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

Eleven previously published models of plant disease epidemics, given as differential equations with a rate and a shape parameter, are compared using general model characteristics as well as their usefulness in fitting observed data. Six out of the eleven models can be solved analytically resulting in epidemic growth functions, while the others can be solved only numerically. When all 11 differential equations were fitted to two data sets, all models showed a similar goodness of fit, although the shape parameter in some models could not be estimated very precisely. With respect to useful characteristics (exponential population growth at the beginning, ability to generate monomolecular disease progression, and flexibility of the inflection point), the models of Fleming, Kosman-Levy, Birch, Richards and Waggoner, and Rich are recommended. Formulas were established to calculate the point of inflection as well as the weighted absolute and relative rate, respectively, depending on the shape and rate parameter. These formulas allow transformation of the parameter values of one model into those of another model in many cases. If the two models are required to have the same temporal position of the disease progress curve, then the initial disease level at the start of the epidemic or the time when the inflection point is reached have to be transformed.