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The use of high temperature short time heat treatment (HTST) of milk (72°C for 15 seconds) to destroy pathogenic bacteria, reduce the number of spoilage organisms and increase shelf life is well established (Juffs and Deeth, 2007).

The history of pasteurization (pasteurisation is also valid) is fascinating and is notable for its public health success and for the insights of many scientists and engineers. Prior to the introduction of pasteurization, consumption of raw cow milk was a major source of infection by bacteria causing tuberculosis. Pasteurization has eliminated heat-treated-milk as a source of infection. Regrettably raw milk and raw milk products remain a major source of new cases of bovine tuberculosis.

Model probability of detecting a pathogen in food using the Poisson Distribution.

Despite the global use of HACCP systems and a legal requirement for the use of HACCP in many jurisdictions' food poisoning remains an endemic problem and large numbers of people continue to be hospitalised, die and as a result companies either face substantial legal costs and / or in many cases are forced to cease trading.

While the use of HACCP systems significantly reduces the need for microbiological end point testing of foods, sampling schemes and microbial analysis have important roles in system validation and quality assurance.

Further information on the mathematics of microbial sampling

Considerable effort has been devoted to modelling the growth of pathogenic and spoilage bacteria in food. This is referred to as predictive microbiology. Mathematical equations are used to describe the effect of environment, for example temperature, or in more complex models temperature, pH, available water (A_{w}) and other factors that affect microbial behaviour.

The advantages of modelling have been described in the article on "Modelling in Food Technology" including reducing the costs and time required in determining the safe shelf life of new products or in undertaking pathogen challenge testing. However, caution and scientific expertise are required e.g. the Food Safety Authority of Ireland (2012) has cautioned the food industry on the use of predictive models.

The purpose of this article and supporting material is to illustrate how published research in predictive microbiology can be used in practice. This is an area in which Food Science and Food Technology undergraduates sometimes find difficulty. Part of the difficulty may exist because the steps in the calculations involved are not usually presented.

This article describes a model for the growth of salmonella on cut tomatoes and a calculator where you can enter the initial numbers of salmonella, the incubation temperature and the incubation time to obtain a prediction of final numbers.

## Modelling microbial growth

Because of the critical importance of temperature early work attempted to modify the Arrhenius Law to describe microbial growth but this was either unsuccessful or the relationships derived were generally too complex for routine use. In a classic paper, Australian workers (Ratkowsky *et al*., 1982) proposed a relatively simple, two–factor empirical equation (equation 1) to describe the influence of temperature on microbial growth up to the maximum growth temperature of an organism, T_{max}. This is often called the square root model.

Cakes are classified as intermediate moisture foods and may be subject to spoilage by moulds. Water activity (a_{w}), the water that is available, unbound or free, for chemical reactions and microbial growth is a major factor that can be utilised to limit or prevent microbial growth. Cakes generally have a_{w} values ranging from 0.65-0.9.

Mould spoilage on cakes tend to occur on the surface and work has been done to model the water vapour pressure above cakes with temperature to derive models for the mould free shelf life (MFSL) of these products. The water vapour pressure above a food is determined by several factors including temperature, the water content of the food, the solutes present and the water activity in the food.

All foods have their own equilibrium relative humidity (ERH). This is the humidity at a given temperature at which the food will neither lose nor absorb moisture to or from the atmosphere.

If the food is held below its ERH it will lose moisture and become drier; above this value, it will absorb moisture from the atmosphere. The gain or loss of water can have a major effect on a food and can influence shelf life significantly. The EHR is determined by exposing the food to carefully controlled atmospheres containing defined water vapour pressures generated using for example standard solutions of salts.

EHR and water activity (a_{w}) are closely related. Water activity represents the ratio of the water vapour pressure of a food to the water vapour pressure of pure water under the same conditions. Water activity is expressed as a fraction. If this is multiplied by 100 then ERH is obtained. Most bacteria cannot grow below an a_{w} of 0.86 (86 % ERH).

