Postharvest Supply Chain with Microbial Travelers: a Farm-to-Retail Microbial Simulation and Visualization Framework

Claire Zoellner,a* Mohammad Abdullah Al-Mamun,b Yrjo Grohn,b Peter Jackson,c Randy Woroboa

aDepartment of Food Science, Cornell University, Ithaca, New York, USAbDepartment of Population Medicine and Diagnostic Sciences, College of Veterinary Medicine, CornellUniversity, Ithaca, New York, USA

cDepartment of Operations Research and Information Engineering, Cornell University, Ithaca, New York, USA

ABSTRACT Fresh produce supply chains present variable and diverse conditions thatare relevant to food quality and safety because they may favor microbial growth andsurvival following contamination. This study presents the development of a simulationand visualization framework to model microbial dynamics on fresh produce movingthrough postharvest supply chain processes. The postharvest supply chain with micro-bial travelers (PSCMT) tool provides a modular process modeling approach andgraphical user interface to visualize microbial populations and evaluate practicesspecific to any fresh produce supply chain. The resulting modeling tool was vali-dated with empirical data from an observed tomato supply chain from Mexico tothe United States, including the packinghouse, distribution center, and supermarketlocations, as an illustrative case study. Due to data limitations, a model-fitting exer-cise was conducted to demonstrate the calibration of model parameter ranges formicrobial indicator populations, i.e., mesophilic aerobic microorganisms (quantifiedby aerobic plate count and here termed APC) and total coliforms (TC). Explorationand analysis of the parameter space refined appropriate parameter ranges and re-vealed influential parameters for supermarket indicator microorganism levels on to-matoes. Partial rank correlation coefficient analysis determined that APC levels in su-permarkets were most influenced by removal due to spray water washing andmicrobial growth on the tomato surface at postharvest locations, while TC levelswere most influenced by growth on the tomato surface at postharvest locations.Overall, this detailed mechanistic dynamic model of microbial behavior is a uniquemodeling tool that complements empirical data and visualizes how postharvest sup-ply chain practices influence the fate of microbial contamination on fresh produce.

IMPORTANCE Preventing the contamination of fresh produce with foodborne patho-gens present in the environment during production and postharvest handling is an im-portant food safety goal. Since studying foodborne pathogens in the environment is acomplex and costly endeavor, computer simulation models can help to understandand visualize microorganism behavior resulting from supply chain activities. Thepostharvest supply chain with microbial travelers (PSCMT) model, presented here,provides a unique tool for postharvest supply chain simulations to evaluate micro-bial contamination. The tool was validated through modeling an observed tomatosupply chain. Visualization of dynamic contamination levels from harvest to the su-permarket and analysis of the model parameters highlighted critical points where in-tervention may prevent microbial levels sufficient to cause foodborne illness. ThePSCMT model framework and simulation results support ongoing postharvest re-search and interventions to improve understanding and control of fresh producecontamination.

KEYWORDS fresh produce, microbial dynamics, postharvest, supply chain

Received 9 April 2018 Accepted 18 June2018

Accepted manuscript posted online 29June 2018

Citation Zoellner C, Al-Mamun MA, Grohn Y,Jackson P, Worobo R. 2018. Postharvest supplychain with microbial travelers: a farm-to-retailmicrobial simulation and visualization framework.Appl Environ Microbiol 84:e00813-18. https://doi.org/10.1128/AEM.00813-18.

Editor Donald W. Schaffner, Rutgers, The StateUniversity of New Jersey

Copyright © 2018 American Society forMicrobiology. All Rights Reserved.

Address correspondence to Claire Zoellner,cez23@cornell.edu.

* Present address: Claire Zoellner, Departmentof Population Medicine and DiagnosticSciences, College of Veterinary Medicine,Cornell University, Ithaca, New York, USA.

FOOD MICROBIOLOGY

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Maintaining the quality and safety of fruits and vegetables from harvest to thesupermarket is essential to the produce industry, as it provides consumers with

abundant, nutritious food products. Depending on environmental conditions, microbialcontamination of fresh produce can occur during production, harvesting, postharvesthandling, distribution, retail and/or final preparation (1, 2). To lower the risk of con-tamination with human pathogens from these various pre- and postharvest sources,fresh produce growers and packinghouses are required to follow good agriculturalpractices and maintain equipment, buildings, and personnel under clean and sanitaryconditions using risk-based intervention strategies (3). While different treatments maybe used to sanitize fresh produce and packing equipment, once a product or surface iscontaminated, these methods typically reduce the number of microorganisms butcannot guarantee safety.

