Kaur A, Takhar P S, Smith D M, Mann J E, Brashears M M
Animal and Food Sciences, Texas Tech Univ., P.O. Box 42141, Lubbock, TX 79409, USA.
J Food Sci. 2008 Oct;73(8):E403-14. doi: 10.1111/j.1750-3841.2008.00932.x.
A fractional differential equations (FDEs)-based theory involving 1- and 2-term equations was developed to predict the nonlinear survival and growth curves of foodborne pathogens. It is interesting to note that the solution of 1-term FDE leads to the Weibull model. Nonlinear regression (Gauss-Newton method) was performed to calculate the parameters of the 1-term and 2-term FDEs. The experimental inactivation data of Salmonella cocktail in ground turkey breast, ground turkey thigh, and pork shoulder; and cocktail of Salmonella, E. coli, and Listeria monocytogenes in ground beef exposed at isothermal cooking conditions of 50 to 66 degrees C were used for validation. To evaluate the performance of 2-term FDE in predicting the growth curves-growth of Salmonella typhimurium, Salmonella Enteritidis, and background flora in ground pork and boneless pork chops; and E. coli O157:H7 in ground beef in the temperature range of 22.2 to 4.4 degrees C were chosen. A program was written in Matlab to predict the model parameters and survival and growth curves. Two-term FDE was more successful in describing the complex shapes of microbial survival and growth curves as compared to the linear and Weibull models. Predicted curves of 2-term FDE had higher magnitudes of R(2) (0.89 to 0.99) and lower magnitudes of root mean square error (0.0182 to 0.5461) for all experimental cases in comparison to the linear and Weibull models. This model was capable of predicting the tails in survival curves, which was not possible using Weibull and linear models. The developed model can be used for other foodborne pathogens in a variety of food products to study the destruction and growth behavior.
基于分数阶微分方程（FDEs）的理论被开发出来，该理论涉及一阶和二阶方程，用于预测食源性病原体的非线性存活和生长曲线。值得注意的是，一阶FDE的解可得到威布尔模型。采用非线性回归（高斯-牛顿法）来计算一阶和二阶FDE的参数。利用火鸡胸肉、火鸡腿肉和猪肩肉中沙门氏菌混合菌液；以及在50至66摄氏度等温烹饪条件下暴露的碎牛肉中沙门氏菌、大肠杆菌和单核细胞增生李斯特氏菌混合菌液的实验失活数据进行验证。为了评估二阶FDE在预测生长曲线方面的性能，选取了碎猪肉和去骨猪排中鼠伤寒沙门氏菌、肠炎沙门氏菌和背景菌群；以及碎牛肉中大肠杆菌O157:H7在22.2至4.4摄氏度温度范围内的生长情况。用Matlab编写了一个程序来预测模型参数以及存活和生长曲线。与线性模型和威布尔模型相比，二阶FDE在描述微生物存活和生长曲线的复杂形状方面更为成功。与线性模型和威布尔模型相比，二阶FDE预测曲线在所有实验情况下具有更高的R(2)值（0.89至0.99）和更低的均方根误差值（0.0182至0.5461）。该模型能够预测存活曲线的尾部，这是威布尔模型和线性模型无法做到的。所开发的模型可用于研究各种食品中其他食源性病原体的破坏和生长行为。
