Snapshot 1: low injury where

and

Snapshot 2: dominant injury where

and

Snapshot 3: low injury and mortality where

and

Snapshot 4: log-linear injury,

and

Most microbial survival curves can be determined by counting the colonies formed by survivors under optimal growth or germination conditions. The result, therefore, does not account for the uncounted injured cells or spores that could repair the damage if given more time, and for those injured and counted as viable that would not grow under less-than-optimal conditions. A way to avoid this problem is to recover the survivors under optimal conditions, yielding the total count, and separately under stressful conditions under which only the intact cells or spores will produce colonies. The difference between the counts is considered the number of injured cells or spores.

In this Demonstration, you can generate Weibullian curves of the total and of the intact survivors and calculate the curve of the injured ones by subtraction. The generated survival model of the total survival is

, and that of the intact is

, where the

are the momentary survival ratios

, where

and

are the momentary and initial numbers, the

are the scale factors in arbitrary time units, and the

are the dimensionless shape factors. The survival curve of the injured is therefore

.

You can use the sliders to enter the values of

,

,

, and

, as well as the plot axes' limits.

To avoid the generation of unrealistic survival curves, the choice of the Weibullian parameters is limited by the conditions

and

.

Notice that

implies that the survival curve has downward concavity, and

implies upper concavity. The traditional first-order kinetic model is just a special case of the Weibullian model, with

.

The Demonstration plots the curves of the total and intact as solid orange and blue lines and of the injured cells or spores as a dashed red line on linear and semi-logarithmic coordinates.

Note that not all allowed parameter combinations have real-life counterparts.

[1] M. G. Corradini and M. Peleg, "A Weibullian Model of Microbial Injury and Mortality,"

*International Journal of Food Microbiology*,

**119**(3), 2007 pp. 319–328.

doi:10.1016/j.ijfoodmicro.2007.08.035.