Comparison of disease progress curves

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Abstract
A method of analysis, involving the comparison of parameters of nonlinear models for disease progress, is described. The method tests the effects of measures for disease control on the dynamics of botanical epidemics. It was applied to published disease progress curves for a range of host-pathogen systems and was used to test whether treatments to control disease did so by slowing or delaying the epidemic or by reducing the asymptotic-carrying capacity of the host population. The treatments included genetical, chemical and cultural methods including soil solarization, varietal differences and fungicide application. The logistic model was used to summarize polycyclic epidemics of Phytophthora infestans (Mont.) de Bary on potato, P. cryptogea Pethyb. & LafT. on raspberry, Fusarium oxysporum f. sp. lycopersicae (Sacc.) Snyd. & Hans, on tomato, and Puccinia recondita Rob. on wheat and triticale. The monomolecular model was used for epidemics of Sclerotium rolfsii Sacc. on carrots and S. cepivorum Berk, on garlic, that were experimentally limited to one cycle of infection. The selected model was first fitted separately to the empirical progress curve for each treatment. Subsequently, one or more common parameters were constrained to fit all treatments while the remaining parameters were separately fitted. Comparison of the changes in residual mean squares permitted approximate tests for the effects of fitting common parameters. The biological meaning of the parameters is discussed in relation to disease control. The method was sensitive in demonstrating differences amongst the treatments. Marked differences in epidemics were shown to occur when control of disease was effected by reduction in the carrying capacity or by delaying the onset of an epidemic. Few treatments, however, affected the rate parameters, especially of the logistic model.