Comparative analysis of flexible two-parameter models of plant disease epidemics

Phytopathology

Volumn 97, Issue 10, 2007, Pages 1231-1244

  Hau, B ^a   Kosman, E ^b  

^a LEIBNIZ UNIVERSITY HANNOVER   (Germany)

^b TEL AVIV UNIVERSITY   (Israel)

Author keywords

Disease progress curves; Growth curves; Nonlinear regression

Indexed keywords

EID: 42649084691     PISSN: 0031949X     EISSN: None     Source Type: Journal    
DOI: 10.1094/PHYTO-97-10-1231     Document Type: Article

References (29)

1. Analytis, S. 1973. Methodik der Analyse von Epidemien dargestellt am Apfelschorf (Venturia inequalis (Cooke) Aderh.). Acta Phytomed. 1:7-75.
2. Berger, R. D. 1981. Comparison of the Gompertz and logistic equations to describe disease progress. Phytopathology 71:716-719.
3. Birch, C. P. D. 1999. A new generalized logistic sigmoid growth equation compared with the Richards growth equation. Ann. Bot. 83:713-723.
4. Campbell, C. L., and Madden, L. V. 1990. Introduction to Plant Disease Epidemiology. John Wiley & Sons, New York.
5. Fleming, R. A. 1983. Development of a simple mechanistic model of cereal rust progress. Phytopathology 73:308-312.
6. Fleming, R. A., and Holling, C. S. 1982. A comparison of disease progress equations for cereal rust. Can. J. Bot. 60:2154-2163.
7. Hastings, N. A. J., and Peacock, J. B. 1975. Statistical Distributions. Butterworths, London.
8. Hau, B., and Kranz, J. 1977. Ein Vergleich verschiedener Transformationen von Befallskurven. Phytopathol. Z. 88:53-68.
9. Hill, A. V. 1913. The combinations of haemoglobin with oxygen and with carbon monoxide. Biochem. J. 7:471-480.
10. Jeger, M. J. 1983. Analyzing epidemics in time and space. Plant Pathol. 32:5-11.
11. Kosman, E., and Levy, Y. 1994. Fungal foliar plant pathogen epidemic: Modelling and qualitative analysis. Plant Pathol. 44:328-337.
12. Madden, L. V. 1980. Quantification of disease progression. Prot. Ecol. 2:159-176.
13. Madden, L. V., and Campbell, C. L. 1990. Nonlinear disease progress curves. Pages 181-229 in: Epidemics of Plant Diseases. 2nd ed. J. Kranz, ed. Springer, Berlin.
14. 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.
15. Ngugi, H. K., King, S. B., Holt, J., and Julian, A. M. 2001. Simultaneous temporal progress of sorghum anthracnose and leaf blight in crop mixtures with disparate patterns. Phytopathology 91:720-729.
16. Park, E. W., and Lim, S. M. 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.
17. Pennypacker, S. P., Knoble, H. D., Antle, C. E., and Madden, L. V. 1980. A flexible model for studying plant disease progression. Phytopathology 70:232-235.
18. Richards, F. J. 1959. A flexible growth function for empirical use. J. Exp. Bot. 10:290-300.
19. Rouse, D. I. 1985. Construction of temporal models: I. Disease progress of airborne pathogens. Pages 11-29 in: Advances in Plant Pathology, Vol. 3, Mathematical Modeling of Crop Disease. C. A. Gilligan, ed. Academic Press, New York.
20. Rouse, D. I., MacKenzie, D. R., and Nelson, R. R. 1981. A relationship between initial inoculum and apparent infection rate in a set of disease progress data for powdery mildew on wheat. Phytopathol. Z. 100:143-149.
21. Thal, W. M., Campbell, C. L., and Madden, L. V. 1984. Sensitivity of Weibull model parameter estimates to variation in simulated disease progression data. Phytopathology 74:1425-1430.
22. Turner, M. E., Jr., Bradley, E. L., Jr., Kirk, K. A., and Pruit, K. M. 1976. A theory of growth. Math. Biosci. 29:367-373.
23. Vanderplank, J. E. 1963. Plant Diseases: Epidemics and Control. Academic Press, New York.
24. von Bertalanffy, L. 1942. Theoretische Biologie. Bornträger, Berlin.
25. Waggoner, P. E. 1981. Models of plant disease. BioScience 31:315-319.
26. Waggoner, P. E. 1986. Progress curves of foliar diseases: Their interpretation and use. Pages 3-37 in: Plant Disease Epidemiology. Vol. 1, Population Dynamics and Management. K. J. Leonard and W. Fry, eds. Macmillan, New York.
27. Waggoner, P. E., and Rich, S. 1981. Lesion distribution, multiple infection, and the logistic increase of plant disease. Proc. Natl. Acad. Sci. USA 78:3293-3295.
28. Weibull, W. 1951. A statistical distribution of wide applicability. J. Appl. Mechanics 18:293-297.
29. Yang, X. B., and TeBeest, D. O. 1992. Dynamic pathogen distribution and logistic increase of plant disease. Phytopathology 82:380-383.