Skip to main content
SpringerLink
Log in

Disease progress in time: modelling and data analysis

  • Chapter
The Epidemiology of Plant Diseases

Abstract

The primary goal of epidemiology is to increase our knowledge of how diseases develop in populations. Epidemiologists perform observational and designed experiments with the purpose of understanding the factors that influence disease development. These factors include aspects of host growth, development and resistance to pathogens; pathogen survival, growth, dissemination and reproduction; components of the environments in which epidemics develop; and disease characteristics such as the incubation, latent and infectious periods. With improved knowledge about how these factors influence epidemic ontogeny, epidemiologists can suggest more efficient and effective management strategies and reduce losses due to diseases.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Afifi, A.A. and Clark, V. (1996) Computer-aided Multivariate Analysis, 3rd edn, Van Nostrand Reinhold, New York, 455 pp.

    Google Scholar 

  • Analytis, S. (1973) Zur Methodik der Analyse von Epidemien dargestellt am Apfelschorf (Venturia inaequalis (Cooke) Aderh.). Acta Phytomedica, 1, 1–75.

    Google Scholar 

  • Analytis, S. (1974) Der Einsatz von Wachstumsfunktionen zur Analyse der Befallskurven von Pflanzenkrankheiten. Phytopathologische Zeitschrift, 81, 133–144.

    Article  Google Scholar 

  • Berger, R.D. and Jones, J.W. (1985) A general model for disease progress with functions for variable latency and lesion expansion on growing host plants. Phytopathology, 75, 792–797.

    Article  Google Scholar 

  • Blaise, Ph. and Gessler, C. (1992) An extended progeny/parent ratio model. I. Theoretical development. Journal of Phytopathology, 134, 39–52.

    Article  Google Scholar 

  • Bliss, C.I. (1935) The comparison of disease-mortality data. Annals of Applied Biology, 22, 307.

    Article  CAS  Google Scholar 

  • Boote, K.J, Jones, J.W., Mishoe, J.W. and Berger, R.D. (1983) Coupling pests to crop growth simulators to predict yield reductions. Phytopathology, 73, 1581–1587.

    Article  Google Scholar 

  • Bowen, K.L. (1997) Analytical models of disease progression, in Exercises in Plant Disease Epidemiology, (eds L.J. Francl and D.A. Neher ), APS Press, St Paul, MN, pp. 16–19.

    Google Scholar 

  • Brasset, P.R. and Gilligan, C.A. (1989) Fitting of simple models for field disease progress data for the take-all fungus. Plant Pathology, 38, 397–407.

    Article  Google Scholar 

  • Buwalda, J.G., Ross, G.J.S., Stribley, D.P. and Tinker, P.B. (1982) The development of endomy-corrhizal root systems: III. The mathematical representation of the spread of vesicular-arbuscular mycorrhizal infection in root systems. New Phytologist, 91, 669–682.

    Article  Google Scholar 

  • Campbell, C.L. and Madden, L.V. (1990) Introduction to Plant Disease Epidemiology, Wiley, New York, 532 pp.

    Google Scholar 

  • Campbell, C.L., Pennypacker, S.P. and Madden, L.V. (1980a) Structural characterization of bean root rot epidemics. Phytopathology, 70, 152–155.

    Article  Google Scholar 

  • Campbell, C.L., Pennypacker, S.P. and Madden L.V. (1980b) Progression dynamics of hypocotyl rot on snapbean. Phytopathology, 70, 487–494.

    Article  Google Scholar 

  • Chester, K.S. (1946) The loss from cotton wilt and the tempo of wilt development: a study of new uses for old data. Plant Disease Reporter, 30, 253–260.

    Google Scholar 

  • Cohlbach, N., Lucas, P. and Meynard, J.-M. (1997) Influence of crop management on take-all development and disease cycles in winter wheat. Phytopathology, 87, 26–32.

    Article  Google Scholar 

  • Correll, J.C., Gordon, T.R. and Elliott, V.J. (1988) Powdery mildew on tomato: the effect of planting date and triadimefon on disease onset, progress, incidence, and severity. Phytopathology, 78, 512–519.

    Article  CAS  Google Scholar 

  • Cox, A.E. and Large, E.C. (1960) Potato Blight Epidemics Throughout the World, Agricultural Handbook 174, US Department of Agriculture, Washington, DC, 230 pp.

