112
Views
30
CrossRef citations to date
0
Altmetric
EPIDEMIOLOGY, CROP LOSS ASSESSMENT, PHYTOPATHOMETRY: A COLLECTION OF PRESENTATIONS AT THE 6th INTERNATIONAL CONGRESS OF PLANT PATHOLOGY

Modelling soil-borne plant pathogens: reaction-diffusion models

Pages 96-108 | Accepted 22 Sep 1994, Published online: 29 Dec 2009

References

  • Anderson , R. M. and May , R. M. 1992 . Infectious diseases of humans: dynamics and control , Oxford : Oxford University Press . 757 pp.
  • Bronshtein , I. N. and Senendyayev , K. A. 1985 . Handbook of Mathematics , New York : VonNostrand Rheinhold . 973 pp.
  • Campbell , C. L. and Noe , J. P. 1985 . The spatial analysis of soilborne pathogens and root diseases . Annu. Rev. Phytopathol. , 23 : 127 – 148 .
  • Campbell , C. L. and Madden , L. V. 1990 . Introduction to Plant Disease Epidemiology , New York : Wiley . 532 pp.
  • Caughley , G. and Lawton , J. H. 1981 . “ Plant-herbivore systems ” . In Theoretical Ecology , Edited by: May , R. M. 132 – 166 . Oxford : Blackwell .
  • Ermentrout , E. B. and Edelstein-Keshet , L. 1993 . Cellular automata approaches to biological modeling . J. Theor. Biol. , 160 : 97 – 133 .
  • Fisher , R. A. 1937 . The wave of advance of advantageous genes . Ann. Eugenics , 7 : 353 – 369 .
  • Gilligan , C. A. 1988 . “ Analysis of the spatial pattern of soilborne pathogens ” . In Techniques in the Study of Plant Disease Epidemiology , Edited by: Kranz , J. and Rotem , J. 85 – 98 . Heidelberg : Springer-Verlag . 299 pp.
  • Gilligan , C. A. 1990a . Comparison of disease progress curves . New Phytologist , 115 : 223 – 242 .
  • Gilligan , C. A. 1990b . Antagonistic interactions involving plant pathogens: fitting and analysis of models to non-monotonic curves for population and disease dynamics . New Phytol. , 115 : 649 – 665 .
  • Gilligan , C. A. 1994 . “ Temporal aspects of the development of root disease epidemics ” . In Epidemiology and Management of Root Diseases , Edited by: Campbell , C. L. and Benson , D. M. 149 – 193 . Heidelberg : Springer-Verlag .
  • Gilligan , C. A. , Simons , S. A. and Hyde , G. A. 1996 . Inoculum density and spatial pattern of Rhizoctonia solani in field plots of Solanum tuberosum: effects of cropping frequency . Plant Pathology , in press
  • Jeger , M. J. and Chan , M. S. 1995 . Theoretical aspects of epidemics: uses of analytical models to make strategic management decisions . Can. J. Plant Pathol. , 17 : 109 – 114 .
  • Kendall , M. G. 1948 . A form of wave propagation associated with the equation of heat conduction . Proc. Phil. Soc. Cambridge , 44 : 591 – 593 .
  • Kierstead , H. and Slobodkin , L. B. 1953 . The size of water masses containing plankton blooms . J. Mar. Res. , 12 : 141 – 147 .
  • Levin , S. A. 1976 . “ Population models and community structure in heterogeneous environments ” . In Mathematical Ecology: An Introduction, Vol. 17, Biomathematics , Edited by: Hallam , T. G. and Levin , S. A. 295 – 320 . Heidelberg : Springer-Verlag . 457 pp.
  • Levin , S. A. and Segel , L. A. 1976 . Hypothesis for origin of planktonic patchiness . Nature , 259 : 659
  • Ludwig , D. , Aronson , D. G. and Weinberger , H. F. 1979 . Spatial patterning of the spruce budworm . J. Math. Biol. , 8 : 217 – 258 .