Following contamination, the postharvest steps involved with moving produce tomarkets (i.e., the supply chain) may present conditions which either encourage ordiscourage microbial growth, survival, and/or transmission (4). As the nature of producesupply chains is increasingly variable and diverse, conditions may have an impact onproduct quality and safety. Particularly, modeling the effect of management andhandling practices throughout the postharvest supply chain on low-level microbialcontamination is of interest for understanding the consequences of such contamina-tion events. For example, the survival of viruses and pathogenic bacteria on freshproduce and surfaces commonly used in food supply chains has been shown (5–7).Transmission of viruses, pathogenic bacteria, and indicator microorganisms betweensurfaces and food, including ready-to-eat products and fresh produce, is well charac-terized (8, 9). Maintenance of consistent and low storage temperatures plays animportant role in limiting subsequent growth (10). However, relatively little quantitativedata are presented on the level, origin, and fate of microorganisms, including potentialhuman pathogens, through the entire system between field and retail, thus limiting theability to adapt recommended management practices to a specific commodity orsupply chain step (2).

The systems biology approach has been utilized for studying outbreaks of food-borne illness in order to obtain an understanding of the biology in an often complex,intricate network (11, 12). For example, risk assessment models have been conductedin various food matrices and production chains, such as fresh pork (13), leafy greens(14–16), cheese (17), poultry (18), and berries (19), as well as on-farm preharvestcontamination pathways (20–22). While these detailed and mechanistic models allowfor both conceptual understanding of contamination dynamics during the entireproduction process and estimations of the impact of the burden to public health, theyare often developed for specific microorganisms in specific food matrices. Alternatively,modular process modeling has been applied to meat and other processed food andinvolves segmenting the production chain into generic processes that encompassmicrobial behavior: growth, survival, inactivation, and transfer (23). This modular ap-proach, also utilized by several software tools (11, 24), is both generic and flexible andshows promise for tracing microbial behavior in a variety of fresh produce commoditiesand postharvest supply chain practices.

Our objective was to develop a simulation and visualization framework for modelingthe fate of microbial contamination on fresh produce across the entirety of postharvestsupply chains. This model, named postharvest supply chain with microbial travelers(PSCMT), provides a generic deterministic framework and graphical user interface (GUI)for modeling and visualizing dynamic microbial populations through any fresh producesupply chain, that is, on fresh produce after harvest until sale at a retail location. Thevalidity of PSCMT was assessed using two model criteria (25) to predict the levels ofmicrobial indicators (aerobic mesophilic microorganisms quantified by aerobic platecount, here termed APC, and total coliforms [TC]) observed on Mexican Roma tomatoesmoving from the packinghouse to supermarkets, as an illustrative case study of apostharvest supply chain of fresh produce. Key assumptions and literature values wereutilized during model development and parameterization.

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RESULTSPSCMT visualization of microbial dynamics. PSCMT was adapted to an observed

postharvest supply chain of fresh Roma tomatoes (Fig. 1) and was parameterized forsimulation of the behavior of both aerobic mesophilic microorganisms (APC and TC) onfresh tomatoes (Table 1). A load of microorganisms, input at the beginning of thesupply chain model as either a single event or a vector of multiple contaminationevents, may be traced across the modeled supply chain operations and displayed onthe PSCMT interface in a pivot chart format for visualization. An example calculationinvolving the introduction of a single tomato observed to contain 1,500 CFU/g of APCat postharvest holding (26) and simulation with 1-min time steps through the pack-inghouse is presented in Table S1 in the supplemental material. In this example, outputover 7 days through the modeled supply chain resulted in dynamic levels due tomicrobial operations of removal, growth, and transfer (Fig. 2). Although the contami-nation level decreased during sorting and washing, the total contamination leaving thepackinghouse increased to 631 CFU/g due to growth during final packing. Contami-nation was also spread among other tomatoes in the packinghouse due to contami-nation of surfaces during both sorting steps (Fig. 2, inset). Subsequent holding timesfrom distribution to the supermarket further increased contamination levels on toma-toes presented to consumers at retail. The flexibility of the PSCMT pivot chart layoutprovides a variety of outputs and formats available for visualizing contaminationdynamics in a modeled supply chain (see model files in the supplemental material).

Fitting of model parameters to observed supply chain. Simulations using PSCMTbaseline parameter values (Table 1) matched observed APC and TC concentrations ontomatoes (Fig. 3). The model predictions fit observed APC levels at the packinghouseand distribution center locations, as values fell within the observed ranges and werenot significantly different after Bonferroni correction (Wilcoxon t test, P � 0.02). TheAPC model predictions differed from observed levels at the supermarket (Wilcoxon ttest, P � 0.02), suggesting differences in modeled and actual conditions related tostorage, handling, and sale of tomatoes. For TC dynamics, the model predictions andobserved levels were not different for packinghouse and supermarket locations (Wil-coxon t test, P � 0.02). TC declined during distribution and storage at the distribution

