A mathematical model for bacterial inactivation

The first order kinetic model, the Buchanan model and Cerfʹs model, can model a linear survival curve, a survival curve with a shoulder and a survival curve with a tailing, respectively. However, they are not suitable for fitting a sigmoidal survival curve. The three models were integrated into a new model that was capable of fitting the four most commonly observed survival curves: linear curves, curves with a shoulder, curves with a tailing (biphasic curves) and sigmoidal curves. The new model was compared with the Whiting–Buchanan model using the survival curves of Staphylococcus aureus. The goodness-of-fit of the proposed model is practically as good as that of the Whiting–Buchanan model. Compared with the Whiting–Buchanan model, the proposed model has a more mechanistic background. Since for non-linear survival curves, such as biphasic and sigmoidal curves, the tm−D value (the time required for an m-log-cycle reduction of microorganisms under a given condition) cannot be estimated accurately by the existing or traditional method, a new method is also proposed to predict accurately the tm−D value for non-linear survival curves.