Development of predictive mathematical model for the growth kinetics of Staphylococcus aureus by response surface model

Abstract

A response surface model was developed for predicting the growth rates of Staphylococcus aureus in tryptic soy broth (TSB) medium as a function of combined effects of temperature, pH, and NaCl. The TSB containing six different concentrations of NaCl (0, 2, 4, 6, 8, and 10%) was adjusted to an initial of six different pH levels (pH 4, 5, 6, 7, 8, 9, and 10) and incubated at 10, 20, 30, and 40 degrees C. In all experimental variables, the primary growth curves were well (r2=0.9000 to 0.9975) fitted to a Gompertz equation to obtain growth rates. The secondary response surface model for natural logarithm transformations of growth rates as a function of combined effects of temperature, pH, and NaCl was obtained by SAS's general linear analysis. The predicted growth rates of the S. aureus were generally decreased by basic (pH 9-10) or acidic (pH 5-6) conditions and higher NaCl concentrations. The response surface model was identified as an appropriate secondary model for growth rates on the basis of correlation coefficient (r=0.9703), determination coefficient (r2=0.9415), mean square error (MSE=0.0185), bias factor (B(f)=1.0216), and accuracy factor (A(f)=1.2583). Therefore, the developed secondary model proved reliable for predictions of the combined effect of temperature, NaCl, and pH on growth rates for S. aureus in TSB medium.