FIG 1 PSCMT model operations for the tomato supply chain used in model fitting. See Table 1 for a description of parameter valuesfor APC and TC for each operation. The supply chain begins with contamination at postharvest (box 1) and continues through activitiesto sort, wash, and pack the tomatoes (boxes 2 to 6) before transportation to and storage in a distribution center (box 7). The supplychain ends with activities to transport and store and then display and sell tomatoes at the supermarket (box 10). The transfer functionis detailed in the inset box: �, transfer coefficient from the product to the surface; �, transfer coefficient from the surface to theproduct; �, growth rate of the microorganism on the surface; and k, length of the surface. The transfer function alters two microbialpopulations in the supply chain: Np, the microbial population in the product, and Ns, the microbial population on the surface. Otheroperation parameters are shown in the supply chain: no, contamination load; �, log10 reduction from washing; and �, microbial growthrate.

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center in the observed supply chain. Although this operation was modeled andparameterized as survival instead of growth (Table 1), there was a significant differencein the mean model and observed TC levels (Wilcoxon t test, P � 0.02), suggesting apoor fit for TC at this model operation. Varying the baseline model parameters by 75%and conducting parameter space simulations with the same initial dynamic input atpostharvest revealed the distribution of possible APC and TC levels on tomatoes atsubsequent locations of the supply chain (Fig. 4, entire). Therefore, searching andfiltering of the parameter space simulations, based on those iterations that resulted inAPC and TC levels within 10% of the median observed levels at the supermarket,identified the subset of plausible parameter values for the Roma tomato postharvestsupply chain (Fig. 4, filtered, and Table 2). Interestingly, filtering of the APC parameterspace based on best fit to supermarket indicated increased median levels at thepackinghouse, distribution center, and supermarket (Fig. 4, APC–filtered), while this wasnot the case for filtering of the TC parameter space (Fig. 4, TC–filtered).

Identification of influential supply chain parameters. Following model fitting,sensitivity analysis simulations were conducted with fixed contamination inputs atpostharvest and the 75% parameter space about the model parameters. Partial rankcorrelation coefficient analysis was used to identify the most influential model param-eters for APC and TC levels at the retail operation of the supermarket location (Fig. 5).Removal from spray washing (�) with chlorinated water was the most influentialparameter on retail APC levels and ranked lower among the influential parameters onTC levels. Growth on tomato surfaces during postharvest holding after packing (�1),transportation to and storage at the distribution center (�2), transport to andstorage at the supermarket (�3), and retail sale (�4) were also important parametersthat increased the final APC and TC concentrations at the supermarket. Cross-contamination from tomatoes to the supply chain surfaces (�) was negativelycorrelated with APC and TC levels, while cross-contamination from surfaces totomatoes and growth on supply chain surfaces (� and �) were not influential fordetermining APC and TC retail levels.

TABLE 1 PSCMT model parameters for behavior of APC and TC on tomatoes in the postharvest supply chain from field to supermarketa

Supply chainlocation

Supply chainstep Operation Time

Parameter

Symbol

Unit(whereapplicable)

APCreference value Source(s)

TCreference value Source(s)

Field Postharvest Contamination 1 min n0 log10 CFU/g 1.9 � 1.1b 26 0.22 � 0.7b 26

Packinghouse Sort 1 Transfer 5 min �1 0.02 30, 43 0.02 30, 43�1 0.01 43 0.01 43�1 min�1 0 Assumed 0 Assumed

Wash Removal 2 min � log10 CFU 0.5 26, 29 0.1 25Dry Transfer 3 min �2 0.02 43 0.02 43

�2 0.01 43 0.01 43�2 min�1 0 Assumed 0 Assumed

Sort 2 Transfer 10 min �3 0.02 30, 43 0.02 30, 43�3 0.01 43 0.01 43�3 min�1 0 Assumed 0 Assumed

Pack Growth 400 min �1 min�1 0.00147 44 0.00138 44

Distributioncenter

Transport andstore 1

Survival 4 days �2 min�1 0.00029 44 �0.000144 Assumed

Supermarket Transport andstore 2

Growth 1 day �3 min�1 0.000656 44 0.000448 44

Display Transfer 5 min �4 0.02 30, 43, 45 0.02 30, 43, 45�4 0.03 43, 45 0.03 43, 45�4 min�1 0.000656 Assumed 0.001 Assumed

Sale Growth 12 h �4 min�1 0.000656 44 0.001 44aAPC, mesophilic aerobic bacteria quantified by aerobic plate count; TC, total coliforms.bGeometric mean � standard deviation of the observed at the postharvest location of the supply chain. The contamination input for baseline simulations was adynamic vector of the exact values (n � 130).

