A model is presented which integrates literature data on the effects of temperature, water activity, pH, and colony size on mold growth and aflatoxin formation. Mathematical forms for the rates of growth and toxin formation are based on assumptions about the biology of toxigenesis. The rate of toxin formation is assumed to be proportional to the rate of production of new cell mass, and the rate of toxin degradation is assumed to be proportional to the product of the concentrations of dead cell mass and aflatoxin; the latter assumption is an attempt to be consistent with the notion that toxin degradation is effected by enzymes released during mycelial lysis. Growth rate and toxin yield are represented by a maximum or reference value times a series of factors dependent on environmental conditions. Temperature and water activity have an interactive effect on growth and toxigenesis in the model. An Arrhenius-like function is postulated for the effects of temperature; shape parameters in the function are selected assuming that optimum temperature bears a fixed relationship to temperature limits for growth and toxigenesis, which vary with water activity. A linear function is postulated for the effect of water activity, with the lower limit dependent on temperature. Parabolic and Monod models are used to describe the effects of pH and colony size, respectively. Toxigenic parameters are estimated by comparing model simulations to the results of two published studies, with fair consistency in the two sets of parameters. In comparisons with other studies, the model did not correctly project the effects of spore load, but did correctly predict toxigenic behaviors relating to the effects of temperature and temperature cycling. The model provides a theoretical explanation for observed temporal shifts in the optimum temperature for toxigenesis, and for a hyperbolic relationship between heat units and time to toxigenesis with and without temperature cycling.

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