    Google Scholar 

  • Culbreath, A.K., Beute, M.K., and Campbell, C.L. (1991) Spatial and temporal aspects of epidemics of Cylindrocladium black rot in resistant and susceptible peanut genotypes. Phytopathology, 81, 144–150.

    Article  Google Scholar 

  • Draper, N.R. and Smith, H. (1981) Applied Regression Analysis, 2nd edn, Wiley, New York, 709 pp.

    Google Scholar 

  • Fargette, D. and Vié, K. (1994) Modelling the temporal primary spread of African cassava mosaic virus into plantings. Phytopathology, 84, 378–382.

    Article  Google Scholar 

  • Farlow, W.G. (1884) The spread of epidemic diseases in plants. Proceedings of the American Association for the Advancement of Science, 32, 307–309.

    Google Scholar 

  • Fleming, R.A. (1983) Development of a simple mechanistic model of cereal rust progress. Phytopathology, 73, 308–312.

    Article  Google Scholar 

  • Fleming, R.A. and Holling C.S. (1982) A comparison of disease progress equations for cereal rust. Canadian Journal of Botany, 60, 2154–2163.

    Article  Google Scholar 

  • Fracker, S.B. (1936) Progressive intensification of uncontrolled plant-disease outbreaks. Journal of Economic Entomology, 29, 923–940.

    Google Scholar 

  • Francl, L.J. and Neher, D.A. (eds) (1997) Exercises in Plant Disease Epidemiology, APS Press, American Phytopathological Society, St Paul, MN, 233 pp.

    Google Scholar 

  • Fry, W.E. (1977) Integrated control of potato late blight–effects of polygenic resistance and techniques of timing fungicide applications. Phytopathology, 67, 1650–1655.

    Google Scholar 

  • Fry, W.E., Apple, A.E., and Bruhn, J.A. (1983) Evaluation of potato late blight forecasts modi-fied to incorporate host resistance and fungicide weathering. Phytopathology, 73, 1054–1059.

    Article  Google Scholar 

  • Gabriel, K.R. (1971) The biplot graphic display of matrices with application to principal component analysis. Biometrika, 58, 453–467.

    Article  Google Scholar 

  • Gäumann, E. (1946) Pflanzliche Infektionslehre, Birkhauser, Basel, 611 pp.

    Google Scholar 

  • Gill, J.L. (1978) Design and Analysis of Experiments in the Animal and Biomedical Sciences, Vol. 2, Iowa State University Press, Ames, 305 pp.

    Google Scholar 

  • Gilligan, C.A. (1985) Construction of temporal models: III Disease progress of soil-borne pathogens, in Advances in Plant Pathology, Volume 3, Mathematical Modelling of Crop Disease, (ed. C.A. Gilligan ), Academic Press, New York, pp. 67–105.

    Google Scholar 

  • Gilligan, C.A. (1990a) Mathematical modelling and analysis of soilborne pathogens, in Epidemics of Plant Diseases: Mathematical Analysis and Modelling, 2nd edn, (ed. J. Kranz ), Springer-Verlag, Berlin, pp. 96–142.

    Chapter  Google Scholar 

  • Gilligan, C.A. (1990b) Comparison of disease progress curves. New Phytologist, 115, 223–242.

    Article  Google Scholar 

  • Gilligan, C.A. (1994) Temporal aspects of the development of root disease epidemics, in Epidemiology and Management of Root Diseases, (eds C.L. Campbell and D.M. Benson) Springer-Verlag, Berlin, pp. 148–194.

    Chapter  Google Scholar 

  • Gutierrez, A.P. and DeVay, J.E. (1986) Studies of plant pathogen-weather interaction: cotton and Verticillium wilt, in Plant Disease Epidemiology: Population Dynamics and Management, Vol. 1, (eds K.J. Leonard and W.E. Fry ), Macmillan, New York, pp. 205–231.

    Google Scholar 

  • Gutierrez, A.P., DeVay, J.E. and Frieverthauser, G.E. (1983a) A model of Verticillium wilt in relation to cotton growth and development. Phytopathology, 73, 89–95.

    Article  Google Scholar 

  • Gutierrez, A.P., DeVay, J.E. and Frieverthauser, G.E. (1983b) A model of Verticillium wilt in relation to cotton growth and the effect of defoliators on its yield. Economic Entomology, 4, 125–136.