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DISCUSSION

Foodborne illness associated with contaminated fresh produce can be mitigated byunderstanding and controlling key supply chain factors. A number of existing riskassessment models have focused on on-farm interventions to describe the impact ofseason and field temperature, animal intrusion, and soil amendments on contaminationof various fresh produce commodities, lettuce and leafy greens in particular (20–22). Inthis study, a detailed and mechanistic model of dynamic microbial behavior wasdeveloped to provide a tool specific to the unique postharvest practices in freshproduce supply chains. This model is not directly intended for extrapolation to post-harvest risks but rather for the individual study of contamination routes and dynamicsin a particular supply chain. Illustration of the PSCMT model and parameter fitting forthe observed supply chain demonstrated (i) how the generic framework can beimplemented for a specific supply chain and fresh produce commodity at a verydetailed scale, (ii) how parameters can be refined to fit supply chain conditions, givenempirical data, (iii) what kinds of results are obtained and how to interpret them, and(iv) how the deterministic framework is an approach for understanding the microbial

FIG 2 Postharvest supply chain with microbial travelers (PSCMT) interface demonstration of options for visualization of microbial dynamics tracking throughthe modeled supply chain. Starting with a single contamination event at postharvest, the change in contamination level (CFU/g tomato) through eachoperation, corresponding with the operation step numbers in Fig. 1, is given per hour on the first day of the supply chain from postharvest through packing(inset) and per day postharvest in the supply chain from distribution center to supermarket (main figure). Overlapping lines indicate no change in concentrationbetween operations over time, as between step 8, “trans n storage” (transportation and storage) and step 9, “display.” The code and instructions provided inthe supplemental material may be referenced to use this interactive interface for presentation of the simulation results in various formats.

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dynamics of postharvest supply chains. In the context of other fresh produce riskassessment models, PSCMT presents a tool for simulating potential contaminationpathways and the fate of microbial contamination levels during postharvest handlingand supply chain conditions to assist in identifying optimal intervention strategies.

The supply chain of fresh produce often resembles a web of growers, packers,distributors, and retailers that handle products via various mechanisms and hold theproducts for various lengths of time under different conditions (2, 4, 27, 28). Therefore,the main contributions of PSCMT lie in the flexible acyclic network and discretization oftime between locations of any fresh produce supply chain. The approach described themicrobial behavior as generic processes that occur throughout handling, distribution,and storage conditions of fresh produce supply chains. The GUI allowed for thecustomization of supply chain operations, conditions, and parameters, as well asvisualization of model output. User-defined time steps both within each operation andacross the supply chain simulation allow for modeling the effects of both instantaneousand prolonged events on microbial populations. In this way, the PSCMT frameworkcaptures in detail the key postharvest processes impacting microorganisms on producesurfaces.

The final model parameters presented dynamics similar to those in the observedsupply chain, and the model-fitting exercise defined the appropriate parameter rangesthat fit the empirical supermarket data. Sensitivity analysis identified influential param-eters and revealed that more research may be needed to understand how supply chainoperations affect more sporadic and low-level microbial populations, such as TC ontomatoes presented in this study. Particularly, removal was the most influential modelparameter for APC but was less influential for TC levels. Removal during washing viadump tanks or spray and brush systems has been studied for several produce com-modities, and the importance of chlorine efficacy is well reported (29–31); however, itis also well established that removal of microorganisms from produce by chlorinatedwashing is unpredictable and prone to the cross-contamination of other products (32,33). Furthermore, growth rates at the packinghouse, distribution center, and retailstorage were highly influential parameters, most likely due to long holding times andvariable conditions suitable for survival and growth. It is well understood that growthand survival of aerobic spoilage organisms on fresh produce surfaces may be influ-enced by temperature fluctuations, improper storage and handling resulting in dam-

FIG 3 Box plots of observed and PSCMT-predicted aerobic plate count (APC) and total coliform (TC) levels (log10 CFU/g)on tomatoes (n � 130) moving along the supply chain locations. The thick horizontal black bars indicate the medians, theshaded boxes indicate the interquartile ranges, whiskers represent the extreme values, and circles represent outlier values.Significant differences between observed and modeled levels at the packinghouse, distribution, and supermarket locationsafter Bonferroni correction of the P value are indicated by an asterisk.

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aged produce, and maturation of the product (34, 35). Narrow ranges for transferbetween surfaces were identified when searching the parameter space, and a small andnegligible correlation suggested that these parameters may be well defined by litera-ture or that cross-contamination is not as influential on microbial populations as otheroperations in the supply chain. As anticipated, the different dynamics between the twomicrobial populations on products in the same supply chain reiterate the need for adetailed and flexible modeling framework, such as PSCMT.

