Empirical Estimation of the Asymptotes of Disease Progress Curves and the Use of the Richards Generalized Rate Parameters for Describing Disease Progress

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Abstract
The effect of fixing the asymptote parameter of growth functions at 1 on estimates of the rate parameter and the use of generalized rate parameters proposed by Richards are discussed. When disease progress curves have asymptotes which are less than 1, the asymptote parameter of growth functions need to be estimated empirically; otherwise, underestimation of the rate parameter of growth functions (e.g., Vanderplank''s apparent infection rate, r) and changes in the rank of estimates of the rate parameter may result from fixing the asymptote parameter of growth functions at 1. The use of the weighted mean absolute growth rate and the weighted mean relative growth rate of the Richards function as the absolute rate of disease progress (Ra) and the relative rate of disease progress (Rr), respectively, is proposed for describing and comparing epidemics with different asymptotes and shapes of disease progress curves. Since they are determined empirically without the unrealistic assumption on the upper limit of disease severity, they provide more accurate information on disease development than Vanderplank''s apparent infection rate or the rate parameter of growth functions with the asymptote value of 1. Development of bacterial [Pseudomonas syringae pv. glycinea] blight in a soybean field [Glycine max] was described using Ra and Rr.