A comparison of disease progress equations for cereal rust

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Abstract
A continuous mathematical model of the progress of cereal rust disease was developed by including many of the natural processes underlying each recurrent infection cycle. This model is subsequently reduced to a single equation and compared with four other models prevalent in the literature: the logistic, Kiyosawa's modified logistic, Waggoner's modified logistic, and the Gompertz. The equation developed here provides a basis for exploring causal linkages between these four models and illuminating some of their implicit assumptions. It is argued that single first-order equation models must contain one or more parameters which group a number of effects to be fitted to disease progress data. This precludes unique biologically meaningful definitions for parameters of such single-parameter models as the logistic with respect to the processes underlying disease progress (e.g., infection, sporulation). The differential equation dx/dt = ax(1−x)/(1 + alx), where a is a rate parameter, l is the length of the latent period, t is time, and x is disease severity, is offered as a potentially useful alternative to previous models of disease progress. Recommendations for further research are provided.