As presented, the deterministic framework was designed to model microbial con-tamination on produce through fixed postharvest supply chain conditions. Althoughthe use of dynamic inputs captured variability in contamination inputs, several aspectsof the current PSCMT model and the observational study present limitations. To ourknowledge, there is no empirical data set on human pathogens within production lotsof fresh produce at different postharvest supply chain locations. Therefore, empiricaldata on microbial indicator populations, APC and TC, were used to demonstrate the fitof PSCMT to an actual supply chain. Although APC and TC are interpreted as indicatororganisms for both quality and hygiene, they were used here to demonstrate a dynamicmicrobial population on the surface of fresh produce. We recognize the limitation inpredicting the risk of human illness based on indicator microorganisms, so we place

FIG 4 PSCMT parameter space simulation results (entire space � 2,000 iterations) and filtered results for the distribution of aerobicplate count (APC) and total coliform (TC) levels (log10 CFU/g) on tomatoes at the packinghouse (A), distribution center (B), andsupermarket (C) locations of the postharvest supply chain.

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more emphasis on the resulting levels and spread of microorganisms through producehandling and transportation from a packinghouse to supermarkets. The model fittingwas conducted via simulations of a single supply chain on a 1-min time step. Theobservational microbial data across fresh produce supply chains was minimal andfragmented, as the data used for model fitting was collected from tomato samples at

TABLE 2 Fitted model parameter values and ranges for APC and TC in the observed supply chaina

Step and supplychain operation Parameter name Symbol

Unit(whereapplicable)

APC mean value(5th, 95th percentile) TC mean value (5th, 95th percentile)

1. Postharvest Load n0 log CFU/g Baseline input Baseline input

2. Sort 1 Transfer coefficient �1 0.02 (0.007, 0.034) 0.02 (0.006, 0.034)Transfer coefficient �1 0.01 (0.003, 0.017) 0.01 (0.003, 0.017)Growth rate �1 min�1 4.83 � 10�4 (4.5 � 10�5, 9.3 � 10�4) 3.8 � 10�4 (4.2 � 10�5, 7.2 � 10�4)

3. Wash Log reduction � log CFU 0.30 (0.14, 0.57) 0.11 (0.03, 0.17)

4. Dry Transfer coefficient �2 0.02 (0.007, 0.034) 0.02 (0.006, 0.033)Transfer coefficient �2 0.01 (0.003, 0.017) 0.01 (0.003, 0.017)Growth rate �2 min�1 5.00 � 10�4 (4.8 � 10�5, 9.3 � 10�4) 3.79 � 10�4 (3.5 � 10�5, 7.2 � 10�4)

5. Sort 2 Transfer coefficient �3 0.02 (0.007, 0.034) 0.02 (0.006, 0.033)Transfer coefficient �3 0.01 (0.003, 0.017) 0.01 (0.003, 0.017)Growth rate �3 min�1 4.86 � 10�4 (4.9 � 10�5, 9.3 � 10�4) 3.75 � 10�4 (4.0 � 10�5, 7.1 � 10�4)

6. Pack Growth rate �1 min�1 1.66 � 10�3 (5.8 � 10�4, 2.5 � 10�3) 1.32 � 10�3 (4.5 � 10�4, 2.3 � 10�3)7. Transport and

store 1Growth rate �2 min�1 3.68 � 10�4 (1.7 � 10�4, 5.0 � 10�4) �1.60 � 10�4 (�2.4 � 10�4, �5.5 � 10�5)

8. Transport andstore 2

Growth rate �3 min�1 7.43 � 10�4 (2.7 � 10�4, 1.1 � 10�3) 4.1 � 10�4 (1.4 � 10�4, 7.4 � 10�4)

9. Display Transfer coefficient �4 0.02 (0.007, 0.033) 0.02 (0.006, 0.033)Transfer coefficient �4 0.03 (0.01, 0.05) 0.03 (0.01, 0.05)Growth rate �4 min�1 6.53 � 10�4 (2.2 � 10�4, 0.001) 4.5 � 10�4 (1.5 � 10�4, 7.5 � 10�4)

10. Sale Growth rate �4 min�1 7.00 � 10�4 (2.3 � 10�4, 0.001) 9.1 � 10�4 (3.0 � 10�4, 1.6 � 10�3)aAPC, mesophilic aerobic bacteria quantified by aerobic plate count; TC, total coliforms.

FIG 5 Identification of the influential model inputs on final aerobic plate count (APC) and total coliform(TC) concentrations on tomato surfaces at the retail step of the supermarket location, ranked by partialrank correlation coefficient (PRCC) values. The description of parameter symbols is as follows: �1, transfercoefficient at sort 1; �, log reduction at wash; �2, transfer coefficient at dry; �3, transfer coefficient at sort2; �1, growth rate at pack; �2, growth rate at transport and store 1; �3, growth rate at transport and store2; �4, transfer coefficient at display; �4, growth rate on display surface; �4, growth rate at sale.