    Google Scholar 

  • Hatcher, L. (1994) A Step-by-Step Approach to Using the SAS System for Factor Analysis and Structural Equation Modelling, SAS Institute, Cary, NC, 232 pp.

    Google Scholar 

  • Hau, B. (1990) Analytical models of plant disease in a changing environment. Annual Review of Phytopathology, 28, 221–245.

    Article  Google Scholar 

  • Hau, B. and Kranz, J. (1977) Ein Vergleich verschiedener Transformationen von Befallskurven. Phytopathologische Zeitschrift, 88, 53–68.

    Article  Google Scholar 

  • Hau, B. and Kranz, J. (1990) Mathematics and statistics for analyses in epidemiology, in Epidemics of Plant Diseases: Mathematical Analysis and Modelling, 2nd edn, (ed. J. Kranz ), Springer-Verlag, Berlin, pp. 12–52.

    Chapter  Google Scholar 

  • Hawkins, D.M. and Fatti, L.P. (1984) Exploring multivariate data using the minor principal components. Statistician, 33, 325–338.

    Article  Google Scholar 

  • Huisman, O.J. (1982) Interrelations of root growth dynamics to epidemiology of root-invading fungi, Annual Review of Phytopathology, 20, 303–327.

    Article  Google Scholar 

  • Jeger, M.J. (1982) Using growth curve relative rates to model disease progress of apple powdery mildew. Protection Ecology, 4, 49–58.

    Google Scholar 

  • Jeger, M.J. (1987a) The influence of root growth and inoculum density on the dynamics of root disease epidemics: Theoretical analysis. New Phytologist, 107, 459–478.

    Article  Google Scholar 

  • Jeger, M.J. (1987b) Modelling the dynamics of pathogen populations, in Populations of Plant Pathogens: Their Dynamics and Genetics, (eds M.S. Wolfe and C.E. Caten ), Blackwell, Oxford, pp. 91–107.

    Google Scholar 

  • Jensen, J.L. and Rostrup, E. (1892) Report on recent experiments in checking potato disease in the United Kingdom and abroad (C-6647), Board of Agriculture, Great Britain and Ireland, London.

    Google Scholar 

  • Johnson, K.B. (1988) Modelling the influences of plant infection rate and temperature on potato foliage and yield losses caused by Verticillium dahliae. Phytopathology, 78, 1198–1205.

    Article  Google Scholar 

  • Johnson, K.B. and Teng, P.S. (1990) Coupling a disease progress model for early blight to a model of potato growth. Phytopathology, 80, 416–425.

    Article  Google Scholar 

  • Jolliffe, I.T. (1986) Principal Components Analysis, Springer-Verlag, Berlin, 271 pp.

    Book  Google Scholar 

  • Knudsen, G.R., Spurr, H.W. Jr and Johnson, C.S. (1987) A computer simulation model for Cercospora leaf spot of peanut. Phytopathology, 77, 1118–1121.

    Article  Google Scholar 

  • Kranz, J. (1968) Eine Analyse von annuellen Epidemien pilzlicher Parasiten. III. Ãœber Korrelationen zwischen quantitativen Merkmalen von Befallskurven und Ähnlichkeit von Epidemien. Phytopathologische Zeitschrift, 61, 205–217.

    Article  Google Scholar 

  • Kranz, J. (1974) Comparison of epidemics. Annual Review of Phytopathology, 12, 355–374.

    Article  Google Scholar 

  • Kranz, J. (1975a) Beziehungen zwischen Blattmasse und Befallsentwicklung bei Blatt Krankheiten. Zeitschrift für Planzenkrankeiten und Pflanzenschutz, 82, 641–654.

    Google Scholar 

  • Kranz, J. (1975b) Das Abklingen von Befallskurven. Zeitschrift für Planzenkrankeiten und Pflanzenschutz, 82, 655–664.

    Google Scholar 

  • Kranz, J. (1977) A study on the maximum severity in plant diseases. Travaux dédiés à G. Viennot-Bourgin. pp. 169–173.

    Google Scholar 

  • Kranz, J. (1978) Comparative anatomy of epidemics, in Plant Disease, Volum 2: How Disease Develops in Populations, (eds J.G. Horsfall and E.B. Cowling ), Academic Press, New York, pp. 33–62.

