Types of PMP Models

Growth Models

The majority of PMP models are growth models. Model variables include atmosphere (aerobic, anaerobic), temperature, pH, water activity, and in some cases nitrite and other additives. Predictions are made for static temperature conditions.

Survival (Non-Thermal Inactivation) Models

The survival models predict the inactivation of bacterial pathogens as a function of temperature, NaCl, pH, nitrite and lactic acid. The publication for each model should be read to determine the acid that was used in the broth models to adjust broth pH. In general, survival models were developed using an organic acid (lactic acid) as the acidulant.

Thermal Inactivation Models

There are three thermal inactivation models in PMP 7.0. These include C. botulinum, E. coli O157:H7 and L. monocytogenes, with variables for temperature, pH, NaCl, and sodium pyrophosphate.

In their current form, PMP models are not suitable for determining process lethality calculations. To make these calculations, it is necessary to know the Z-value and Tref temperature, and to calculate F-values over a range of changing temperatures.

Cooling Models

You can enter up to 50 combinations of time and temperature in the cooling profile box. You must measure the internal temperature of the product. The minimum recommended cooling times listed in the USDA Food Safety and Inspection Service Appendix B ( are a guide for safely cooling meat products. Depending on the food product, these times may result in a prediction of more than 1 log10 of growth. As stated in Appendix B “If the product remains between 120°F (48.9°C) and 80°F (26.7°C) more than one hour, compliance with the performance standard is less certain.” However, you would need to validate the model in your food product before knowing that the model makes accurate predictions.

The USDA Food Safety & Inspection Service (9CFR-Docket 95-033F) states that the cooling profile of a product cannot result in growth of C. botulinum. In some instances, the PMP C. botulinum cooling model may predict a value of growth that is greater than 0 but less than 0.3 log10. A predicted value lower than 0.3 log10 does not represent growth, because the log10 for one cell division (1 cell becoming 2 cells) is 0.3 log10.

Choosing a PMP Model

Models are developed for specific environmental conditions. For example, the model may have been developed from data generated in a microbiological broth, in a specific food, or in synthetic food. In each case, the accuracy of model predictions is known only for the food for which it was developed. To learn more about the specific conditions under which a model was produced, read the associated references shown in the Source and/or Relevant Publications window.

In certain instances, there may be multiple forms of a model, such as aerobic and anaerobic versions. In this case, choose the model that is closest to your product. For example, choose an anaerobic model if your product is vacuum packaged. Choose an aerobic model if you wish to understand how the bacteria will react when the package is opened and exposed to oxygen. In general, if bacteria can grown under either aerobic or anaerobic conditions, growth is typically faster under aerobic conditions.

In many cases, you will not find a model that exactly matches your food product formulation. In this case, it is better to choose a model that will provide more liberal estimations of growth or inactivation. For example, culture media (broth) models typically predict shorter Generation Times (or higher growth rates) than those observed in food containing other microorganisms and additives. This is true as long as you set the environmental parameters (temperature, pH, water activity/NaCl) to the values that match your food. A similar example is that a sterile raw food model will normally predict shorter Generation Times (or higher growth rates) than a non-sterile raw food or one that contains inhibitory additives.

Operating the PMP Program

The model predictions were developed for a specific range of environmental conditions. For example, the Aerobic A. hydrophila in Culture Media model was developed over a temperature range of 41°F (5°C) to 107.6°F (42°C). The accuracy of predictions made inside (interpolation) this range is known. However, the accuracy of predictions made outside (extrapolation) of this range (e.g., 150°F) is not known. The software does not permit values outside this range of temperature to be entered.

Model Interpretation

Without experience in the use of models, it is difficult to know if the model that you use will over- or under-predict bacterial growth or inactivation when applied to another food matrix. As such, it is best to use models to understand potential trends in bacterial behavior as the environmental conditions change. Only through validation studies (e.g. inoculated pack studies) would you be able to have confidence in model interpretation for your specific food of interest.

Depending on the pathogen, spoilage flora (e.g., bacteria, fungi) can markedly inhibit the growth of pathogenic bacteria. This is especially apparent at refrigeration temperatures where the growth rates of psychotropic (cold-liking) spoilage organisms may be greater than that of the pathogen. Therefore, in these situations, the maximum population density (level at stationary phase) of a pathogen may be 3 to 5 log10 levels less than that observed in a pure culture. Also, the growth rate may be inhibited. Therefore, in general, Generation Times will be shorter, and growth rates and maximum population densities will be higher in sterile culture systems compared to systems containing spoilage flora. Again, only through validation studies (e.g. inoculated pack studies) would you be able to have confidence in model interpretation for your food of interest.