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four locations in the supply chain, not continuously over time. The application ofPSCMT to other tomato supply chains or more data points within the supply chainwould improve model fitting and determination of appropriate parameter ranges. Thecurrent PSCMT model is deterministic, so time and parameter values relevant to thesupply chain were fixed, as opposed to sampled from probability distributions, whichmay limit the extrapolation to other supply chain scenarios. For example, the modeledsupply chain operations did not have dynamic time durations within or betweensimulations, which may not appropriately encompass the variety of holding times orhandling events. As the tool is intended primarily for visualization analyses, varyingnode parameters in individual deterministic simulations is sufficient for alternatescenarios. A future direction for PSCMT and intervention analyses may be to incorpo-rate stochasticity to enable more robust inference into model uncertainty and the mosteffective practices in reducing contamination risks.

In conclusion, the irregular distribution, in time and location, of contaminated freshproduce challenges research efforts to understand and control contamination factors.Moreover, fresh produce supply chains are increasingly complex, with variable post-harvest handling practices that may impact produce safety and/or quality. The PSCMTmodel simulates the change in microbial load due to postharvest handling andconditions between entering a packinghouse and being displayed at the supermarket.The generic framework would allow for additional applications to different freshproduce commodities and their pertinent pathogens (e.g., melon and Listeria monocy-togenes, leafy greens and Escherichia coli O157:H7). The visualization of contaminationdynamics and parameter fitting presented here supports future research and decision-making around postharvest risk mitigation strategies. As the most influential parame-ters in the fitted model were removal and growth parameters, these are areas in whichinterventions may have the most impact. Further experimental studies to determineappropriate parameter distributions will improve model predictions. Subsequent sen-sitivity analyses of output from other operations in the supply chain (e.g., packinghouseand distribution center) may indicate additional intervention areas. PSCMT is a uniquemodeling tool that complements empirical data and evaluates postharvest supplychain practices that influence microbial contamination of fresh produce. Future workcould include scenario analyses, including cleaning and sanitation, minimizing holdingtimes, and controlling growth on tomato surfaces, as well as incorporation of stochas-ticity into supply chain simulations.

MATERIALS AND METHODSPSCMT model. The PSCMT tool was designed for handling the variety of practices involved in

packing, distributing, and selling fresh produce. However, unlike the flow of fresh produce items, the flowof microorganisms was modeled at a more detailed and dynamic level within the supply chain. To thisend, operations were defined to describe changes in microbial populations on produce and equipmentsurfaces typical in postharvest supply chains. The four operations, encompassing typical microbialbehavior further explained below, that were used repetitively as needed to represent a supply chain weredefined as follows: (i) contamination, (ii) removal, (iii) growth, and (iv) transfer. The initial event mustalways be contamination at a specific point in the supply chain with a specified population ofmicroorganisms and duration of the contamination event, and the microbial flow in the product isupdated across supply chain locations according to the operations and designated time steps. Opera-tions were connected by arcs (or links) to assemble the supply chain through which microorganisms andfresh produce were to flow. The full set of supply chain operations was assumed to be acyclic anddirected such that the yield of a preceding operation gives rise to flow to the next operation and thereis a unique solution to the system of difference equations. This assumption allowed for the conservationof product and microbial flows along the links between model operations. Time was discrete andarbitrarily divided into equal segments, depending on the user inputs, and numbered from the time ofan initial event. The number of microorganisms (CFU per gram) (N) on product (P) input (I) into anoperation at time t was given by NP,t

I and was distinguished from NP,tO , which was the number of

microorganisms on product output (O) from the operation at time t.(i) Contamination. Contamination was considered the introduction of microorganisms into the system

from an external source, such as an animal, employee or other environmental source, and could occurmultiple times throughout the supply chain. Regardless of the source, contamination was modeled as

NP,tO � NP,t

I � n1{tE} (1)

where n is the load or the number of microorganisms (CFU/g) arriving on the product in each time period

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of the contamination episode, E, and 1A is an indicator of the event A (1A � 1 if A is true, and 1A � 0 ifA is false). A contamination episode was defined by a start period and a duration. It was assumed thatcontamination was homogeneously distributed among the product flow.

(ii) Removal. Removal was defined as the physical elimination of products and/or microorganismsfrom the system due to cleaning and sanitation or culling of damaged produce, for example. Removalwas modeled as

NP,tO � NP,t

I ⁄(10� · 1{tR}) (2)

where � is the load, i.e., the log reduction or base 10 logarithm of the number of microorganisms (log10

CFU/g) removed from the product in each time period of the removal episode, R, and 1A is an indicatorof the event A (1A � 1 if A is true, and 1A � 0 if A is false). The removal episode was given by a dwelltime of the product in the operation. It was assumed that contamination was uniformly distributed onproduce surfaces and therefore individual microbial cells were removed with equal probability. Removalfrom food contact surfaces by means of regular cleaning and sanitation was also modeled, as describedbelow, but was assumed to be completely effective, and the surface population was set to zero duringrepeated intervals of cleaning and sanitation (see equation 8).

