 14.
- Diekmann, O. and Heesterbeek, J.A.P. (2000) Mathematical Epidemiology of Infectious Diseases : Model Building, Analysis and Interpretation. Wiley, Chichester. MR 1882991
- 15.
- Driessche, P. van den and Watmough, J. (2002) Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosc. 180 : 29-48. MR 1950747
- 16.
- Ewald, P.W. (1994) Evolution of Infectious Disease. Oxford University Press.
- 17.
- Ferguson, N.M., Donnelly, C.A. and Anderson, R.M. (2001) Transmission intensity and impact of control policies on the foot and mouth epidemic in Great Britain. Nature 413 : 542-548.
- 18.
- Fisher, R.A. (1937) The wave of advance of advantageous genes. Ann. Eugen. London 7 : 355-369.
- 19.
- Garrett, L. (1994) The Coming Plague. Penguin Books, London.
- 20.
- Haccou, P., Jagers, P. and Vatutin, V.A. (2005) Branching Processes : Variation, Growth and Extinction of Populations. Cambridge University Press.
- 21.
- Hengeveld, R. (1989) Dynamics of Biological Invasions. Chapman and Hall, London.
- 22.
- Hethcote, H.W. (2000) The mathematics of infectious diseases. SIAM Review 42 : 599-653. MR 1814049
- 23.
- Keeling, M.J. et al. (2003) Modelling vaccination strategies against foot-and-mouth disease. Nature 421 : 136-142.
- 24.
- Kendall D.G. (1965) Mathematical models of the spread of infection. pp. 213-225 in : Mathematics and Computer Science in Biology and Medicine, HMSO, London.
- 25.
- Kolmogorov, A., Petrovski, I. and Piscounov, N. (1937) Étude de l'équation de la diffusion avec croissance de la quantité de matière et son application a un problème biologique. Moscow Univ. Bull. Ser. International Sect. A 1 (6) : 1-25.
- 26.
- McNeill, W.H. (1979) Plagues and Peoples. Penguin Books, London.
- 27.
- Mollison, D. (1977) Spatial contact models for ecological and epidemic spread. J. Roy. Stat. Soc. B 39 : 283-326.
- 28.
- Nåsell, I. (1985) Hybrid Models of Tropical Infections. Springer, Berlin. MR 0812057
- 29.
- Newman, M.E.J. (2003) The structure and function of complex networks. SIAM Review 45 : 167-256. MR 2010377
- 30.
- Noble, J.V. (1974) Geographic and temporal development of plagues. Nature 250 : 726-728.
- 31.
- Okubo, A. and Levin, S.A. (2001) Diffusion and Ecological Problems. Springer, New York. MR 1895041
- 32.
- van Saarloos, W. (2003) Front propagation into unstable states. Physics Reports 386 : 29-222.
- 33.
- Shigesada, N. and Kawasaki, K. (1997) Biological Invasions: Theory and Practice. Oxford University Press.
- 34.
- Skellam, J.G. (1951) Random dispersal in theoretical populations. Biometrica 38 : 196-218. MR 0043440
- 35.
- Skellam, J.G. (1973) The formulation and interpretation of mathematical models of diffusionary processes in population biology. pp. 63-85 in : The Mathematical Theory of the Dynamics of Biological Populations, Bartlett, M.S. and Hiorns, R.W., eds., Academic Press, New York. MR 0504003
- 36.
- Thieme, H.R. (2003) Mathematics in Population Biology. Princeton University Press. MR 1993355
- 37.
- Tilman, D. and Kareiva, P. (1997) Spatial Ecology : The Role of Space in Population Dynamics and Interspecific Interactions. Princeton University Press.
- 38.
- Weinberger, H.F. (1982) Long-time behaviour of a class of biological models. SIAM J. Math. Anal. 13 : 353-396. MR 0653463
- 39.
- Winslow, C.E.A. (1980) The Conquest of Epidemic Disease. A Chapter in History of Ideas. University of Wisconsin Press, Madison.
Review Information:
Reviewer:
Odo Diekmann
Affiliation:
Utrecht University
Journal:
Bull. Amer. Math. Soc.
42 (2005), 521-527
Published electronically:
April 1, 2005
Review copyright:
© Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.