    Google Scholar 

  • Kranz, J. (1980) Comparative epidemiology: an evaluation of scope, concepts and methods, in Comparative Epidemiology, (eds J. Palti and J. Kranz ), Centre for Agricultural Publishing and Documentation, Wageningen, pp. 18–28.

    Google Scholar 

  • Kranz, J. (1988) Measuring plant disease, in Experimental Techniques in Plant Disease Epidemiology, (eds J. Kranz and J. Rotem), Springer, Berlin, pp. 35–50.

    Google Scholar 

  • Kranz, J. and Lörincz, D. (1970) Methoden zum automatischen Vergleich epidemischer Abläufe bei Pflanzenkrankheiten. Phytopathologische Zeitschrift, 67, 225–233.

    Article  Google Scholar 

  • Kushalappa, A.C. and Ludwig. A. (1982) Calculation of apparent infection rate in plant diseases: development of a method to correct for host growth. Phytopathology, 72, 1373–1377.

    Article  Google Scholar 

  • Lalancette, N. and Hickey, K.D. (1986) Disease progression as a function of plant growth. Phytopathology, 76, 1171–1175.

    Article  Google Scholar 

  • Large, E.C. (1945) Field trials of copper fungicides for the control of potato blight I. Foliage protection and yield. Annals of Applied Biology, 32, 319–329.

    Article  CAS  Google Scholar 

  • Large, E.C. (1952) The interpretation of progress curves for potato blight and other plant diseases. Plant Pathology, 1, 109–117.

    Article  Google Scholar 

  • Lebeda, A. and Jendrulek, T. (1988) Applications of methods of multivariate analysis in comparative epidemiology and research into field resistance. Zeitschrift für Pflanzenkrankheiten und Pflanzenschutz, 95, 495–505.

    Google Scholar 

  • Littell, R.C., Freund, R.J.and Spector, P.C. (1991) SAS System for Linear Models, SAS Series in Statistical Applications, SAS Institute, Cary, NC, 329 pp.

    Google Scholar 

  • Madden, L.V. (1986) Statistical analysis and comparison of disease progress curves, in Plant Disease Epidemiology: Population Dynamics and Management, Vol. 1, (eds K.J. Leonard and W.E. Fry ), Macmillan, New York, pp. 55–84.

    Google Scholar 

  • Madden, L.V. and Campbell, C.L. (1990) Nonlinear disease progress curves, in Epidemics of Plant Diseases, 2nd edn, (ed. J. Kranz ), Springer-Verlag, Berlin, pp. 181–229.

    Chapter  Google Scholar 

  • Madden, L.V. and Pennypacker, S.P. (1979) Principal component analysis of tomato early blight epidemics. Phytopathologische Zeitschrift, 95, 364–369.

    Article  Google Scholar 

  • Madden, L.V., Pirone, T.P. and Raccah, B. (1987) Temporal analysis of two viruses increasing in the same tobacco fields. Phytopathology, 77, 974–980.

    Article  Google Scholar 

  • Mardia, K.V., Kent, J.T. and Bibby, J.M. (1979) Multivariate Analysis, Academic Press, New York, 521 pp.

    Google Scholar 

  • M’Kendrick, A.G. and Kesava Pai, M. (1911) The rate of multiplication of micro-organisms: a mathematical study. Proceedings of the Royal Dublin Society, 22 (N.S.), 69.

    Google Scholar 

  • Monlezun, C.J., Blouin, D.C. and Malone, L.C. (1984) Contrasting split plot and repeated measures experiments and analysis. American Statistician, 38, 21–27.

    Google Scholar 

  • Moore, W.C. (1943) The measurement of plant diseases in the field; preliminary report of a sub-committee of the society’s plant pathology committee. Transactions of the British Mycological Society, 26, 28–35.

    Article  Google Scholar 

  • Mora-Aguilera, G. and Campbell, C.L. (1997) Multivariate techniques for selection of epidemiological variables, in Exercises in Plant Disease Epidemiology, (eds. L.J. Fand and D.A. Neher ), APS Press, St Paul, MN, pp. 51–58.

    Google Scholar 

  • Mora-Aguilera, G., Nieto-Angel, D., Campbell, C.L. et al. (1996) Multivariate comparison of papaya ringspot epidemics. Phytopathology, 86, 70–78.