(iii) Growth and survival. The dynamic logistic growth equation (14) was used to model microbialsurvival and growth on produce and equipment surfaces:

NP,t�dO �

�NP,tI �Ke�d

K � �NP,tI �e(�d1) (3)

where K is the carrying capacity (CFU/g), � is the daily microbial growth rate or the survival rate (time�1)if � is �0 or � is �0, respectively, and d is the dwell time in this operation. This model could also beexpanded to include a lag time, if appropriate; however, lag times were not modeled here as a necessarysimplification, given the data limitations for growth on tomato and supply chain surfaces.

(iv) Transfer. Following contamination, the spread of microorganisms throughout the system is under-stood to be influenced by their survival on surfaces and contact with subsequent products (32, 36–38).Therefore, transfer was defined as the cross-contamination of microorganisms from one surface to anotherwithin the system, either a unit of fresh produce or a food contact surface. The transfer was modeled asa linear conveyor divided into discrete sequential segments (K) to articulate the numerous interactionsbetween the contaminated product and the food contact surface. The dwell time of the product in eachsegment (k) was exactly the time step of our model. Each segment had a set of time-denominatedattributes, traced cumulatively over the dwell time in the operation, that measured the number ofmicroorganisms on the product in segment k at time t (NP,k,t; CFU/g) and the number of microorganismson the equipment surface in segment k at time t (NS,k,t; CFU/cm2), thus conserving the overall flow ofmicroorganisms through the transfer operation. These attributes were updated according to

NP,k�1,t�1 � (1 �k)NP,k,t � �kNS,k,t (4)

NS,k,t�1 � (1 �k)NS,k,t � �kNP,k,t (5)

where �k is the deposition rate of microorganisms from product to surface and �k is the contaminationrate from surface to product, both unit-less, and with regards to the surface in segment k. The input levelof microorganisms in the product (CFU/g) along the link coming from the previous operation immedi-ately entered the first segment of the transfer function. Similarly, the overall output level of microor-ganisms in the product that will pass from the transfer operation to the subsequent operation wasderived from the level in the final segment of the transfer function.

NP,0,t � NP,tI (6)

NP,tO � NP,K,t (7)

Removal from food contact surfaces by means of regular cleaning and sanitation was also modeledto reset the surface population to zero during repeated intervals of this cycle.

NS,k,t � 0, when t % j �� 0 (8)

for all segments, k � 1, 2, . . ., K, where j is the rejuvenation or cleaning cycle and t % j is the modulusof t and j and is exactly equal to 0 (i.e., t % j �� 0) only when t is an integer multiple of j.

Furthermore, following a transfer event, microorganisms on food contact surfaces may have theopportunity to survive or grow prior to or in conjunction with subsequent transfer events. The transferfunction was expanded to include exponential growth on the surface:

Ns,k,t�1 � �(1 �k)NS,k,t � �kNP,k,t� · e�k (9)

where �k is the microbial growth rate or survival rate (time�1) if �k is �0 or �k is �0, respectively, onsurface segment k.

(v) Microbial flow at junction points: mixing and fractionation. Certain steps along a freshproduce supply chain may involve merging product flows into a single stream (for example, copackingproducts) or splitting a product flow into separate streams (for example, breaking a pallet into smallerorders). Therefore, PSCMT was designed to also handle these typical events. Mixing was defined as thecombination of two or more product flows, and the associated microbial flow, into a single supply chainoperation. If there are incoming links from multiple operations, it was assumed that the mixing orblending occurred in the first segment of the operation. On the other hand, fractionation was a split ofthe product flow, and its associated microbial flow, into multiple flows or when a large unit becomesseveral smaller units. Likewise, if there are any outgoing links to multiple operations, it was assumed that

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the splitting occurred in the last segment of the operation. With these processes, the unit size or productflow is modified and the associated microbial flows are reallocated, updating the number of cells per unit(39). It was assumed that the prevalence of microorganisms within the product was uniform andhomogeneous. Consequently, a split in product flow was assumed to produce a proportional split in thebacterial flow. That is, the microbial population was divided across arcs, leaving the operation inproportion to the product flow rates on these arcs.