Cauvain and Seiler (1992) found that the logarithm of the MFSL had a linear relationship with EHR over the range 74-90% at 21° and 27°C. The equations derived (equations 1 and 2):

Equation 1. Log10 (MFSL, days at 27°C) =6.42 - (0.065 x ERH%)

Equation 2. Log10 (MFSL, days at 21°C) =7.91 - (0.081 x ERH%)

can be used to determine the shelf life of new cake products rapidly and inexpensively. These equations are available in expensive commercial software for determining the MFSL of cakes.

Determine the mould free shelf life of cakes.

**Literature Cited**

Cauvain, S.P. and Seiler, D.A.L. (1992). Equilibrium relative humidity and the shelf life of cakes. FMBRA Report No. 150, CCFRA, Chipping Campden, UK.

**How to cite this article**

Mullan, W.M.A. (2015).
[On-line]. Available from: __https://www.dairyscience.info/index.php/food-model.html .__ Accessed: 2 April, 2020.

# Modelling the spoilage of pasteurized milk

Spoilage of pasteurized milk is almost always due to the growth of microorganisms. These are generally introduced after heat treatment and are referred to as post process contaminants (PPCs).

The shelf life of pasteurized milk is largely dependent on the number of PPCs and storage temperature (e.g. Muir, 1996). Muir (1996) has described a simple equation (equation 1) relating the number of number of PPCs and storage temperature to shelf life of pasteurised milk.

Equation 1. Shelf life (h)={0.00621*(T+273-(269.55-0.74))*(CFC^{15})-0.11 x ( CFC_{15}) x 2} ^{-2}.

Where T = storage temperature in °K; CFC_{15}, =log10 count after pre-incubation of pasteurized milk at 15°C for 24 hours enumeration on milk agar containing a selective supplement for pseudomonads called cetrimide-fucidincephaloridine (CFC).

Muir (1996) has explained that the equation can predict shelf life at storage temperatures between 6°C and 14°C to within 1 day for between 60 and 90% of samples. The accuracy of the equation has been reported to increase as the storage temperature of the pasteurized milk increases.

Go to Shelf Life of Pasteurized Milk Calculator .

**Literature cited**

Muir, D.D. (1996) The shelf-life of dairy products: 2. Raw milk and fresh products. Journal of the Society of Dairy Technology. 49, 44-48.

**How to cite this article**

Mullan, W.M.A. (2015).
[On-line]. Available from: __https://www.dairyscience.info/index.php/food-model.html .__ Accessed: 2 April, 2020.

**Characteristics of ***Listeria monocytogenes*

*Listeria monocytogenes*

Commercially, cold-filled acidic pickles, sauces (e.g. salad cream, mayonnaise) and food dressings are preserved, and their microbiological safety assured, by the use of acetic acid, salt (NaCl) and sugar. This article provides an overview of a preservation model and access to the model to enable the effect of sauce components and pH to be investigated.

The Comite´ des Industries des Mayonnaises et Sauces Condimentaires de la Communaute´ Économique Européenne (CIMSCEE) has provided guidance on a safety value, Σs, for a microbiologically safe product preserved using acetic acid (Anonymous, 1993). A safe product has been defined as one which is so formulated that when an inoculum of viable cells of *Escherichia coli *is * *added to the product this is reduced by 3 log cycles in less than 72 h. Products exhibiting this level of antibacterial activity have a CIMSCEE safety value (Σs) of greater than 63. Σs is calculated using equation 1: Σs =15.75 (1 - ɑ) (total acetic acid %) + 3.08 (salt %) + (hexose %) + 0.5 (disaccharide %) + 40 (4-pH).

Models in food technology, at the simplest level, are equations showing the relationship between two or more variables. Dunn (1986) defined a mathematical model of a process as a 'system of equations whose solution, given specified input data, is representative of the response to a corresponding set of inputs'.