    Article  Google Scholar 

  • Neher, D.A. and Campbell, C.L. (1992) Underestimation of disease progress rates with the logistic, monomolecular, and Gompertz models when maximum disease intensity is less than 100 percent. Phytopathology, 82, 811–814.

    Google Scholar 

  • Neher, D.A. and Campbell, C.L. (1997) Analysis of disease progress curves using nonlinear regression, in Exercises in Plant Disease Epidemiology, (eds L.J. Fand and D.A. Neher ), APS Press, St Paul, MN, pp. 38–41.

    Google Scholar 

  • Neher, D.A. and Duniway, J.M. (1991) Relationship between among of Phytophthora parasitica added to field soil and the development of root rot in processing tomatoes. Phytopathology, 81, 1124–1129.

    Article  Google Scholar 

  • Neher, D.A., Reynolds, K.L. and Campbell, C.L. (1997) Analysis of disease progress curves using linear models, in Exercises in Plant Disease Epidemiology, (eds L.J. Fand and D.A. Neher ), APS Press, St Paul, MN, pp. 29–33.

    Google Scholar 

  • Nelson, R.R. (1973) The meaning of disease resistance in plants, in Breeding Plants for Disease Resistance: Concepts and Applications, (ed. R.R. Nelson ), Pennsylvania State University Press, University Park, PA, pp. 13–25.

    Google Scholar 

  • Nutter, F.W. Jr and Parker, S.K. (1997) Fitting disease progress curves using EPIMODEL, in Exercises in Plant Disease Epidemiology, (eds L.J. Fand and D.A. Neher ), APS Press, St Paul, MN, pp. 24–28.

    Google Scholar 

  • Park, E.W. and Lim, S. (1985) Empirical estimation of the asymptotes of disease progress curves and the use of the Richards generalized rate parameters for describing disease progress. Phytopathology, 75, 786–791.

    Article  Google Scholar 

  • Pataky, J.K., Headrick, J.M., and Suparyono, J.M. (1988) Classification of sweet corn hybrid reactions to common rust, north leaf blight, Stewart’s wilt, and Goss’ wilt and associated yield reductions. Phytopathology, 78, 172–178.

    Article  Google Scholar 

  • Pearl, R. and Reed, L.J. (1920) On the rate of growth of the population of the United States since 1790 and its mathematical representation. Proceedings of the National Academy of Science, 6, 275–288.

    Article  CAS  Google Scholar 

  • Pfender, W.F. (1982) Monocyclic and polycyclic root diseases: distinguishing between the nature of the disease cycle and the shape of the disease progress curve. Phytopathology, 72, 31–32.

    Article  Google Scholar 

  • Populer, C. (1978) Changes in host susceptibility with time, in Plant Disease: An Advanced Treatise, Vol. II. How Disease Develops in Populations, (eds J.G. Horsfall and E.B. Cowling ), Academic Press, New York, pp. 239–260.

    Google Scholar 

  • Rawlings, J.O. (1988) Applied Regression Analysis: A Research Tool, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA, 553 pp.

    Google Scholar 

  • Reynolds, K.L. and Neher, D.A. (1997) Statistical comparison of epidemics, in Exercises in Plant Disease Epidemiology, (eds L.J. Fand and D.A. Neher ), APS Press, St Paul, MN, pp. 34–37.

    Google Scholar 

  • Richards, F.J. (1959) A flexible growth function for empirical use. Journal of Experimental Botany, 10, 290–300.

    Article  Google Scholar 

  • Singh, U.P., Zargar, G.H. and Fazili, M.A. (1986) Growth of foliage of pigeon pea (Cajanus cajan [L.]Millsp.) and disease progress of Alternaria blight. Journal of Phytopathology, 115, 147–151.

    Article  Google Scholar 

  • Smith, S.E. and Walker, N.A. (1981) A quantitative study of mycorrhizal infection in Trifolium: separate determination of the rates of infection and of mycelial growth. New Phytologist, 89, 225–240.

    Article  Google Scholar 

  • Smith, V.L., Campbell, C.L., Jenkins, S.F. and Benson, D.M. (1988) Effects of host density and number on disease foci on epidemics of southern blight of processing carrot. Phytopathology, 78, 595–600.