Using a Static Temperature PMP Model for Changing Conditions

Currently, there are dynamic temperature models for C. botulinum and C. perfringens. For all other models, predictions are made for static temperatures. We are in the process of producing dynamic temperature models for a variety of other pathogens, and expect these to be available in future versions of the PMP.

To use a static model for situations where temperature changes over time, you will need to calculate the growth at specific temperatures, and then add these individual growth calculations to determine the total predicted growth over the entire time-temperature range. For example, suppose you want to predict the growth of L. monocytogenes in a product that has the following time-temperature profile:

0.0 hours 98.6°F

0.5 hours 71.2°F

1.5 hours 63.4°F

3.5 hours 50.1°F

For fail-safe predictions, we will assume that the product was at 98.6°F for 0.5 hours, at 71.2°F for 1 hour, and at 63.4°F for 2 hours. More conservative estimations can be made if you collect time-temperature data in shorter time intervals.

First, set the environmental conditions to match your product. In this example we will use the aerobic broth culture L. monocytogenes model for NaCl. Set the conditions to: pH=6.5, NaCl=1.0%, 0 ppm nitrite. Set the “Initial Level” to 3.0.

Next, set the temperature to 98.6°F (37°C) then click the box “Calculate Growth Data”.

Next, click the “No Lag” box (for fail-safe predictions). Since we are assuming that the product was at 98.6°F for 0.5 hours, we subtract log 3.0 (from the Initial Level) from the “log(CFU/ml)” value at 0.5 hours. However, you will notice that there is no value given at 0.5 hours. Therefore, average the count for 0.4 (3.64 log[CFU/ml]) and 0.6 hours (3.76 log[CFU/ml]). This would equal (3.64 + 3.76)/2 = 3.70. Subtract 3.0 (starting level) from 3.7 and this equals 0.70 log CFU/ml. Record this number.

Next do the same calculation at 71.2°F (21.8ºC) for 1 hour, keeping the initial level at 3.0. The prediction at 1.0 hour is 3.63 log CFU/ml. Therefore, subtract 3.0 from 3.63, and this equals 0.63 log CFU/ml. Record this number.

Finally, repeat this procedure at 63°F (17.2ºC). At 2 hours the prediction is 3.67 log CFU/ml. Subtract 3.0 again from 3.67, and this equals 0.67 log CFU/ml. Record this number.

Now add all three numbers: 0.70+0.63+0.67 = 2.0. Therefore, the fail-safe prediction is for 2.0 logs of growth with this cooling profile.

As with all PMP models, you need to validate the predictions for food types and formulations that are different from the model.

Using Models in HACCP Plans

Models are only valid for the conditions used to produce the model. For example, the reference(s) found in the PMP “Source and/or Related Publications” window presents an explanation of the methodologies used to produce the model. Therefore, if the conditions (e.g., food formulation) used to produce the PMP model do not match your food system, then you must validate the model for your specific application. Validation normally involves independent laboratory studies where your product is inoculated with a specific bacteria and then you record the levels of growth or inactivation. These data can then be compared to model predictions to see if they are within the predicted 95% confidence intervals, and/or if they are fail-safe. If they do not match, then the model is not valid (safe) for your application and should not be used in HACCP plans to make safety decisions. Assuming sufficient experimental data have been collected, your data may instead be used to develop a new model that would be valid for your food product.

References for Models

The reference(s) or source for each model is shown in the “Source and/or Relevant Publications” window. For references in which the senior author(s) is a government employee, the PDF file is provided. For articles with other types of authorship, the reference is not provided as a PDF file, due to copyright restrictions. Note - there may be multiple publications for a model. Typically this is because different environmental parameters were modeled at different dates.

Model Inputs


This input window is where you enter the temperature.

In the case of C. perfringens and C. botulinum dynamic cooling models, a time-temperature profile must be entered. You can directly type in the cooling profile data in the table on the left side of the screen or you can import the data from a file. To learn how to input the data, click on the “Show me how” button at the bottom of the time-temperature window. After following these directions, you can import the time-temperature data by clicking on the “Import Cooling Profile” button at the bottom of the time-temperature window.


In this window, you enter the pH value.

Water activity/NaCl Concentration

In general, the models allow you to input the %NaCl. A corresponding water activity (Aw) value is automatically calculated to the right of the NaCl value. (Note – the water activity value is calculated using a standard equation based on adding NaCl. The water activity of a food product may be different based on other components of the food, such as carbohydrates (sugars), amino acids and food additives.) It is more accurate to measure the water activity of your product, and then set the %NaCl to match the desired water activity.

Initial Level and Level of Interest

The “Initial Level” is an arbitrary value that you can set to indicate an actual or assumed initial level of bacteria in the sample at the beginning of the growth scenario. The lowest and highest values that you can select are restricted based on the levels used to generate the model data.

