represent something else and a mathematical model is one constructed
using mathematical concepts such as constants, variables, functions,
equations,etc.
Mathematical models are not entirely new to food microbiology
having been used with great success since the 1920s for predicting the
probability ofClostridium botulinumspores surviving a particular heat
process and enabling the design of heat processes for low acid canned
foods with an acceptable safety margin (see Section 4.1.5).
The log-linearC. botulinummodel is an inactivation model, describing
microbial survival, but models predicting the potential for microbial
growth to occur under a range of conditions can also be constructed.
These are generally more complex but their development has been
facilitated by the availability and accessability of powerful modern
computers.
There are four essential steps in developing a model.
(1)Planning. This requires a clear definition of the problem:(i) are we interested in spoilage or safety, which organisms
are our main concern?
(ii) what is the appropriate response or dependent variable,
e.g.growth rate, toxin production, time to spoilage?
(iii) what are the relevant explanatory or independent varia-
bles,e.g.temperature, pH,aw?(2)Data collection. The response variable identified in the planning
stage is measured for various levels of the explanatory variables.
These should cover the full range in which we may be interested
since the predictive value of the model is limited to situations
where unknown values can be interpolated. Extrapolation into
areas where there are no data points will not yield valid predic-
tions.
(3)Model fitting. Different models which relate the response variable
to the explanatory variables are tested to see how well they fit the
experimental data.
(4)Model validation. The model is evaluated using experimental data
not used in building the model.A number of different types of model are commonly used. Probabi-
listic models give a quantitative assessment of the chance that a partic-
ular microbiological event will occur within a given time and are most
suited to situations where the hazard is severe. The event most often
described in such models is the probability of toxin formation
(i.e.growth) byC. botulinum.The work was initially prompted by the
54 Factors Affecting the Growth and Survival of Micro-organisms in Foods