Case study of a specific supply chain. After building the generic PSCMT framework, we simulatedobserved microbial indicator organisms in an existing fresh produce supply chain using this tool. Wechose a Roma tomato supply chain from Mexico to the United States that was previously described byZoellner et al. (26) with four locations: postharvest, packinghouse, distribution center, and supermarket.The characteristics and conditions of this Roma tomato supply chain were assembled as a network ofPSCMT operations with 1-min time steps (as shown in Fig. 1). Briefly, tomatoes were grown underprotected agricultural systems (greenhouses and shade houses) in Nuevo Leon, Mexico, using dripfertigation with groundwater and were hand harvested. In the packinghouse, the tomatoes were spraywashed with chlorinated water (150 ppm total chlorine) on brush rollers, dried on foam rollers, and handpacked into 25-lb boxes, at room temperature. Pallets of boxes were transported in refrigerated trucksto a distribution center in Texas, USA, where they were stored at 48 to 50°F until sold to retailsupermarket locations. Tomato samples were taken from the same lots moving along the four supplychain locations (postharvest [n � 130], packinghouse [n � 130], distribution center [n � 144],supermarket [n � 71]) and were analyzed for surface microbial indicator populations by gently washingthe surface in peptone water and plating on the respective microbiological media. These events weremodeled deterministically by assembling the relevant PSCMT microbial operations and parameterizingeach operation using existing literature values or assumptions when necessary. We used the determin-istic model to simulate the contamination dynamics within the lot of tomatoes moving through the supplychain. A vector of APC (mean � standard deviation, 1,260 � 3,870 CFU/g tomato) and TC (115 � 960 CFU/gtomato) values for individual tomatoes (n � 130) was used as the initial contamination level entering thesupply chain at postharvest. The model contamination levels were not reset in between each tomato. Thesupply chain was simulated for 1 week, and the Wilcoxon test was used to assess the model fit to observedvalues at the packinghouse, distribution, and supermarket locations, with corrections for multiple compari-sons according to the Bonferroni method (new P value � 0.05/3 � 0.02).

Model fitting and sensitivity analysis. Due to the lack of fit in supermarket and distributionlocations for APC and TC, respectively, and data limitations for parameter values, the model wascalibrated to observed values with the goal of identifying the subset of parameter values that producedAPC and TC levels consistent with the observed data (39). Our approach to fitting parameters for thissupply chain involved the same baseline input vector at postharvest, with many simulations of alterna-tive sets of parameter values. Because no prior information was available for parameter distributions orranges, each model parameter was varied by 75% to create the specified range of possible values for usein simulations, and all parameters were assumed to follow a uniform distribution. Altogether, theparameter ranges for all 16 model variables created the 16-dimension parameter space from which toassess the combination of values that predicted microbial levels consistent with observed values at thesupermarket. In each simulation, the Latin hypercube sampling (LHS) technique was applied to theparameter space (40, 41) to select parameter values, and all 16 parameters were varied simultaneously(42). The LHS technique aimed to spread the sample points more evenly across all possible values, thusensuring that the entire possible range of values for each parameter was represented during calibrationsimulations. The stability of the coefficient of variation in APC and TC levels at the supermarket after2,000 iterations was used to determine the appropriate number of parameter space simulations to run.After parameter space simulations, the resulting parameter combinations were evaluated to identifythose resulting in APC and TC values (log10 CFU/g) within 10% of the observed median value at thesupermarket. We reported the mean and 5th to 95th percentile for each calibrated parameter.

In demonstrating the generalizability of the PSCMT framework to fit postharvest supply chains, theuncertainty in Roma tomato supply chain model parameters for both APC and TC was assessed throughsensitivity analysis. For deterministic models, where the output is completely determined by theparameter values and model structure, the only uncertainty affecting the output is variation in parametervalues (12). The same parameter space approach described above was used to vary the modelparameters; however, the sensitivity analysis simulations used the mean APC and 95th percentile TCconcentrations (as the mean concentration was zero) from the postharvest location as a single contam-ination input. The most influential model parameters for APC and TC levels at the supermarket weredetermined using a partial rank correlation coefficient (PRCC) method (12).

Model files and software. The PSCMT modeling tool was written in the JavaScript language with aprototypical graphical user interface (GUI) in HTML, documented in the supplemental material. ThePSCMT tool can be found at https://drive.google.com/file/d/1UzxmFCMEkMAxNKCBjRRElsD9v1Bzz-ef/view?usp�sharing. MATLAB 2014a (Natick, MA, USA) was used for generation and sampling of thesimulation space, and R 3.3.2 (Vienna, Austria) was used for statistical and sensitivity analyses (epiRpackage).

SUPPLEMENTAL MATERIAL

Supplemental material for this article may be found at https://doi.org/10.1128/AEM.00813-18.

SUPPLEMENTAL FILE 1, PDF file, 0.4 MB.

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ACKNOWLEDGMENTSThis work was supported by a USDA National Needs Fellowship awarded to R.W.

(award 2013-38420-20519).C.Z., P.J., Y.G., and R.W. conceived the idea for the conceptual model. P.J. imple-

mented the algorithm and wrote the codes. C.Z. collected the observational data, fit themodel, and wrote the manuscript. M.A.A.-M. conducted parameter space simulationsand assisted in the writing of the manuscript.

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