Abstract
Abstract The Weibull model is a flexible growth model that describes both general population growth and plant disease progress. However, lack of an asymptotic parameter has limited its wider application. In the present study, an asymptotic parameter K was introduced into the original Weibull model, written as; y = K {1 − exp [− ( t − a ) c ]}, in which a , b , c and K are location, scale, shape, and asymptotic parameters, respectively, y is the proportion of disease and t is time. A wide range of simulated disease progress data sets were generated using logistic, Gompertz and monomolecular models by specifying different parameter values, and fitted to both original and modified Weibull models. The modified model provided statistically better fits for all data than the original model. The modified model can thus improve the curve‐fitting ability of the original model which often failed to converge, especially 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. The modified model provided a statistically better fit than the original model, and model estimates of asymptotic parameter K were nearly identical to the actual disease maxima reflecting the characteristics of the host‐pathosystem. Comparison of logistic, Gompertz, and Weibull models including parameter K by fitting to the observed data on wheat leaf rust and tomato root rot revealed the applicability of the modified Weibull model, which in a majority of cases provided a statistically superior fit.
Abstract from the paper’s OpenAlex record, shown for indexing and research. Copyright remains with the authors or the publisher. Read at the source ↗
The text the model read, with the source record’s inline markup (italics, sub- and superscripts) rendered and its character entities decoded; quote offsets refer to the raw text.
Claims 5
Claim · model-written summary
The modified Weibull model gave statistically better fits than the original model for all simulated disease progress data.
Verbatim
e1“The modified model provided statistically better fits for all data than the original model”
Claim · model-written summary
On wheat leaf rust data the modified Weibull model gave a statistically better fit than the original model.
- Taxon
- wheat
Triticum aestivume3 - Outcome
- statistically better fite5
- Comparator
- original modele5
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e3“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”
e5“The modified model provided a statistically better fit than the original model”
Claim · model-written summary
On tomato root rot data the modified Weibull model gave a statistically better fit than the original model.
- Taxon
- tomato
Solanum lycopersicume3 - Outcome
- statistically better fite5
- Comparator
- original modele5
Organisms pictured · Representative pictures of the matched species, not figures from the paper.
Verbatim
e3“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”
e5“The modified model provided a statistically better fit than the original model”
Claim · model-written summary
Estimates of asymptotic parameter K were nearly identical to the actual disease maxima.
Verbatim
e2“model estimates of asymptotic parameter K were nearly identical to the actual disease maxima”
Claim · model-written summary
The modified Weibull model gave a statistically superior fit in most cases compared with logistic and Gompertz models.
Verbatim
e4“which in a majority of cases provided a statistically superior fit”
e7“Comparison of logistic, Gompertz, and Weibull models”