Death rates of bacterial spores: mathematical models

The concave survivor curves produced as a result of spore heterogeneity were analyzed to determine whether they were caused by inmate characteristics of the spores or by the acquisition of heat resistance during the heating process. Mathematical models developed for the two hypotheses revealed that the concave survivor curve (on semi-log paper) caused by innate heterogeneity is parabolic and that caused by acquired heat resistance is exponential. The mathematical models were applied to several published survivor curves of different organisms, and heat resistance parameters and the cause of curvilinearity were determined. For the cases studied, the cause of curvilinearity appears to be acquisition of heat resistance rather than innate heterogeneity of spore population.