Mathematical Model of Thermal Destruction of Bacillus stearothermophilus Spores

The experimental survival curves of Bacillus stearothermophilus spores in aqueous suspension, for six constant temperatures ranging from 105 to 130 degrees C, displayed an initial shoulder before a linear decline. To interpret these observations, we supposed that, before the heat treatment, the designated spore suspension contained a countable and mortal N(0) population of activated spores and an M(0) population of dormant spores which remained masked during spore counting and had to be activated before being destroyed by heat. We also hypothesized that the mechanisms of both activation and destruction are, at constant temperature, ruled by first-order kinetics, with velocity constants k(A) and k(D), respectively. Mathematical analysis showed that this model could represent not only our experimental survival curves, but also all other shapes (linear and biphasic) of survival curves found in the literature; also, there is an inherent symmetry in the model formulation between the activation and destruction reactions, and we showed that the dormancy rate (tau = M(0)/N(0)) is the only parameter which permits a distinction between the two reactions. By applying the model to our experimental data and considering that the dormancy rate is not dependent on the treatment temperature, we showed that, for the studied suspension, the limiting reaction was the activation reaction.