MATHEMATICAL FUNCTIONS TO DESCRIBE DISEASE PROGRESS CURVES OF DOUBLE SIGMOID PATTERN

Ten mathematical functions used to describe disease progress curves of double sigmoid pattern were tested using data from epidemics of sugar cane smut. Four of the functions represent the sum of two simple equat ions (logistic + logistic, Gompertz + Gompertz. monomolecular + logist ic, and monomolecular + Gompertz); the other six functions are general izations of simple models (logistic, monomolecular, and Gompertz) with four and five parameters. For all the functions, high coefficients of determination (R2 > 0.95) were obtained in the nonlinear regression a nalyses of the progress curves of sugarcane smut. To choose the most a ppropriate function, the coefficients of determination, the residual s ums of squares for error, the biological meaning of each parameter, an d the accuracy in estimating the upper asymptote were utilized. The ge neralized monomolecular function and the generalized Gompertz function , each with five parameters, were considered the most useful functions to fit disease progress curves of sugarcane smut.