  • Maini , P. K. , Benson , D. L. and Sherratt , J. A. 1992 . Pattern formation in reaction-diffusion models with spatially inhomogeneous diffusion coefficients . J. Math. Appl. Med. & Biol. , 9 : 197 – 213 .
  • May , R. M. 1974 . Stability and Complexity in Model Ecosystems , Princeton : Princeton University Press . 265 pp.
  • Mimura , M. and Murray , J. D. 1978 . On a diffusive prey-predator model which exhibits patchiness . J. Theor. Biol. , 75 : 249 – 262 .
  • Minogue , K. P. and Fry , W. E. 1983 . Models for the spread of disease . Phytopathology , 73 : 1168 – 1173 .
  • Mollison , D. 1991 . Dependence of epidemic and population velocities on basic parameters . Math. Biosci. , 107 : 255 – 287 .
  • Murray , J. D. 1989 . Mathematical Biology. Vol. 19, Bio-mathematics , Heidelberg : Springer-Verlag . 767 pp.
  • Nagle , R. K. and Saff , E. B. 1989 . Fundamentals of Differential Equations , 2nd ed. , New York : Benjamin Cummings . 682 pp.
  • Nisbet , R. M. and Gurney , W. S. C. 1982 . Modelling Fluctuating Populations , New York : Wiley . 379 pp.
  • Okubo , A. 1980 . Diffusion and Ecological Problems: Mathematical Models. Vol. 10, Biomathematics , Heidelberg : Springer-Verlag . 254 pp.
  • Pielou . 1977 . Mathematical Ecology , New York : Wiley . 385 pp.
  • Prosser , J. I. 1993 . Growth kinetics of mycelial colonies and aggregates of ascomycetes . Mycol. Res. , 97 : 513 – 528 .
  • Reynolds , K. M. and Madden , L. V. 1988 . Analysis of epidemics using spatio-temporal autocorrelation . Phytopathology , 78 : 240 – 246 .
  • Rubinow , S. I. 1975 . Introduction to Mathematical Biology , New York : Wiley . 386 pp.
  • Segel , L. A. and Jackson , J. L. 1972 . Dissipative structure: an explanation and an ecological example . J. Theor. Biol. , 37 : 545 – 559 .
  • Shigesada , N. , Kawasaki , K. and Teramoto , E. 1987 . “ The spread of traveling frontal waves in heterogeneous environments ” . In Mathematical Topics in Population Biology, Morphogenesis and Neurosciences , Edited by: Teramoto , E. and Yamaguli , Y. 88 – 97 . Heidelberg : Springer-Verlag .
  • Skellam , J. G. 1951 . Random dispersal in theoretical populations . Biometrika , 38 : 196 – 218 .
  • Turing , A. M. 1952 . The chemical basis of morphogenesis . Phil. Trans Roy. Soc. Lond. , B237 : 37 – 72 .
  • van den Bosch , F. , Metz , J. A. J. and Diekmann , O. 1990 . The matics by computer. Addison-Wesley, Redwood City. 961 velocity of spatial population expansion . J. Math. Biol. , 28 : 529 – 565 .
  • van den Bosch , F. , Zadoks , J. C. and Metz , J. A. J. 1988 . Focus expansion in plant disease. II: Realistic parameter-sparse models . Phytopathology , 78 : 59 – 64 .
  • Wolfram , S. 1991 . Mathematica™: a system for doing mathe-matics by computer , Redwood City : Addison-Wesley . 961 pp.
  • Yakowitz , S. , Gani , J. and Hayes , R. 1990 . Cellular automata modeling of epidemics . Appl. Math. Comput. , 40 : 41 – 54 .
  • Zawolek , M. W. and Zadoks , J. C. 1992 . Studies in focus development: an optimum for the dual dispersal of plan pathogens . Phytopathology , 82 : 1288 – 1297 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.