The “Level of Interest” is an arbitrary level that you select for a target level of growth. There is no recommended Level of Interest. You must select the level.

The calculated time to reach the Level of Interest will be shown in the box labeled “Time to Increase [Level of Interest minus Initial Level] logs”.

The level of a pathogen that poses a health risk depends on many factors, such as the susceptibility of the affected population and the quantity of food that is consumed. We do not indicate an acceptable level of a pathogen in food.

Lag and No Lag Options for Growth Models

Selecting the “Lag” option will result in a prediction of the Lag Phase Duration (LPD) based on the experimental data for the model. Selecting “No Lag” will remove the period of time for the calculated Lag Phase, and will begin predictions with immediate growth of the bacteria. Note - a portion of the curvature between the LPD and the Growth Phase is included in the Growth Phase. Therefore, the starting level that appears in the chart and table will not be the same as the value that you set as the Initial Level. The time calculated to reach the Level of Concern will use the Initial Level, although it will not appear in the table or chart.

Model Output

Confidence Limits and More Fail-Safe Predictions

The Upper (UCL) and Lower Confidence Limits (LCL) indicate the variation in the predictions at a confidence level of 95%. If you are looking for more fail-safe predictions, then use the UCL. Use the LCL if you want more conservative estimates.

For growth models, chose the “No Lag” prediction option to get a more fail-safe prediction. This option does not add a Lag Time to the growth scenario. Also, models that were developed in a sterile broth system are more fail-safe for Generation Time. Typically, the Generation Time/Growth Rate observed in broth media under optimum conditions for NaCl/water activity and pH is equal to or greater than that observed in food containing other microorganisms.

For inactivation models, more fail-safe predictions can be attained by setting the environmental parameters to values that predict a greater inactivation rate.


In version 7.0, to print the graph, place your mouse over the graph, right-click, and select “Print.” To print the table, place your mouse over the table, right-click, select “Select All”, then right-click again and select “Print Selected.” To print only specific portions of the table, highlight the cells that you want to print, then right-click and select “Print Selected.” To print the entire PMP window, in the Toolbar select “File” then “Print Form.”

Note - this will not print portions of the table, graph or publication window that are not visible on the screen. To print all of the publication information, highlight the text with your mouse, then hold the CTRL key and press the C key. You can then paste this text into another document, such as Microsoft Word7, and print from that document.

Copying, Distributing and Citing the PMP

We encourage you to distribute the PMP to other interested persons and organizations. Prior permission is not required from the USDA-ARS for distributing or copying the PMP. You do not need permission to download the PMP. You do not need permission to make copies. There is no cost to download or use the PMP. You can copy and distribute the PMP to other persons or computers.

We do request that you credit the producers of the PMP and/or the authors of a specific PMP model when including PMP information in an article, journal or other type of publication.

The citation for the PMP can include the following information:

“US Department of Agriculture, Agricultural Research Service, Eastern Regional Research Center, Wyndmoor, Pennsylvania, USA. [The year of the PMP version, e.g. 2003 for version 7.0].

The web address,, can be referenced as a site to download the PMP.

When citing a specific model in the PMP, we request that you use the reference(s) that appears in the model window. For example, for the Aerobic A. hydrophila model in Culture Media, there are two citations:

S.A. Palumbo, D.R. Morgan and R.L. Buchanan. Influence of Temperature, NaCl, and pH on the Growth of Aeromonas hydrophila, Journal of Food Science (1985) 50:1417-1421 -

S.A. Palumbo, A.C. Williams, R.L. Buchanan and J.G. Phillips. Model for the Aerobic Growth of Aeromonas hydrophila K144: Journal of Food Protection (1991) 54:429-435 -

ARS Scientists Currently Managing the PMP

Dr. Vijay Juneja -; tel. 215-233-6500

Dr. Tom Oscar -; tel. 410-651-6062

FSIS Advisor

Dr. Tim Mohr –; tel. 503-399-5831

Questions about specific models

Some of our models list the author(s) of the studies. If so, please contact the author(s) for specific questions.

Others Sources of Information and Data

Click on the Reference tab on the File menu and select the article "Model Development." This article provides an abbreviated overview about model development. Also, in the same Reference tab, you can select "Publications List" and look for other publications that are offered in PDF format or as a citation.

Another source, although more technical in nature, is a book titled Predictive Microbiology: Theory and Application by McMeekin et al. (1993). A good book on general Food Microbiology is Modern Food Microbiology by James Jay (2000).

The published literature is a good source of information about bacterial behavior in food. However, the behavior of bacteria has not been described for the majority of formulated foods. Another source for data is a free on-line database called ComBase, located at http://www. This database contains thousands of records for various pathogenic and spoilage bacteria under many different environmental conditions.

