Survival Curves of Bacilli Spores with an Activation Shoulder

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This Demonstration simulates and plots realistic survival curves of heat-treated Bacilli spores, at least some of which can be dormant and activated by high temperature. It is based on a purely phenomenological empirical model that accounts for activation and inactivation separately. The activation accounts for the finite number of dormant spores while inactivation accounts for either log-linear or non-log-linear survival kinetics.

Contributed by: Mark D. Normand and Micha Peleg (March 2011)
Open content licensed under CC BY-NC-SA



Snapshot 1: intensive activation followed by accelerated inactivation

Snapshot 2: moderate activation followed by moderate accelerated inactivation

Snapshot 3: little activation followed by moderate log-linear inactivation

Survival curves having an "activation shoulder" have been described by different mathematical models. This Demonstration generates and plots isothermal survival curves of Bacilli spores having an activation shoulder with a four-parameter empirical model. Its equation is: where is the base-10 logarithm of the momentary survival ratio at time , is the hypothetical initial number of dormant spores, is a time constant of the dormant spores' activation, is a characteristic time of the inactivation, and is a parameter that controls the survival curve's post-peak curvature. The activation and inactivation parameters, , , , and , and the plot's time axis maximum and log survival axis minimum are all entered with sliders. The plot shows the survival curve in red, the asymptotic level of the first term in the equation, , in orange, and the hypothetical activation curve (had there been no inactivation) as a dashed gray line. Note that the activation and inactivation rates are characteristic of the bacterial species and vary with temperature. Also note that when the post-peak inactivation is log linear.


M. Peleg, Advanced Quantitative Microbiology for Foods and Biosystems, Boca Raton: CRC Press, 2006.

M. A. J. S. van Boekel, Kinetic Modeling of Reactions in Foods, Boca Raton: CRC Press, 2009.

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