Cl. Xiao et al., INCORPORATING AN ASYMPTOTIC PARAMETER INTO THE WEIBULL MODEL TO DESCRIBE PLANT-DISEASE PROGRESS, Journal of phytopathology, 144(7-8), 1996, pp. 375-382
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.