Other Topics

In general, bacterial numbers decline when the product is frozen. The extent of decline is based on various factors, such as the freezing temperature and the rate of temperature change to reach a frozen state.


Acid Tolerance

Microorganism survival can be affected by the free hydrogen ions (pH value) of the dissociated acids, and to the un-dissociated acids that may penetrate into the cell and inhibit important metabolic processes. Some microorganisms exhibit less inhibition or lethal effect of acids (disinfectants, lactic acid). Such tolerance is dependent on the type of acid.


A substance added to food or beverages to lower pH and/or to impart a tart, acidic taste.


A microorganism requiring oxygen (O2) for growth.


An organism that does not require oxygen (O2) for growth.

aw (water activity)

Symbol for water activity, referring to the amount of water available for growth and multiplication of microorganisms. Water activity corresponds to the relative humidity (rH) above a food in a closed space after equilibrium, e.g. 70% rh/100 = 0.70 (aw).

Bacterial Growth Curve

A graph indicating the growth of a bacterial population over time.

Confidence Limits, Upper (UCL) and Lower (LCL)

These indicate the variation in predictions at a specific confidence level, typically 95%. If you are looking for more fail-safe predictions, then use the UCL. Use the LCL if you want more conservative estimates.

Colony Forming Units (CFU)

Enumerating microorganisms by measuring the number of colonies formed on an agar medium.


The decimal reduction time, or the time that is required to destroy 90% of the organisms. This value is numerically equal to the time for the survivor curve to transverse one log cycle.

Death Phase

A decrease in viable microorganisms.

Dynamic Temperature Model

A model where temperature changes over time.

Extrinsic Factors

The properties of the storage environment (temperature, relative humidity, presence or absence of gasses) that affect both the food and the microorganisms.


The log reduction in cell numbers over a time-temperature profile, expressed at a specific reference temperature (Tref).

Generation Time

The time that it takes for bacteria to divide (double in number). To convert this to Growth Rate, simply divide 0.301 by the Generation Time. The value 0.301 is the log10 of 2.

Growth Rate

The change in bacterial numbers over time, typically expressed as log10 CFU/hour. To convert this value to Generation Time, divide 0.301 by the Growth Rate.

Hazard Analysis and Critical Control Points (HACCP)

A system to identify, evaluate and control hazards to an acceptable level of risk.

Heat Inactivation Model

Models that predict the effect of heat on organism inactivation.


To introduce a microorganism into a matrix, such as culture media, food or host.

Intrinsic Factors

Food-related factors such as moisture, pH, additives, and available nutrients that influence microbial behavior.

Lag Phase (Duration)

The time required for the cell population to adjust to the broth or food environment and begin growth.

Level of Concern

An arbitrary level selected for a targeted level of growth. The calculated time to reach the Level of Concern is shown in the box labeled “Time to Increase __ logs”.

Maximum Population Density

The highest level of microbial growth observed in the sample. This is commonly expressed as colony forming unit per gram or milliliter.

Minimum Growth Temperature

The lowest temperature at which an organism will grow.


A disease-causing organism.


The symbol for hydrogen ion (H+) concentration; a measure of the relative acidity or alkalinity of an environment.

Primary Models

Models that describe changes in microbial numbers or other microbial responses over time. The model may quantify colony-forming units per ml, toxin formation, or substrate levels (which are direct measures of the response), or absorbance or impedance (which are indirect measures of the response). A mathematical equation or function describes the change in a response over time with a characteristic set of parameter values. Examples of primary growth models are the Baranyi and Gompertz.

Plate Count

A method of determining the number of bacteria in a sample by counting the number of colony forming units on a solid culture medium.

Secondary Models

Models that describe changes in a primary model parameter as a function of changes in the environment, such as temperature, pH, or water activity. Examples of secondary models are the response surface model, Arrhenius relationship and square root model.

Static Temperature Model

A model where temperature remains constant.

Stationary Phase

The phase of microbial growth where the population growth ceases over a period of time.

Survival Models

In the PMP, this refers to non-thermal inactivation models.

Tertiary Models

Computer software routines that turn the primary and secondary models into "user-friendly" interfaces for model users.

Thermal Death Time (TDT)

This is the time necessary to kill a given number of organisms at a specified temperature.


Bacteria that can withstand higher than normal temperatures.


A compound produced by a bacterium that can cause illness in a living organism. Examples are enterotoxins that affect the intestine and neurotoxins that attack the nervous system.

Validation (model)

Laboratory studies where a product is inoculated with bacteria and the level of growth or inactivation is recorded. These data are then compared to model predictions to determine if they are within the predicted confidence intervals.


The change in temperature necessary for a 10-fold reduction in the D-value.