Survival Models

Survival models are applied to microorganisms in environments that do not permit growth, but where the microorganisms remain alive for times ranging from hours to months (Whiting, 1995). Examples include refrigerated foods and semi-preserved foods, having low water activity, high acidity, or high salt levels, such as refrigerated fresh orange juice (low temperature and pH), yogurt (low temperature and pH, lactate ion), and salami (low pH and water activity, lactate, salt). Inactivation and survival modeling are similar; inactivation is a more active rather than passive process, and the time period is generally seconds and minutes instead of days to months. Plots for primary level data may show a linear decline comparable to plots for thermal inactivation. They may also show lag or shoulder periods in which all of the microorganisms survive before the linear decline begins. The linear model is shown in Eq. 5.14:

where a is the slope and equals — l/D, and t\ is the shoulder period.

More complex two-phase behavior with a longer-lived subpopulation is occasionally observed. The logistic model with a shoulder and one declining slope is shown in Eq. 5.15:

\og(M,/M0) = log[l + exp(-fai)] - log{1 + exp[£(? - tx)}} (5.15)

The model can be expanded to include a resistant subpopulation. Factors that control inactivation, particularly the survival period, are not well understood. The physiological state of the microorganisms may play an important role in determining the length of time they can survive before inactivation starts (shoulder period).

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