INCORPORATING AN ASYMPTOTIC PARAMETER INTO THE WEIBULL MODEL TO DESCRIBE PLANT-DISEASE PROGRESS

The Weibull model is a flexible growth model that describes both gener al population growth and plant disease progress. However, lack of an a symptotic parameter has limited its wider application. In the present study, an asymptotic parameter K was introduced into the original Weib ull model, written as: y = K{1 - exp[ - ((t - a)/b)(c)]}, in which a, b, c and K are location, scale, shape, and asymptotic parameters, resp ectively, y is the proportion of disease and t is time. A wide range o f simulated disease progress data sets were generated using logistic, Gompertz and monomolecular models by specifying different parameter va lues, and fitted to both original and modified Weibull models. The mod ified model provided statistically better fits for all data than the o riginal model. The modified model can thus improve the curve-fitting a bility of the original model which often failed to converge, especiall y when the asymptote is less than 1.0. Actual disease progress data on wheat leaf rust and tomato root rot with different asymptotic values were also used to compare the original and modified Weibull models. Th e modified model provided a statistically better fit than the original model, and model estimates of asymptotic parameter K were nearly iden tical to the actual disease maxima reflecting the characteristics of t he host-patho-system. Comparison of logistic, Gompertz, and Weibull mo dels including parameter K by fitting to the observed data on wheat le af rust and tomato root rot revealed the applicability of the modified Weibull model, which in a majority of cases provided a statistically superior fit.