Botrytis cinerea is a ubiquitous fungal pathogen mainly found on citrus and stone fruits. The use of mathematical models to quantify and predict microbial growth curves has received much attention because of its usefulness in decision making for preventing risk to human and animal health. In this study, we used sodium propionate to inhibit mycelial growth of the pathogenic fungus B. cinerea in vitro and modeled the efficacy of sodium propionate using a mathematical model. The antifungal efficacy of different concentrations (0.1–2.2 % w/v) of sodium propionate was evaluated by measuring mycelial growth. The higher the concentration of sodium propionate tested, the greater the inhibitory effect on B. cinerea. Three mathematical models were used as deterministic models: the modified logistic model, the modified Gompertz model, and the Baranyi and Roberts model. The modified logistic model showed the best performance with satisfactory statistical indices (root mean squared error: RMSE, and R2), indicating that it was a better fit than the other models tested in this study. Furthermore, a stochastic modified logistic model that assumes a multivariate normal distribution of two random kinetic parameters successfully described the growth behavior of B. cinerea mycelia at various concentrations of sodium propionate as a probability distribution. Although the performance of sodium propionate in inhibiting B. cinerea was not ideal, Monte Carlo simulation may be a useful tool for predicting the probability of events based on the variability of B. cinerea growth behavior.
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