VIEW ARTICLE

Ecology and Epidemiology

Mathematical Functions to Describe Disease Progress Curves of Double Sigmoid Pattern. B. Hau, Biometrie & Populationsgenetik, Justus-Liebig Universität, 6300 Giessen, Germany; L. Amorim(2), and A. Bergamin Filho(3). (2)(3)Dpto. Fitopatologia, ESALQ-USP, Caixa Postal 9, 13400 Piracicaba, SP, Brazil. Phytopathology 83:928-932. Accepted for publication 19 April 1993. Copyright 1993 The American Phytopathological Society. DOI: 10.1094/Phyto-83-928.

Ten mathematical functions used to describe disease progress curves of double sigmoid pattern were tested using data from epidemics of sugarcane smut. Four of the functions represent the sum of two simple equations (logistic + logistic, Gompertz + Gompertz, monomolecular + logistic, and monomolecular + Gompertz); the other six functions are generalizations of simple models (logistic, monomolecular, and Gompertz) with four and five parameters. For all the functions, high coefficients of determination (R² > 0.95) were obtained in the nonlinear regression analyses of the progress curves of sugarcane smut. To choose the most appropriate function, the coefficients of determination, the residual sums of squares for error, the biological meaning of each parameter, and the accuracy in estimating the upper asymptote were utilized. The generalized monomolecular function and the generalized Gompertz function, each with five parameters, were considered the most useful functions to fit disease progress curves of sugarcane smut.