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.