    Article  Google Scholar 

  • Thal, W.M. and Campbell, C.L. (1988) Analysis of progress of alfalfa leaf spot epidemics. Phytopathology, 78, 389–395.

    Article  Google Scholar 

  • Thompson, J.P. and Rees, R.G. (1979) Pattern analysis in epidemiological evaluation of cultivar resistance. Phytopathology, 69, 545–549.

    Article  Google Scholar 

  • Tinker, P.B. (1985) Effects of vesicular-arbuscular mycorrhizas on higher plants. Symposia of the Society for Experimental Biology, 29, 325–349.

    Google Scholar 

  • Turner, M.E., Blumenstein, B.A. and Sebaugh, J.L. (1969) A generalization of the logistic law of growth. Biometrics, 25, 577–580.

    Article  PubMed  Google Scholar 

  • Van der Plank, J.E. (1960) Analysis of epidemics, in Plant Pathology: An Advanced Treatise, Vol. 3, (eds J.G. Horsfall and E.B. Cowling ), Academic Press, New York, pp. 229–289.

    Google Scholar 

  • Van der Plank, J.E. (1963) Plant Diseases: Epidemics and Control, Academic Press, New York, 344 pp.

    Google Scholar 

  • Van der Plank, J.E. (1968) Disease Resistance in Plants, Academic, New York, 206 pp.

    Google Scholar 

  • Van der Plank, J.E. (1984) Disease Resistance in Plants, 2nd edn, Academic, New York, 192 pp.

    Google Scholar 

  • Verhulst, P.F. (1838) Notice sur la loi que la population suit dans son d’accroissement. Correspondence en Mathematique et Physique, 10, 113–121.

    Google Scholar 

  • Waggoner, P.E. (1986) Progress Curves of Foliar Diseases: their interpretation and use, (eds K.J. Leonard and W.E. Fry), Macmillan, New York, pp. 3–37.

    Google Scholar 

  • Walker, N.A. and Smith, S.E. (1984) The quantitative study of mycorrhizal infection. II. The relation of rate of infection and speed of fungal growth to propagule density, the mean length of the infection unit and the limiting value of the fraction of the root infected. New Phytologist, 96, 55–69.

    Article  Google Scholar 

  • Ward, H.M. (1901) Diseases in Plants, Macmillan, London, 309 pp.

    Google Scholar 

  • Ware, J.O. and Young, V.H. (1934) Control of cotton wilt and ‘rust’, University of Arkansas Agricultural Experiment Station Bulletin 308, Fayetteville, AR, 23 pp.

    Google Scholar 

  • Ware, J.O., Young„ V.H. and Janssen, G. (1932) Cotton wilt studies. III. The behavior of certain cotton varieties grown on soil artificially infested with the cotton wilt organism, University of Arkansas Agricultural Experiment Station Bulletin 269, Fayetteville, AR, 51 pp.

    Google Scholar 

  • Weibull, W. (1951) A statistical distribution of wide applicability. Journal of Applied Mechanics, 18, 293–297.

    Google Scholar 

  • Wiens, J.A. (1989) Spatial scaling in ecology. Functional Ecology, 3, 385–397.

    Article  Google Scholar 

  • Williams, J.R., Jones, C.A., Kiniry, J.R. and Spaniel, D.A. (1989) The EPIC crop growth model. Transactions American Society of Agricultural Engineering, 32, 497–511.

    Google Scholar 

  • Williams, J.R., Jones, C.A. and Dyke, P.T. (1990) The EPIC model. EPIC — Erosion/Productivity Impact Calculator 1. Model Documentation, USDA-ARS Technical Bulletin 1768, Washington, DC, 227 pp.

    Google Scholar 

  • Zadoks, J.C. (1961) Yellow rust on wheat. Tijdschrift Plantenziekten, 67, 69–256.

    Google Scholar 

Download references

Authors
  1. C. Lee Campbell
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Hillview, Dene Road, Tone Vale, Taunton, Somerset, TA4 1DG, UK

    D. Gareth Jones

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Campbell, C.L. (1998). Disease progress in time: modelling and data analysis. In: Jones, D.G. (eds) The Epidemiology of Plant Diseases. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3302-1_9

Download citation

  • DOI: https://doi.org/10.1007/978-94-017-3302-1_9

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-017-3304-5

  • Online ISBN: 978-94-017-3302-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation